MRP in RxInfer

In [1]:

import pandas as pd
import numpy as np
import os
import itertools
import gc
from scipy.optimize import brentq
from transforms import logit, invlogit, rescale
from model_builder import MRPModelBuilder

import matplotlib.colors as mcolors
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
import geopandas as gpd
from shapely.geometry import box
import matplotlib as mpl
mpl.rcParams['figure.dpi'] = 700

if 'mrp-replication' in os.listdir('.'):
    os.chdir('mrp-replication')

run_full_models = True

########################################################################################
### labels
########################################################################################

reg_lkup = [3,4,4,3,4,4,1,1,5,3,3,4,4,2,2,2,2,3,3,1,1,1,2,2,3,2,4,2,4,1,1,4,1,3,2,2,3,4,1,1,3,2,3,3,4,1,3,4,1,2,4]
reg_label = ["Northeast", "Midwest", "South", "West", "DC"]
eth_label = ["White", "Black", "Hispanic", "Other"]
inc_label = ["$0-20k", "$20-40k", "$40-75k", "$75-150k", "$150k+"]
age_label = ["18-29", "30-44", "45-64", "65+"]

n_reg = len(reg_label)
n_stt = 51 # 50 states + DC
n_eth = len(eth_label)
n_inc = len(inc_label)
n_age = len(age_label)

state_abb = [
    "AL", "AK", "AZ", "AR", "CA", "CO", "CT", "DE", "DC", "FL", "GA", "HI", "ID", "IL", "IN", "IA", "KS", "KY", "LA", "ME",
    "MD", "MA", "MI", "MN", "MS", "MO", "MT", "NE", "NV", "NH", "NJ", "NM", "NY", "NC", "ND", "OH", "OK", "OR", "PA", "RI",
    "SC", "SD", "TN", "TX", "UT", "VT", "VA", "WA", "WV", "WI", "WY"
]
state_name = [
    "Alabama", "Alaska", "Arizona", "Arkansas", "California", "Colorado", "Connecticut", "Delaware", "District of Columbia",
    "Florida", "Georgia", "Hawaii", "Idaho", "Illinois", "Indiana", "Iowa", "Kansas", "Kentucky", "Louisiana", "Maine",
    "Maryland", "Massachusetts", "Michigan", "Minnesota", "Mississippi", "Missouri", "Montana", "Nebraska", "Nevada",
    "New Hampshire", "New Jersey", "New Mexico", "New York", "North Carolina", "North Dakota", "Ohio", "Oklahoma", "Oregon",
    "Pennsylvania", "Rhode Island", "South Carolina", "South Dakota", "Tennessee", "Texas", "Utah", "Vermont", "Virginia",
    "Washington", "West Virginia", "Wisconsin", "Wyoming"
]
stt_label = state_abb

########################################################################################
### get data
########################################################################################

### state-level data
dat_stt = pd.read_csv("data/state-stats.dat", sep="\t")
dat_stt['z.inc2000'] = rescale(dat_stt['inc2000'])
dat_stt['z.inc2004'] = rescale(dat_stt['inc2004'])
dat_stt['z.inc2007'] = rescale(dat_stt['inc2007'])
dat_stt['z.rep1996'] = rescale(dat_stt['rep1996'])
dat_stt['z.rep2000'] = rescale(dat_stt['rep2000'])
dat_stt['z.rep2004'] = rescale(dat_stt['rep2004'])
dat_stt['z.rep2008'] = rescale(dat_stt['rep2008'])
dat_stt['z.trn1996'] = rescale(dat_stt['vote1996']/dat_stt['pop1996'])
dat_stt['z.trn2000'] = rescale(dat_stt['vote2000']/dat_stt['pop2000'])
dat_stt['z.trn2004'] = rescale(dat_stt['vote2004']/dat_stt['pop2004'])
dat_stt['z.trn2008'] = rescale(dat_stt['vote2008']/dat_stt['pop2007'])
dat_stt['stt'] = np.arange(1, len(dat_stt) + 1) # 1-based index

### CPS data for modeling turnout
dat_cps = pd.read_csv("data/cps2000-04-08-DKs.dat", sep="\t")
cols_to_check = dat_cps.columns[:8]
ok = (dat_cps[cols_to_check].isna().sum(axis=1) == 0) & ((dat_cps['cit'] == 1) | dat_cps['cit'].isna())
dat_cps = dat_cps[ok].copy()
dat_cps['reg'] = dat_cps['stt'].apply(lambda x: reg_lkup[x-1])
year_map = {'2000-cps': 2000, '2004-cps': 2004, '2008-cps': 2008}
dat_cps['year'] = dat_cps['file'].map(year_map)
dat_cps = dat_cps[dat_cps['year'] != 2000].copy()

### annenberg / pew data for modeling vote choice
dat_vot = pd.read_csv("data/votechoice2000-04-08.dat", sep="\t")
dat_vot['weight'] = dat_vot['weight'].fillna(1)
cols_to_check_vot = dat_vot.columns[:8]
ok_vot = (dat_vot[cols_to_check_vot].isna().sum(axis=1) == 0) & \
         ((dat_vot['cit'] == 1) | dat_vot['cit'].isna()) & \
         ((dat_vot['regist'] == "registered") | dat_vot['regist'].isna())
dat_vot = dat_vot[ok_vot].copy()
dat_vot['reg'] = dat_vot['stt'].apply(lambda x: reg_lkup[x-1])
year_map_vot = {'2000-ann': 2000, '2004-ann': 2004, '2008-pew': 2008}
dat_vot['year'] = dat_vot['file'].map(year_map_vot)
dat_vot = dat_vot[dat_vot['year'] != 2000].copy()

### census data from PUMS for population cell sizes
dat_pop = pd.read_csv("data/census-pums-pop-2000-04-08.dat", sep="\t")

### prepare data for looping through years
years = [2004, 2008]
L_z_incstt = [dat_stt['z.inc2004'], dat_stt['z.inc2007']]
L_z_repprv = [dat_stt['z.rep2000'], dat_stt['z.rep2004']]
L_z_trnprv = [dat_stt['z.trn2000'], dat_stt['z.trn2004']]

print("Preprocessing complete.", flush=True)

########################################################################################
### multilevel models
########################################################################################

# Create grid D
stt_range = range(n_stt) # 0 to 50
eth_range = range(n_eth) # 0 to 3
inc_range = range(n_inc) # 0 to 4
age_range = range(n_age) # 0 to 3

D = pd.DataFrame(list(itertools.product(stt_range, eth_range, inc_range, age_range)), 
                 columns=["stt", "eth", "inc", "age"])

D['grp'] = D.apply(lambda row: f"{row['stt']}_{row['eth']}_{row['inc']}_{row['age']}", axis=1)
D['ix'] = np.arange(len(D))

reg_lkup_0 = np.array(reg_lkup) - 1 
D['reg'] = D['stt'].apply(lambda x: reg_lkup_0[x])

def encode_interaction(df, cols):
    return df[cols].apply(lambda row: "_".join(row.values.astype(str)), axis=1).astype('category').cat.codes

interaction_cols = [
    ['reg', 'eth'], ['reg', 'inc'], ['reg', 'age'],
    ['stt', 'eth'], ['stt', 'inc'], ['stt', 'age'],
    ['eth', 'inc'], ['eth', 'age'], ['inc', 'age'],
    # 3-way interactions commented out due to OOM issues with Pathfinder
    # ['stt', 'eth', 'inc'], ['stt', 'eth', 'age'], ['stt', 'inc', 'age'], ['eth', 'inc', 'age']
]

for cols in interaction_cols:
    name = "_".join(cols)
    D[name] = encode_interaction(D, cols)

D['z_inc'] = rescale(D['inc'])

def get_model_data(year, data_source, D_grid, target_col):
    # Filter by year
    tmp = data_source[data_source['year'] == year].copy()
    
    # Align indices (assuming data is 1-based, grid is 0-based)
    tmp['stt_0'] = tmp['stt'] - 1
    tmp['eth_0'] = tmp['eth'] - 1
    tmp['inc_0'] = tmp['inc'] - 1
    tmp['age_0'] = tmp['age'] - 1
    
    tmp['grp'] = tmp.apply(lambda row: f"{int(row['stt_0'])}_{int(row['eth_0'])}_{int(row['inc_0'])}_{int(row['age_0'])}", axis=1)
    
    def weighted_mean(x):
        if len(x) == 0: return 0
        w = x['weight']
        v = x[target_col]
        return np.sum(v * w) / np.sum(w)

    def design_effect(x):
        if len(x) <= 1: return 1
        w = x['weight']
        norm_w = w / w.mean()
        return 1 + np.var(norm_w, ddof=1)

    grouped = tmp.groupby('grp')
    mr = pd.DataFrame({
        'n': grouped.size(),
        'ybar_wt': grouped.apply(weighted_mean, include_groups=False),
        'des_eff_cell': grouped.apply(design_effect, include_groups=False)
    })
    
    D_tmp = D_grid.merge(mr, on='grp', how='left')
    D_tmp['n'] = D_tmp['n'].fillna(0)
    D_tmp['des_eff_cell'] = D_tmp['des_eff_cell'].fillna(1)
    
    mask = D_tmp['n'] > 1
    if mask.sum() > 0:
        des_eff = np.average(D_tmp.loc[mask, 'des_eff_cell'], weights=D_tmp.loc[mask, 'n'])
    else:
        des_eff = 1
        
    D_tmp['n_eff'] = D_tmp['n'] / des_eff
    D_tmp.loc[D_tmp['n_eff'] == 0, 'ybar_wt'] = 0.5
    
    D_tmp['trials'] = D_tmp['n_eff']
    D_tmp['successes'] = D_tmp['ybar_wt'] * D_tmp['n_eff']
    
    D_tmp['trials_int'] = D_tmp['trials'].round().astype(int)
    D_tmp['successes_int'] = D_tmp['successes'].round().astype(int)
    
    return D_tmp

L_z_incstt_map = {2004: dat_stt['z.inc2004'].values, 2008: dat_stt['z.inc2007'].values}
L_z_repprv_map = {2004: dat_stt['z.rep2000'].values, 2008: dat_stt['z.rep2004'].values}
L_z_trnprv_map = {2004: dat_stt['z.trn2000'].values, 2008: dat_stt['z.trn2004'].values}

for year in years:
    print(f"***** Multilevel Models for {year}", flush=True)
    
    # Update D with year-specific state predictors
    z_incstt_vals = L_z_incstt_map[year]
    z_repprv_vals = L_z_repprv_map[year]
    z_trnprv_vals = L_z_trnprv_map[year]
    
    D['z_incstt'] = D['stt'].apply(lambda x: z_incstt_vals[x])
    D['z_repprv'] = D['stt'].apply(lambda x: z_repprv_vals[x])
    D['z_trnprv'] = D['stt'].apply(lambda x: z_trnprv_vals[x])
    
    # --- Turnout Model ---
    print("*****   CPS Turnout Model", flush=True)
    data_cps = get_model_data(year, dat_cps, D, 'vote')
    
    # Filter observed
    observed_mask = data_cps['trials_int'] > 0
    df_obs = data_cps[observed_mask].copy()
    
    # Add interaction columns to df_obs (they are in D, merged in get_model_data)
    # get_model_data merges D_grid (which has interactions) with stats.
    # So df_obs has them.
    
    # Config
    if run_full_models:
        turnout_config = {
            'fixed_effects': ['z_inc', 'z_incstt', 'z_trnprv'],
            'fixed_interactions': [('z_inc', 'z_incstt'), ('z_inc', 'z_trnprv')],
            'random_effects': {
                'reg': {'idx_col': 'reg', 'n_cats': n_reg, 'slope_col': 'z_inc'},
                'stt': {'idx_col': 'stt', 'n_cats': n_stt, 'slope_col': 'z_inc'},
                'eth': {'idx_col': 'eth', 'n_cats': n_eth, 'slope_col': 'z_inc'},
                'inc': {'idx_col': 'inc', 'n_cats': n_inc, 'slope_col': None},
                'age': {'idx_col': 'age', 'n_cats': n_age, 'slope_col': 'z_inc'},
            }
        }
        
        # Add interactions to random effects
        for cols in interaction_cols:
            name = "_".join(cols)
            n_cats = int(D[name].max() + 1)
            turnout_config['random_effects'][name] = {'idx_col': name, 'n_cats': n_cats, 'slope_col': None}
    else:
        turnout_config = {
            'fixed_effects': [],
            'random_effects': {
                'stt': {'idx_col': 'stt', 'n_cats': n_stt, 'slope_col': None},
                'eth': {'idx_col': 'eth', 'n_cats': n_eth, 'slope_col': None},
                'inc': {'idx_col': 'inc', 'n_cats': n_inc, 'slope_col': None},
                'age': {'idx_col': 'age', 'n_cats': n_age, 'slope_col': None},
            }
        }
        
    coords = {"obs_id": df_obs.index}
    
    builder = MRPModelBuilder(df_obs, coords, turnout_config)
    print("Building Turnout Model...", flush=True)
    builder.build_model()
    print("Fitting Turnout Model...", flush=True)
    builder.fit(method="pathfinder", num_paths=10, num_draws=200, random_seed=42)
    
    print("Predicting Turnout...", flush=True)
    D[f'turn{year}_M'] = builder.predict(D)
    print("Turnout Prediction complete.", flush=True)
    
    # --- Vote Choice Model ---
    print("*****   Annenberg/Pew Vote Choice Model", flush=True)
    data_vot = get_model_data(year, dat_vot, D, 'rvote')
    observed_mask_vot = data_vot['trials_int'] > 0
    df_obs_vot = data_vot[observed_mask_vot].copy()
    
    if run_full_models:
        vote_config = {
            'fixed_effects': ['z_inc', 'z_incstt', 'z_repprv'],
            'fixed_interactions': [('z_inc', 'z_incstt'), ('z_inc', 'z_repprv')],
            'random_effects': {
                'reg': {'idx_col': 'reg', 'n_cats': n_reg, 'slope_col': 'z_inc'},
                'stt': {'idx_col': 'stt', 'n_cats': n_stt, 'slope_col': 'z_inc'},
                'eth': {'idx_col': 'eth', 'n_cats': n_eth, 'slope_col': 'z_inc'},
                'inc': {'idx_col': 'inc', 'n_cats': n_inc, 'slope_col': None},
                'age': {'idx_col': 'age', 'n_cats': n_age, 'slope_col': 'z_inc'},
            }
        }
        
        for cols in interaction_cols:
            name = "_".join(cols)
            n_cats = int(D[name].max() + 1)
            vote_config['random_effects'][name] = {'idx_col': name, 'n_cats': n_cats, 'slope_col': None}
    else:
        vote_config = {
            'fixed_effects': [],
            'random_effects': {
                'stt': {'idx_col': 'stt', 'n_cats': n_stt, 'slope_col': None},
                'eth': {'idx_col': 'eth', 'n_cats': n_eth, 'slope_col': None},
                'inc': {'idx_col': 'inc', 'n_cats': n_inc, 'slope_col': None},
                'age': {'idx_col': 'age', 'n_cats': n_age, 'slope_col': None},
            }
        }
        
    coords_vot = {"obs_id": df_obs_vot.index}
    
    builder_vot = MRPModelBuilder(df_obs_vot, coords_vot, vote_config)
    print("Building Vote Choice Model...", flush=True)
    builder_vot.build_model()
    print("Fitting Vote Choice Model...", flush=True)
    builder_vot.fit(method="pathfinder", num_paths=10, num_draws=200, random_seed=42)
    
    print("Predicting Vote Choice...")
    D[f'vote{year}_M'] = builder_vot.predict(D)
    print("Vote Choice Prediction complete.")
    
    del builder, builder_vot, data_cps, data_vot, df_obs, df_obs_vot
    gc.collect()

########################################################################################
### poststratification
########################################################################################

print("Starting Poststratification...", flush=True)

# Align indices for dat_pop
dat_pop['stt_0'] = dat_pop['stt'] - 1
dat_pop['eth_0'] = dat_pop['eth'] - 1
dat_pop['inc_0'] = dat_pop['inc'] - 1
dat_pop['age_0'] = dat_pop['age'] - 1

dat_pop['grp'] = dat_pop.apply(lambda row: f"{int(row['stt_0'])}_{int(row['eth_0'])}_{int(row['inc_0'])}_{int(row['age_0'])}", axis=1)

pop_agg = dat_pop.groupby('grp')[['wtd2004', 'wtd2008']].sum().reset_index()
pop_agg.rename(columns={'wtd2004': 'pop2004', 'wtd2008': 'pop2008'}, inplace=True)

D = D.merge(pop_agg, on='grp', how='left')
D['pop2004'] = D['pop2004'].fillna(0)
D['pop2008'] = D['pop2008'].fillna(0)

D = D.sort_values('ix')

### add up and alter based on actual turnout and vote estimates

def correct_weighted(a, w, target_val):
    logit_a = logit(a)
    def func(delta):
        pred = invlogit(logit_a + delta)
        return np.sum(pred * w) - target_val
            
    try:
        delta_opt = brentq(func, -10, 10)
    except ValueError:
        if np.sum(w) == 0: return a
        try:
            delta_opt = brentq(func, -100, 100)
        except:
            return a
    return invlogit(logit_a + delta_opt)

D['turn2004_adj'] = np.nan
D['turn2008_adj'] = np.nan
D['vote2004_adj'] = np.nan
D['vote2008_adj'] = np.nan

print("Starting Calibration...", flush=True)

for i in range(n_stt):
    stt_row = dat_stt.iloc[i]
    mask = D['stt'] == i
    
    if mask.sum() == 0: continue
    
    # Turnout 2004
    if 'turn2004_M' in D.columns:
        D.loc[mask, 'turn2004_adj'] = correct_weighted(
            D.loc[mask, 'turn2004_M'].values,
            D.loc[mask, 'pop2004'].values,
            stt_row['vote2004']
        )
    
    # Turnout 2008
    if 'turn2008_M' in D.columns:
        D.loc[mask, 'turn2008_adj'] = correct_weighted(
            D.loc[mask, 'turn2008_M'].values,
            D.loc[mask, 'pop2008'].values,
            stt_row['vote2008']
        )
    
    # Vote 2004
    if 'vote2004_M' in D.columns:
        w_vot_04 = D.loc[mask, 'pop2004'].values
        if w_vot_04.sum() > 0:
            w_vot_04 = w_vot_04 / w_vot_04.sum()
            
        D.loc[mask, 'vote2004_adj'] = correct_weighted(
            D.loc[mask, 'vote2004_M'].values,
            w_vot_04,
            stt_row['rep2004']
        )
    
    # Vote 2008
    if 'vote2008_M' in D.columns:
        w_vot_08 = D.loc[mask, 'pop2008'].values
        if w_vot_08.sum() > 0:
            w_vot_08 = w_vot_08 / w_vot_08.sum()
            
        D.loc[mask, 'vote2008_adj'] = correct_weighted(
            D.loc[mask, 'vote2008_M'].values,
            w_vot_08,
            stt_row['rep2008']
        )

print("MRP Replication complete.")

Preprocessing complete.
***** Multilevel Models for 2004
*****   CPS Turnout Model
Building Turnout Model...
Fitting Turnout Model...

Output()

/Users/erik/Projects/pytensor/pytensor/tensor/math.py:3023: RuntimeWarning: divide by zero encountered in matmul
  output_storage[0][0] = np.matmul(*inputs)

/Users/erik/Projects/pytensor/pytensor/tensor/math.py:3023: RuntimeWarning: overflow encountered in matmul
  output_storage[0][0] = np.matmul(*inputs)

/Users/erik/Projects/pytensor/pytensor/tensor/math.py:3023: RuntimeWarning: invalid value encountered in matmul
  output_storage[0][0] = np.matmul(*inputs)

Pathfinder Results                            
                                              
  No. model parameters     941                
                                              
  Configuration:                              
  num_draws_per_path       1000               
  history size (maxcor)    21                 
  max iterations           1000               
  ftol                     1.00e-05           
  gtol                     1.00e-08           
  max line search          1000               
  jitter                   2.0                
  epsilon                  1.00e-08           
  ELBO draws               10                 
                                              
  LBFGS Status:                               
  CONVERGED                7                  
  INIT_FAILED              3                  
  L-BFGS iterations        mean 312 ± std 48  
                                              
  Path Status:                                
  SUCCESS                  7                  
  LBFGS_FAILED             3                  
  ELBO argmax              mean 100 ± std 37  
                                              
  Importance Sampling:                        
  Method                   psis               
  Pareto k                 10.50              
                                              
  Timing (seconds):                           
  Compile                  5.95               
  Compute                  98.46              
  Total                    104.41             

Warnings:
  - INIT_FAILED: LBFGS failed to initialize. Consider reparameterizing the model or reducing jitter if this        
  occurence is high relative to the number of paths.                                                               

Output()

Predicting Turnout...
Turnout Prediction complete.
*****   Annenberg/Pew Vote Choice Model
Building Vote Choice Model...
Fitting Vote Choice Model...

Output()

/Users/erik/Projects/pytensor/pytensor/tensor/math.py:3023: RuntimeWarning: overflow encountered in matmul
  output_storage[0][0] = np.matmul(*inputs)

/Users/erik/Projects/pytensor/pytensor/tensor/math.py:3023: RuntimeWarning: invalid value encountered in matmul
  output_storage[0][0] = np.matmul(*inputs)

Pathfinder Results                            
                                              
  No. model parameters     941                
                                              
  Configuration:                              
  num_draws_per_path       1000               
  history size (maxcor)    21                 
  max iterations           1000               
  ftol                     1.00e-05           
  gtol                     1.00e-08           
  max line search          1000               
  jitter                   2.0                
  epsilon                  1.00e-08           
  ELBO draws               10                 
                                              
  LBFGS Status:                               
  CONVERGED                7                  
  INIT_FAILED              3                  
  L-BFGS iterations        mean 329 ± std 51  
                                              
  Path Status:                                
  SUCCESS                  7                  
  LBFGS_FAILED             3                  
  ELBO argmax              mean 53 ± std 15   
                                              
  Importance Sampling:                        
  Method                   psis               
  Pareto k                 12.01              
                                              
  Timing (seconds):                           
  Compile                  4.20               
  Compute                  108.80             
  Total                    113.00             

Warnings:
  - INIT_FAILED: LBFGS failed to initialize. Consider reparameterizing the model or reducing jitter if this        
  occurence is high relative to the number of paths.                                                               

Output()

Predicting Vote Choice...
Vote Choice Prediction complete.
***** Multilevel Models for 2008
*****   CPS Turnout Model
Building Turnout Model...
Fitting Turnout Model...

Output()

/Users/erik/Projects/pytensor/pytensor/tensor/math.py:3023: RuntimeWarning: divide by zero encountered in matmul
  output_storage[0][0] = np.matmul(*inputs)

/Users/erik/Projects/pytensor/pytensor/tensor/math.py:3023: RuntimeWarning: overflow encountered in matmul
  output_storage[0][0] = np.matmul(*inputs)

/Users/erik/Projects/pytensor/pytensor/tensor/math.py:3023: RuntimeWarning: invalid value encountered in matmul
  output_storage[0][0] = np.matmul(*inputs)

Pathfinder Results                            
                                              
  No. model parameters     941                
                                              
  Configuration:                              
  num_draws_per_path       1000               
  history size (maxcor)    21                 
  max iterations           1000               
  ftol                     1.00e-05           
  gtol                     1.00e-08           
  max line search          1000               
  jitter                   2.0                
  epsilon                  1.00e-08           
  ELBO draws               10                 
                                              
  LBFGS Status:                               
  CONVERGED                7                  
  INIT_FAILED              3                  
  L-BFGS iterations        mean 284 ± std 43  
                                              
  Path Status:                                
  SUCCESS                  7                  
  LBFGS_FAILED             3                  
  ELBO argmax              mean 79 ± std 22   
                                              
  Importance Sampling:                        
  Method                   psis               
  Pareto k                 9.31               
                                              
  Timing (seconds):                           
  Compile                  2.81               
  Compute                  81.21              
  Total                    84.02              

Warnings:
  - INIT_FAILED: LBFGS failed to initialize. Consider reparameterizing the model or reducing jitter if this        
  occurence is high relative to the number of paths.                                                               

Output()

Predicting Turnout...
Turnout Prediction complete.
*****   Annenberg/Pew Vote Choice Model
Building Vote Choice Model...
Fitting Vote Choice Model...

Output()

/Users/erik/Projects/pytensor/pytensor/tensor/math.py:3023: RuntimeWarning: divide by zero encountered in matmul
  output_storage[0][0] = np.matmul(*inputs)

/Users/erik/Projects/pytensor/pytensor/tensor/math.py:3023: RuntimeWarning: overflow encountered in matmul
  output_storage[0][0] = np.matmul(*inputs)

/Users/erik/Projects/pytensor/pytensor/tensor/math.py:3023: RuntimeWarning: invalid value encountered in matmul
  output_storage[0][0] = np.matmul(*inputs)

Pathfinder Results                            
                                              
  No. model parameters     941                
                                              
  Configuration:                              
  num_draws_per_path       1000               
  history size (maxcor)    21                 
  max iterations           1000               
  ftol                     1.00e-05           
  gtol                     1.00e-08           
  max line search          1000               
  jitter                   2.0                
  epsilon                  1.00e-08           
  ELBO draws               10                 
                                              
  LBFGS Status:                               
  CONVERGED                8                  
  INIT_FAILED              2                  
  L-BFGS iterations        mean 294 ± std 46  
                                              
  Path Status:                                
  SUCCESS                  8                  
  LBFGS_FAILED             2                  
  ELBO argmax              mean 39 ± std 19   
                                              
  Importance Sampling:                        
  Method                   psis               
  Pareto k                 11.80              
                                              
  Timing (seconds):                           
  Compile                  2.94               
  Compute                  94.99              
  Total                    97.94              

Warnings:
  - INIT_FAILED: LBFGS failed to initialize. Consider reparameterizing the model or reducing jitter if this        
  occurence is high relative to the number of paths.                                                               

Output()

Predicting Vote Choice...
Vote Choice Prediction complete.
Starting Poststratification...
Starting Poststratification...
Starting Calibration...
MRP Replication complete.

In [4]:

def color_alpha(colors, alpha=1.0):
    # colors can be a list of hex or names
    rgba = mcolors.to_rgba_array(colors)
    rgba[:, 3] = alpha
    return rgba

def color_groups(x, x_seq, color1, color2, color3, alpha=1.0):
    # x is a series or array
    x = np.array(x)
    x = np.round(x)
    x = np.clip(x, x_seq[0], x_seq[1])
    # Normalize to 0-1 for colormap
    norm = mcolors.Normalize(vmin=x_seq[0], vmax=x_seq[1])
    cmap = mcolors.LinearSegmentedColormap.from_list("custom", [color1, color2, color3])
    return cmap(norm(x), alpha=alpha)

def plot_bubble(x, y, sz, bg="white", fg="black", title="", xlab="", ylab="", xlim=(0,1), ylim=(0,1), ax=None):
    if ax is None:
        fig, ax = plt.subplots()
    
    # Sort by size descending
    idx = np.argsort(sz)[::-1]
    x = np.array(x)[idx]
    y = np.array(y)[idx]
    sz = np.array(sz)[idx]
    
    if isinstance(bg, (list, np.ndarray)):
        if len(bg) == len(x): bg = np.array(bg)[idx]
    if isinstance(fg, (list, np.ndarray)):
        if len(fg) == len(x): fg = np.array(fg)[idx]
        
    ax.scatter(x, y, s=sz*15000, c=bg, edgecolors=fg, linewidth=0.5)
    ax.set_xlim(xlim)
    ax.set_ylim(ylim)
    ax.set_title(title)
    ax.set_xlabel(xlab)
    ax.set_ylabel(ylab)
    # Add grid lines
    ax.axvline(np.mean(xlim), color='grey', linestyle=':', linewidth=0.5)
    ax.axhline(np.mean(ylim), color='grey', linestyle=':', linewidth=0.5)
    return ax

_us_states_gdf = None

def get_us_map():
    global _us_states_gdf
    if _us_states_gdf is None:
        # Use a reliable GeoJSON source for US states
        url = "https://eric.clst.org/assets/wiki/uploads/Stuff/gz_2010_us_040_00_500k.json"
        try:
            gdf = gpd.read_file(url)
            _us_states_gdf = gdf
        except Exception as e:
            print(f"Error loading map: {e}")
            return None
    return _us_states_gdf.copy()

def plot_map(ax, colors, title=""):
    # colors: array-like of colors (strings or RGBA), aligned with state_name (0-50)
    
    gdf = get_us_map()
    if gdf is None:
        ax.text(0.5, 0.5, "Map Error", ha='center')
        return

    # Map colors to gdf
    # Create a dict mapping NAME to color
    name_to_color = {}
    for idx, name in enumerate(state_name):
        if idx < len(colors):
            name_to_color[name] = colors[idx]
            
    gdf['color'] = gdf['NAME'].map(name_to_color).fillna('lightgrey')
    
    # Reproject to Albers Equal Area for better shape
    try:
        gdf = gdf.to_crs("EPSG:5070")
    except:
        pass

    # Separate AK, HI, and Lower 48
    ak = gdf[gdf['NAME'] == 'Alaska']
    hi = gdf[gdf['NAME'] == 'Hawaii']
    lower48 = gdf[~gdf['NAME'].isin(['Alaska', 'Hawaii', 'Puerto Rico'])]
    
    # Plot Lower 48
    lower48.plot(ax=ax, color=lower48['color'], edgecolor='white', linewidth=0.5)
    
    # Inset for Alaska
    if not ak.empty:
        ax_ak = ax.inset_axes([0.0, 0.0, 0.25, 0.25]) # Bottom left
        ak.plot(ax=ax_ak, color=ak['color'], edgecolor='white', linewidth=0.5)
        ax_ak.axis('off')
        # Zoom to AK
        minx, miny, maxx, maxy = ak.total_bounds
        ax_ak.set_xlim(minx, maxx)
        ax_ak.set_ylim(miny, maxy)

    # Inset for Hawaii
    if not hi.empty:
        ax_hi = ax.inset_axes([0.25, 0.0, 0.15, 0.15]) # Next to AK
        hi.plot(ax=ax_hi, color=hi['color'], edgecolor='white', linewidth=0.5)
        ax_hi.axis('off')
        # Zoom to HI
        minx, miny, maxx, maxy = hi.total_bounds
        ax_hi.set_xlim(minx, maxx)
        ax_hi.set_ylim(miny, maxy)

    ax.set_title(title, fontsize=10)
    ax.axis('off')

In [5]:

print("Generating Figure 1...")

# Subset data
mask_fig1 = (dat_vot['year'] == 2008) & (dat_vot['eth'] == 1)
df_fig1 = dat_vot[mask_fig1].copy()
df_fig1['stt_idx'] = df_fig1['stt'] - 1
df_fig1['trials_int'] = 1
df_fig1['successes_int'] = df_fig1['rvote'].astype(int)


# M1: rvote ~ inc + (1 | stt)
config_m1 = {
    'fixed_effects': ['inc'],
    'random_effects': {
        'stt': {'idx_col': 'stt_idx', 'n_cats': n_stt, 'slope_col': None}
    }
}
coords_fig1 = {"obs_id": df_fig1.index}
builder_m1 = MRPModelBuilder(df_fig1, coords_fig1, config_m1)
builder_m1.build_model()
builder_m1.fit(method="mcmc", draws=50, tune=50, chains=1, progressbar=False)

# M2: rvote ~ inc + (1 + inc | stt)
config_m2 = {
    'fixed_effects': ['inc'],
    'random_effects': {
        'stt': {'idx_col': 'stt_idx', 'n_cats': n_stt, 'slope_col': 'inc'}
    }
}
builder_m2 = MRPModelBuilder(df_fig1, coords_fig1, config_m2)
builder_m2.build_model()
builder_m2.fit(method="mcmc", draws=50, tune=50, chains=1, progressbar=False)

# Predictions
dat_pc = pd.DataFrame(list(itertools.product(range(n_stt), range(1, 6))), columns=['stt_idx', 'inc'])
dat_pc['stt'] = dat_pc['stt_idx'] + 1
dat_pc['M1'] = builder_m1.predict(dat_pc)
dat_pc['M2'] = builder_m2.predict(dat_pc)

def get_raw_mean(row):
    mask = (df_fig1['stt_idx'] == row['stt_idx']) & (df_fig1['inc'] == row['inc'])
    if mask.sum() == 0: return np.nan
    return np.average(df_fig1.loc[mask, 'rvote'], weights=df_fig1.loc[mask, 'weight'])

dat_pc['raw'] = dat_pc.apply(get_raw_mean, axis=1)

# Plotting
fig1, axes = plt.subplots(1, 3, figsize=(15, 5), sharey=True)
titles = ["Raw Values", "Income coefficient\nconsistent across states", "Income coefficient\nvarying by state"]
data_cols = ['raw', 'M1', 'M2']

rep2008 = dat_stt['rep2008'].values
stt_colors = color_groups(rep2008 * 100, [25, 75], "darkblue", "grey", "darkred")

bold_states = ["MS", "OH", "CT"]
bold_indices = [state_abb.index(s) for s in bold_states]

for i, ax in enumerate(axes):
    ax.set_title(titles[i])
    ax.set_xticks(range(1, 6))
    ax.set_xticklabels(inc_label, rotation=90)
    ax.set_ylim(0, 1)
    
    for stt_idx in range(n_stt):
        if stt_idx in bold_indices: continue
        subset = dat_pc[dat_pc['stt_idx'] == stt_idx]
        ax.plot(subset['inc'], subset[data_cols[i]], color=stt_colors[stt_idx], linewidth=0.5, alpha=0.7)
        
    for stt_idx in range(n_stt):
        if stt_idx not in bold_indices: continue
        subset = dat_pc[dat_pc['stt_idx'] == stt_idx]
        ax.plot(subset['inc'], subset[data_cols[i]], color=stt_colors[stt_idx], linewidth=2)
        ax.text(0.9, subset[subset['inc']==1][data_cols[i]].values[0], state_abb[stt_idx], ha='right', fontsize=8)
        ax.text(5.1, subset[subset['inc']==5][data_cols[i]].values[0], state_abb[stt_idx], ha='left', fontsize=8)

plt.tight_layout()
plt.savefig("figs/1.png")
print("Figure 1 saved.")

Only 50 samples per chain. Reliable r-hat and ESS diagnostics require longer chains for accurate estimate.

Generating Figure 1...

Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [b_0, b_inc, stt::sigma, stt::raw]
Sampling 1 chain for 50 tune and 50 draw iterations (50 + 50 draws total) took 13 seconds.
The number of samples is too small to check convergence reliably.
Only 50 samples per chain. Reliable r-hat and ESS diagnostics require longer chains for accurate estimate.
Initializing NUTS using jitter+adapt_diag...
Sequential sampling (1 chains in 1 job)
NUTS: [b_0, b_inc, stt::sigma, stt::raw, stt::sigma_slope, stt::raw_slope]
Sampling 1 chain for 50 tune and 50 draw iterations (50 + 50 draws total) took 27 seconds.
The number of samples is too small to check convergence reliably.

Figure 1 saved.

In [6]:

print("Generating Figure 2...")

# Aggregations
D['plot_grp'] = D.apply(lambda row: f"{row['stt']}_{row['inc']}", axis=1)
D2 = D.groupby('plot_grp').apply(
    lambda x: pd.Series({
        'stt': x['stt'].iloc[0],
        'inc': x['inc'].iloc[0],
        'vote2008': np.sum(x['vote2008_adj'] * x['pop2008']) / np.sum(x['pop2008'])
    }), include_groups=False
).reset_index()

D3 = D[D['eth'] == 0].groupby('plot_grp').apply( # eth 0 is White
    lambda x: pd.Series({
        'stt': x['stt'].iloc[0],
        'inc': x['inc'].iloc[0],
        'vote2008': np.sum(x['vote2008_adj'] * x['pop2008']) / np.sum(x['pop2008'])
    }), include_groups=False
).reset_index()

stt_inc_grid = pd.DataFrame(list(itertools.product(range(n_stt), range(n_inc))), columns=['stt', 'inc'])
stt_inc_grid['fit1'] = np.nan
stt_inc_grid['se1'] = np.nan
stt_inc_grid['mu1'] = np.nan
stt_inc_grid['fit2'] = np.nan
stt_inc_grid['se2'] = np.nan
stt_inc_grid['mu2'] = np.nan

# We need to compute weighted means and SEs from dat_vot
# dat_vot uses 1-based stt and inc.
# stt_inc_grid uses 0-based.

for i, row in stt_inc_grid.iterrows():
    s, inc = int(row['stt']), int(row['inc'])
    
    # All voters
    mask = (dat_vot['stt'] == s + 1) & (dat_vot['inc'] == inc + 1) & (dat_vot['year'] == 2008)
    if mask.sum() > 1:
        # Model fit
        fit_val = D2.loc[(D2['stt'] == s) & (D2['inc'] == inc), 'vote2008']
        if not fit_val.empty:
            stt_inc_grid.at[i, 'fit1'] = fit_val.values[0]
        
        # Raw data
        w = dat_vot.loc[mask, 'weight']
        v = dat_vot.loc[mask, 'rvote']
        mu = np.average(v, weights=w)
        mu = min(0.98, max(0.02, mu))
        se = np.sqrt((mu * (1 - mu)) / mask.sum())
        stt_inc_grid.at[i, 'mu1'] = mu
        stt_inc_grid.at[i, 'se1'] = se
        
    # White voters
    mask_w = mask & (dat_vot['eth'] == 1)
    if mask_w.sum() > 1:
        fit_val = D3.loc[(D3['stt'] == s) & (D3['inc'] == inc), 'vote2008']
        if not fit_val.empty:
            stt_inc_grid.at[i, 'fit2'] = fit_val.values[0]
            
        w = dat_vot.loc[mask_w, 'weight']
        v = dat_vot.loc[mask_w, 'rvote']
        mu = np.average(v, weights=w)
        mu = min(0.98, max(0.02, mu))
        se = np.sqrt((mu * (1 - mu)) / mask_w.sum())
        stt_inc_grid.at[i, 'mu2'] = mu
        stt_inc_grid.at[i, 'se2'] = se

# Plotting Fig 2
fig2 = plt.figure(figsize=(10, 10))
sort_state = np.argsort(dat_stt['rep2008'].values[:n_stt])[::-1] # Descending
count = 0
rows, cols = 7, 7

for idx in sort_state:
    if state_abb[idx] in ["AK", "HI", "DC"]: continue
    
    count += 1
    ax = fig2.add_subplot(rows, cols, count)
    
    # Axis labels only on edges
    if count % cols == 1:
        ax.set_yticks([0.02, 0.5, 0.95])
        ax.set_yticklabels(["0%", "50%", "100%"], fontsize=8)
    else:
        ax.set_yticks([])
        
    if count > (48 - cols):
        ax.set_xticks([0, 2, 4])
        ax.set_xticklabels(["poor", "mid", "rich"], fontsize=8)
    else:
        ax.set_xticks([])
        
    ax.axhline(0.5, color='gray', linewidth=0.5)
    ax.set_ylim(0, 1)
    ax.set_xlim(-0.5, 4.5)
    
    tmp = stt_inc_grid[stt_inc_grid['stt'] == idx]
    
    # All voters (gray)
    ax.errorbar(tmp['inc'], tmp['mu1'], yerr=tmp['se1'], fmt='o', color='gray', markersize=3, elinewidth=1)
    ax.plot(tmp['inc'], tmp['fit1'], color='gray', linewidth=1)
    
    # White voters (orange)
    ax.errorbar(tmp['inc'] + 0.1, tmp['mu2'], yerr=tmp['se2'], fmt='o', color='darkorange', markersize=3, elinewidth=1)
    ax.plot(tmp['inc'], tmp['fit2'], color='darkorange', linewidth=1)
    
    ax.text(2, 0.9, state_name[idx], ha='center', fontsize=9)

plt.tight_layout()
plt.savefig("figs/2.png")
print("Figure 2 saved.")

Generating Figure 2...
Figure 2 saved.

In [7]:

print("Generating Figure 3...")

fig3, axes = plt.subplots(1, 3, figsize=(18, 6))

# 1. State x Eth
D['grp_plot'] = D.apply(lambda row: f"{row['stt']}_{row['eth']}", axis=1)
D_plot = D.groupby('grp_plot').apply(
    lambda x: pd.Series({
        'eth': x['eth'].iloc[0],
        'vote2008': np.sum(x['vote2008_adj'] * x['turn2008_adj'] * x['pop2008']) / np.sum(x['turn2008_adj'] * x['pop2008']),
        'turn2008': np.sum(x['turn2008_adj'] * x['pop2008']) / np.sum(x['pop2008']),
        'pop2008': np.sum(x['pop2008'])
    }), include_groups=False
).reset_index()

eth_colors = ['white', 'black', 'red', 'green']
bg_colors = [eth_colors[int(e)] for e in D_plot['eth']]
fg_colors = ['grey'] * len(D_plot)

plot_bubble(D_plot['vote2008'], D_plot['turn2008'], np.sqrt(D_plot['pop2008'])/15000, 
            bg=bg_colors, fg=fg_colors, title="State x Ethnicity", 
            xlab="McCain Vote 2008", ylab="Turnout 2008", ax=axes[0])

# 2. State x Eth x Inc
D['grp_plot'] = D.apply(lambda row: f"{row['stt']}_{row['eth']}_{row['inc']}", axis=1)
D_plot = D.groupby('grp_plot').apply(
    lambda x: pd.Series({
        'eth': x['eth'].iloc[0],
        'vote2008': np.sum(x['vote2008_adj'] * x['turn2008_adj'] * x['pop2008']) / np.sum(x['turn2008_adj'] * x['pop2008']),
        'turn2008': np.sum(x['turn2008_adj'] * x['pop2008']) / np.sum(x['pop2008']),
        'pop2008': np.sum(x['pop2008'])
    }), include_groups=False
).reset_index()

bg_colors = [eth_colors[int(e)] for e in D_plot['eth']]
fg_colors = ['grey'] * len(D_plot)
plot_bubble(D_plot['vote2008'], D_plot['turn2008'], np.sqrt(D_plot['pop2008'])/15000, 
            bg=bg_colors, fg=fg_colors, title="State x Ethnicity x Income", 
            xlab="McCain Vote 2008", ylab="", ax=axes[1])

# 3. State x Eth x Inc x Age
D['grp_plot'] = D.apply(lambda row: f"{row['stt']}_{row['eth']}_{row['inc']}_{row['age']}", axis=1)
D_plot = D.groupby('grp_plot').apply(
    lambda x: pd.Series({
        'eth': x['eth'].iloc[0],
        'vote2008': np.sum(x['vote2008_adj'] * x['turn2008_adj'] * x['pop2008']) / np.sum(x['turn2008_adj'] * x['pop2008']),
        'turn2008': np.sum(x['turn2008_adj'] * x['pop2008']) / np.sum(x['pop2008']),
        'pop2008': np.sum(x['pop2008'])
    }), include_groups=False
).reset_index()

bg_colors = [eth_colors[int(e)] for e in D_plot['eth']]
fg_colors = ['grey'] * len(D_plot)
plot_bubble(D_plot['vote2008'], D_plot['turn2008'], np.sqrt(D_plot['pop2008'])/15000, 
            bg=bg_colors, fg=fg_colors, title="State x Ethnicity x Income x Age", 
            xlab="McCain Vote 2008", ylab="", ax=axes[2])

plt.tight_layout()
plt.savefig("figs/3.png")
print("Figure 3 saved.")

Generating Figure 3...

/var/folders/6h/4989_pyx21d34x6ywybxzydc0000gn/T/ipykernel_34372/427786064.py:29: RuntimeWarning: invalid value encountered in scalar divide
  'vote2008': np.sum(x['vote2008_adj'] * x['turn2008_adj'] * x['pop2008']) / np.sum(x['turn2008_adj'] * x['pop2008']),
/var/folders/6h/4989_pyx21d34x6ywybxzydc0000gn/T/ipykernel_34372/427786064.py:30: RuntimeWarning: invalid value encountered in scalar divide
  'turn2008': np.sum(x['turn2008_adj'] * x['pop2008']) / np.sum(x['pop2008']),
/var/folders/6h/4989_pyx21d34x6ywybxzydc0000gn/T/ipykernel_34372/427786064.py:46: RuntimeWarning: invalid value encountered in scalar divide
  'vote2008': np.sum(x['vote2008_adj'] * x['turn2008_adj'] * x['pop2008']) / np.sum(x['turn2008_adj'] * x['pop2008']),
/var/folders/6h/4989_pyx21d34x6ywybxzydc0000gn/T/ipykernel_34372/427786064.py:47: RuntimeWarning: invalid value encountered in scalar divide
  'turn2008': np.sum(x['turn2008_adj'] * x['pop2008']) / np.sum(x['pop2008']),

Figure 3 saved.

In [8]:

print("Generating Figure 4...")

# Prepare data
ok_grp = np.zeros(len(D), dtype=bool)
for i in range(n_stt):
    mask = D['stt'] == i
    tmp = D.loc[mask, 'pop2008'] * D.loc[mask, 'turn2008_adj']
    threshold = tmp.sum() / 100
    ok_grp[mask] = (tmp >= threshold)

fig4, axes = plt.subplots(n_inc, n_age, figsize=(15, 10))
fig4.suptitle("McCain 2008 minus Bush 2004 among whites", fontsize=16)

for i_age in range(n_age):
    for i_inc in range(n_inc):
        ax = axes[i_inc, i_age]
        
        # Filter
        mask = (D['age'] == i_age) & (D['inc'] == i_inc) & (D['eth'] == 0) # eth 0 is White
        subset = D[mask].copy()
        
        # Ensure we have data for all states in order
        # subset might be missing states if they were filtered out earlier, but D is a grid.
        # However, D was created with itertools, so it should be complete.
        # We sort by stt to be sure.
        subset = subset.sort_values('stt')
        
        if len(subset) != n_stt:
            # Should not happen given D construction, but safety check
            subset = subset.set_index('stt').reindex(range(n_stt))
        
        # Calculate values
        vals = (subset['vote2008_adj'] - subset['vote2004_adj']) * 100
        
        # Get colors
        colors = color_groups(vals, [-25, 25], "darkblue", "white", "darkred", alpha=0.75)
        
        # Apply mask for small groups
        # ok_grp is aligned with D. We need it for this subset.
        # Since subset is sorted by stt and filtered by age/inc/eth, 
        # we need to extract corresponding ok_grp values.
        # We can use the index of subset (which comes from D) to index ok_grp.
        subset_indices = subset.index
        grp_mask = ok_grp[subset_indices]
        
        # Set alpha to 0 for masked
        colors[~grp_mask] = [0, 0, 0, 0]
        
        plot_map(ax, colors, title=f"Age {age_label[i_age]}\nInc {inc_label[i_inc]}")

plt.tight_layout()
plt.savefig("figs/4.png")
print("Figure 4 saved.")

Generating Figure 4...
Figure 4 saved.

In [9]:

print("Generating Figure 5...")

agg_mean = np.sum(D['pop2008'] * D['turn2008_adj']) / np.sum(D['pop2008']) - \
           np.sum(D['pop2004'] * D['turn2004_adj']) / np.sum(D['pop2004'])

fig5, axes = plt.subplots(n_age, n_eth, figsize=(12, 12), sharex=True, sharey=True)
fig5.suptitle("Turnout Swing (08-04)", fontsize=16)

for i_eth in range(n_eth):
    for i_age in range(n_age):
        ax = axes[i_age, i_eth]
        
        mask = (D['eth'] == i_eth) & (D['age'] == i_age)
        subset = D[mask]
        
        # Aggregate by income
        res = []
        for i_inc in range(n_inc):
            mask2 = mask & (D['inc'] == i_inc)
            sub2 = D[mask2]
            p04 = sub2['pop2004'].sum()
            t04 = np.sum(sub2['pop2004'] * sub2['turn2004_adj']) / p04 if p04 > 0 else 0
            p08 = sub2['pop2008'].sum()
            t08 = np.sum(sub2['pop2008'] * sub2['turn2008_adj']) / p08 if p08 > 0 else 0
            res.append([p04, t04, p08, t08])
            
        res = np.array(res)
        res[:, 0] = res[:, 0] / res[:, 0].sum() / 2 # pop04
        res[:, 2] = res[:, 2] / res[:, 2].sum() / 2 # pop08
        
        grp_mean = np.sum(subset['pop2008'] * subset['turn2008_adj']) / np.sum(subset['pop2008']) - \
                   np.sum(subset['pop2004'] * subset['turn2004_adj']) / np.sum(subset['pop2004'])
                   
        col1 = "lightblue" if grp_mean > 0.05 else "lightgrey"
        col2 = "darkblue" if grp_mean > 0.05 else "black"
        
        x = np.arange(n_inc)
        ax.bar(x, res[:, 2], color=col1, width=0.8)
        
        swing = res[:, 3] - res[:, 1]
        ax.plot(x, swing, 'o-', color=col2, markersize=4)
        
        ax.axhline(0, linestyle=':', color='black')
        ax.axhline(agg_mean, linestyle=':', color='red')
        
        ax.set_ylim(-0.05, 0.2)
        
        if i_age == 0:
            ax.set_title(eth_label[i_eth])
        if i_eth == 0:
            ax.set_ylabel(age_label[i_age])
            
        if i_age == 3:
            ax.set_xticks(x)
            ax.set_xticklabels(inc_label, rotation=90)

plt.tight_layout()
plt.savefig("figs/5.png")
print("Figure 5 saved.")

Generating Figure 5...
Figure 5 saved.

In [10]:

print("Generating Figure 6...")

D['plot_grp'] = D.apply(lambda row: f"{row['stt']}_{row['eth']}_{row['age']}", axis=1)
D3 = D.groupby('plot_grp').apply(
    lambda x: pd.Series({
        'stt': x['stt'].iloc[0],
        'eth': x['eth'].iloc[0],
        'age': x['age'].iloc[0],
        'pop2008': np.sum(x['pop2008']),
        'turn2008': np.sum(x['pop2008'] * x['turn2008_adj']) / np.sum(x['pop2008'])
    }), include_groups=False
).reset_index()

ok_grp = np.zeros(len(D3), dtype=bool)
for i in range(n_stt):
    mask = D3['stt'] == i
    tmp = D3.loc[mask, 'pop2008']
    threshold = tmp.sum() / 100
    ok_grp[mask] = (tmp >= threshold)

from matplotlib.colors import LinearSegmentedColormap
fig6, axes = plt.subplots(n_age, n_eth, figsize=(15, 12))
fig6.suptitle("Turnout among Young Whites and Minorities Over-Emphasized", fontsize=16)

dark_red = [0.5, 0.0, 0.0]
white = [1.0, 1.0, 1.0]
dark_green = [0.0, 0.5, 0.0]
color_nodes = [
    (0.0, dark_red),    # Start at 0.0 (vmin) with dark_red
    (0.6, white),       # Pass through white at the 0.6 point
    (1.0, dark_green)   # End at 1.0 (vmax) with dark_green
]
custom_cmap = LinearSegmentedColormap.from_list("RedWhiteGreen", color_nodes)

for i_age in range(n_age):
    for i_eth in range(n_eth):
        ax = axes[i_age, i_eth]
        
        mask = (D3['age'] == i_age) & (D3['eth'] == i_eth)
        subset = D3[mask].copy()
        
        subset = subset.sort_values('stt')
        if len(subset) != n_stt:
            subset = subset.set_index('stt').reindex(range(n_stt))
            
        vals = subset['turn2008']
        colors = color_groups(vals, [0.4, 0.8], "darkred", "white", "green", alpha=0.75)
        
        # Apply mask
        subset_indices = subset.index
        grp_mask = ok_grp[subset_indices]
        colors[~grp_mask] = [0, 0, 0, 0]
       
        rplot = plot_map(ax, colors, title="")
        
        ax.axis("on")
        ax.tick_params(left=False, bottom=False, labelleft=False, labelbottom=False)
        for spine in ax.spines.values():
            spine.set_visible(False)
        if i_eth == 0:
            ax.set_ylabel(age_label[i_age], loc="center", fontsize=12)
            
        # Apply X-label only to the last row (i_age == n_age - 1)
        if i_age == 0:
            ax.set_title(eth_label[i_eth], y=1.0, fontsize=12)
            # ax.set_xlabel(eth_label[i_eth], loc="center")
            # ax.xaxis.set_label_position('top')

norm = mpl.colors.Normalize(vmin=np.min(colors[colors != 0]), vmax=np.max(colors))
sm = plt.cm.ScalarMappable(cmap=custom_cmap, norm=norm)
sm.set_array([]) 
cbar = fig6.colorbar(sm, ax=ax)
cbar.set_label('Turnout', rotation=270, labelpad=15)
plt.tight_layout()
plt.savefig("figs/6.png")
print("Figure 6 saved.")

Generating Figure 6...

/var/folders/6h/4989_pyx21d34x6ywybxzydc0000gn/T/ipykernel_34372/1415949281.py:10: RuntimeWarning: invalid value encountered in scalar divide
  'turn2008': np.sum(x['pop2008'] * x['turn2008_adj']) / np.sum(x['pop2008'])

Figure 6 saved.

In [11]:

year = 2008
z_incstt_vals = L_z_incstt_map[year]
z_repprv_vals = L_z_repprv_map[year]
z_trnprv_vals = L_z_trnprv_map[year]

D['z_incstt'] = D['stt'].apply(lambda x: z_incstt_vals[x])
D['z_repprv'] = D['stt'].apply(lambda x: z_repprv_vals[x])
D['z_trnprv'] = D['stt'].apply(lambda x: z_trnprv_vals[x])

# --- Turnout Model ---
print("*****   CPS Turnout Model", flush=True)
data_cps = get_model_data(year, dat_cps, D, 'vote')

# Filter observed
observed_mask = data_cps['trials_int'] > 0
df_obs = data_cps[observed_mask].copy()

# Add interaction columns to df_obs (they are in D, merged in get_model_data)
# get_model_data merges D_grid (which has interactions) with stats.
# So df_obs has them.

# Config
if run_full_models:
    turnout_config = {
        'fixed_effects': ['z_inc', 'z_incstt', 'z_trnprv'],
        'fixed_interactions': [('z_inc', 'z_incstt'), ('z_inc', 'z_trnprv')],
        'random_effects': {
            'reg': {'idx_col': 'reg', 'n_cats': n_reg, 'slope_col': 'z_inc'},
            'stt': {'idx_col': 'stt', 'n_cats': n_stt, 'slope_col': 'z_inc'},
            'eth': {'idx_col': 'eth', 'n_cats': n_eth, 'slope_col': 'z_inc'},
            'inc': {'idx_col': 'inc', 'n_cats': n_inc, 'slope_col': None},
            'age': {'idx_col': 'age', 'n_cats': n_age, 'slope_col': 'z_inc'},
        }
    }
    
    # Add interactions to random effects
    for cols in interaction_cols:
        name = "_".join(cols)
        n_cats = int(D[name].max() + 1)
        turnout_config['random_effects'][name] = {'idx_col': name, 'n_cats': n_cats, 'slope_col': None}
else:
    turnout_config = {
        'fixed_effects': [],
        'random_effects': {
            'stt': {'idx_col': 'stt', 'n_cats': n_stt, 'slope_col': None},
            'eth': {'idx_col': 'eth', 'n_cats': n_eth, 'slope_col': None},
            'inc': {'idx_col': 'inc', 'n_cats': n_inc, 'slope_col': None},
            'age': {'idx_col': 'age', 'n_cats': n_age, 'slope_col': None},
        }
    }
    
coords = {"obs_id": df_obs.index}

builder = MRPModelBuilder(df_obs, coords, turnout_config)
print("Building Turnout Model...", flush=True)
builder.build_model()
print("Fitting Turnout Model...", flush=True)
builder.fit(method="pathfinder", num_paths=10, num_draws=200, random_seed=42)

*****   CPS Turnout Model
Building Turnout Model...
Fitting Turnout Model...

Output()

/Users/erik/Projects/pytensor/pytensor/tensor/math.py:3023: RuntimeWarning: divide by zero encountered in matmul
  output_storage[0][0] = np.matmul(*inputs)

/Users/erik/Projects/pytensor/pytensor/tensor/math.py:3023: RuntimeWarning: overflow encountered in matmul
  output_storage[0][0] = np.matmul(*inputs)

/Users/erik/Projects/pytensor/pytensor/tensor/math.py:3023: RuntimeWarning: invalid value encountered in matmul
  output_storage[0][0] = np.matmul(*inputs)

Pathfinder Results                            
                                              
  No. model parameters     941                
                                              
  Configuration:                              
  num_draws_per_path       1000               
  history size (maxcor)    21                 
  max iterations           1000               
  ftol                     1.00e-05           
  gtol                     1.00e-08           
  max line search          1000               
  jitter                   2.0                
  epsilon                  1.00e-08           
  ELBO draws               10                 
                                              
  LBFGS Status:                               
  CONVERGED                7                  
  INIT_FAILED              3                  
  L-BFGS iterations        mean 284 ± std 43  
                                              
  Path Status:                                
  SUCCESS                  7                  
  LBFGS_FAILED             3                  
  ELBO argmax              mean 79 ± std 22   
                                              
  Importance Sampling:                        
  Method                   psis               
  Pareto k                 9.31               
                                              
  Timing (seconds):                           
  Compile                  2.88               
  Compute                  83.67              
  Total                    86.55              

Warnings:
  - INIT_FAILED: LBFGS failed to initialize. Consider reparameterizing the model or reducing jitter if this        
  occurence is high relative to the number of paths.                                                               

Output()

Out[11]:

arviz.InferenceData

• posterior

  <xarray.Dataset> Size: 3MB
  Dimensions:               (chain: 1, draw: 200, age::raw_dim_0: 4,
                             age::raw_slope_dim_0: 4, age::re_dim_0: 4,
                             age::re_slope_dim_0: 4, eth::raw_dim_0: 4,
                             eth::raw_slope_dim_0: 4, eth::re_dim_0: 4,
                             eth::re_slope_dim_0: 4, eth_age::raw_dim_0: 16,
                             eth_age::re_dim_0: 16, eth_inc::raw_dim_0: 20,
                             ...
                             reg_inc::re_dim_0: 25, stt::raw_dim_0: 51,
                             stt::raw_slope_dim_0: 51, stt::re_dim_0: 51,
                             stt::re_slope_dim_0: 51, stt_age::raw_dim_0: 204,
                             stt_age::re_dim_0: 204, stt_eth::raw_dim_0: 204,
                             stt_eth::re_dim_0: 204, stt_inc::raw_dim_0: 255,
                             stt_inc::re_dim_0: 255)
  Coordinates: (12/38)
    * chain                 (chain) int64 8B 0
    * draw                  (draw) int64 2kB 0 1 2 3 4 5 ... 195 196 197 198 199
    * age::raw_dim_0        (age::raw_dim_0) int64 32B 0 1 2 3
    * age::raw_slope_dim_0  (age::raw_slope_dim_0) int64 32B 0 1 2 3
    * age::re_dim_0         (age::re_dim_0) int64 32B 0 1 2 3
    * age::re_slope_dim_0   (age::re_slope_dim_0) int64 32B 0 1 2 3
      ...                    ...
    * stt_age::raw_dim_0    (stt_age::raw_dim_0) int64 2kB 0 1 2 3 ... 201 202 203
    * stt_age::re_dim_0     (stt_age::re_dim_0) int64 2kB 0 1 2 3 ... 201 202 203
    * stt_eth::raw_dim_0    (stt_eth::raw_dim_0) int64 2kB 0 1 2 3 ... 201 202 203
    * stt_eth::re_dim_0     (stt_eth::re_dim_0) int64 2kB 0 1 2 3 ... 201 202 203
    * stt_inc::raw_dim_0    (stt_inc::raw_dim_0) int64 2kB 0 1 2 3 ... 252 253 254
    * stt_inc::re_dim_0     (stt_inc::re_dim_0) int64 2kB 0 1 2 3 ... 252 253 254
  Data variables: (12/60)
      age::raw              (chain, draw, age::raw_dim_0) float64 6kB -0.8859 ....
      age::raw_slope        (chain, draw, age::raw_slope_dim_0) float64 6kB -1....
      age::re               (chain, draw, age::re_dim_0) float64 6kB -0.13 ... ...
      age::re_slope         (chain, draw, age::re_slope_dim_0) float64 6kB -0.1...
      age::sigma            (chain, draw) float64 2kB 0.1467 0.1487 ... 0.1354
      age::sigma_slope      (chain, draw) float64 2kB 0.1318 0.1466 ... 0.1118
      ...                    ...
      stt_eth::raw          (chain, draw, stt_eth::raw_dim_0) float64 326kB -0....
      stt_eth::re           (chain, draw, stt_eth::re_dim_0) float64 326kB -0.0...
      stt_eth::sigma        (chain, draw) float64 2kB 0.01946 0.02484 ... 0.01923
      stt_inc::raw          (chain, draw, stt_inc::raw_dim_0) float64 408kB 0.0...
      stt_inc::re           (chain, draw, stt_inc::re_dim_0) float64 408kB 0.00...
      stt_inc::sigma        (chain, draw) float64 2kB 0.0077 0.01054 ... 0.004776
  Attributes:
      created_at:     2025-12-05T12:59:15.097280+00:00
      arviz_version:  0.22.0

  xarray.Dataset

  • Dimensions:
    • chain: 1
    • draw: 200
    • age::raw_dim_0: 4
    • age::raw_slope_dim_0: 4
    • age::re_dim_0: 4
    • age::re_slope_dim_0: 4
    • eth::raw_dim_0: 4
    • eth::raw_slope_dim_0: 4
    • eth::re_dim_0: 4
    • eth::re_slope_dim_0: 4
    • eth_age::raw_dim_0: 16
    • eth_age::re_dim_0: 16
    • eth_inc::raw_dim_0: 20
    • eth_inc::re_dim_0: 20
    • inc::raw_dim_0: 5
    • inc::re_dim_0: 5
    • inc_age::raw_dim_0: 20
    • inc_age::re_dim_0: 20
    • reg::raw_dim_0: 5
    • reg::raw_slope_dim_0: 5
    • reg::re_dim_0: 5
    • reg::re_slope_dim_0: 5
    • reg_age::raw_dim_0: 20
    • reg_age::re_dim_0: 20
    • reg_eth::raw_dim_0: 20
    • reg_eth::re_dim_0: 20
    • reg_inc::raw_dim_0: 25
    • reg_inc::re_dim_0: 25
    • stt::raw_dim_0: 51
    • stt::raw_slope_dim_0: 51
    • stt::re_dim_0: 51
    • stt::re_slope_dim_0: 51
    • stt_age::raw_dim_0: 204
    • stt_age::re_dim_0: 204
    • stt_eth::raw_dim_0: 204
    • stt_eth::re_dim_0: 204
    • stt_inc::raw_dim_0: 255
    • stt_inc::re_dim_0: 255
  • Coordinates: (38)
    • chain
      (chain)
      int64
      0

      array([0])

    • draw
      (draw)
      int64
      0 1 2 3 4 5 ... 195 196 197 198 199

      array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,
              14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,
              28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,
              42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,
              56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,
              70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,
              84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,
              98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,
             112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,
             126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,
             140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,
             154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,
             168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181,
             182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195,
             196, 197, 198, 199])

    • age::raw_dim_0
      (age::raw_dim_0)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • age::raw_slope_dim_0
      (age::raw_slope_dim_0)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • age::re_dim_0
      (age::re_dim_0)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • age::re_slope_dim_0
      (age::re_slope_dim_0)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • eth::raw_dim_0
      (eth::raw_dim_0)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • eth::raw_slope_dim_0
      (eth::raw_slope_dim_0)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • eth::re_dim_0
      (eth::re_dim_0)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • eth::re_slope_dim_0
      (eth::re_slope_dim_0)
      int64
      0 1 2 3

      array([0, 1, 2, 3])

    • eth_age::raw_dim_0
      (eth_age::raw_dim_0)
      int64
      0 1 2 3 4 5 6 ... 10 11 12 13 14 15

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15])

    • eth_age::re_dim_0
      (eth_age::re_dim_0)
      int64
      0 1 2 3 4 5 6 ... 10 11 12 13 14 15

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15])

    • eth_inc::raw_dim_0
      (eth_inc::raw_dim_0)
      int64
      0 1 2 3 4 5 6 ... 14 15 16 17 18 19

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19])

    • eth_inc::re_dim_0
      (eth_inc::re_dim_0)
      int64
      0 1 2 3 4 5 6 ... 14 15 16 17 18 19

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19])

    • inc::raw_dim_0
      (inc::raw_dim_0)
      int64
      0 1 2 3 4

      array([0, 1, 2, 3, 4])

    • inc::re_dim_0
      (inc::re_dim_0)
      int64
      0 1 2 3 4

      array([0, 1, 2, 3, 4])

    • inc_age::raw_dim_0
      (inc_age::raw_dim_0)
      int64
      0 1 2 3 4 5 6 ... 14 15 16 17 18 19

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19])

    • inc_age::re_dim_0
      (inc_age::re_dim_0)
      int64
      0 1 2 3 4 5 6 ... 14 15 16 17 18 19

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19])

    • reg::raw_dim_0
      (reg::raw_dim_0)
      int64
      0 1 2 3 4

      array([0, 1, 2, 3, 4])

    • reg::raw_slope_dim_0
      (reg::raw_slope_dim_0)
      int64
      0 1 2 3 4

      array([0, 1, 2, 3, 4])

    • reg::re_dim_0
      (reg::re_dim_0)
      int64
      0 1 2 3 4

      array([0, 1, 2, 3, 4])

    • reg::re_slope_dim_0
      (reg::re_slope_dim_0)
      int64
      0 1 2 3 4

      array([0, 1, 2, 3, 4])

    • reg_age::raw_dim_0
      (reg_age::raw_dim_0)
      int64
      0 1 2 3 4 5 6 ... 14 15 16 17 18 19

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19])

    • reg_age::re_dim_0
      (reg_age::re_dim_0)
      int64
      0 1 2 3 4 5 6 ... 14 15 16 17 18 19

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19])

    • reg_eth::raw_dim_0
      (reg_eth::raw_dim_0)
      int64
      0 1 2 3 4 5 6 ... 14 15 16 17 18 19

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19])

    • reg_eth::re_dim_0
      (reg_eth::re_dim_0)
      int64
      0 1 2 3 4 5 6 ... 14 15 16 17 18 19

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19])

    • reg_inc::raw_dim_0
      (reg_inc::raw_dim_0)
      int64
      0 1 2 3 4 5 6 ... 19 20 21 22 23 24

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24])

    • reg_inc::re_dim_0
      (reg_inc::re_dim_0)
      int64
      0 1 2 3 4 5 6 ... 19 20 21 22 23 24

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24])

    • stt::raw_dim_0
      (stt::raw_dim_0)
      int64
      0 1 2 3 4 5 6 ... 45 46 47 48 49 50

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])

    • stt::raw_slope_dim_0
      (stt::raw_slope_dim_0)
      int64
      0 1 2 3 4 5 6 ... 45 46 47 48 49 50

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])

    • stt::re_dim_0
      (stt::re_dim_0)
      int64
      0 1 2 3 4 5 6 ... 45 46 47 48 49 50

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])

    • stt::re_slope_dim_0
      (stt::re_slope_dim_0)
      int64
      0 1 2 3 4 5 6 ... 45 46 47 48 49 50

      array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50])

    • stt_age::raw_dim_0
      (stt_age::raw_dim_0)
      int64
      0 1 2 3 4 5 ... 199 200 201 202 203

      array([  0,   1,   2, ..., 201, 202, 203], shape=(204,))

    • stt_age::re_dim_0
      (stt_age::re_dim_0)
      int64
      0 1 2 3 4 5 ... 199 200 201 202 203

      array([  0,   1,   2, ..., 201, 202, 203], shape=(204,))

    • stt_eth::raw_dim_0
      (stt_eth::raw_dim_0)
      int64
      0 1 2 3 4 5 ... 199 200 201 202 203

      array([  0,   1,   2, ..., 201, 202, 203], shape=(204,))

    • stt_eth::re_dim_0
      (stt_eth::re_dim_0)
      int64
      0 1 2 3 4 5 ... 199 200 201 202 203

      array([  0,   1,   2, ..., 201, 202, 203], shape=(204,))

    • stt_inc::raw_dim_0
      (stt_inc::raw_dim_0)
      int64
      0 1 2 3 4 5 ... 250 251 252 253 254

      array([  0,   1,   2, ..., 252, 253, 254], shape=(255,))

    • stt_inc::re_dim_0
      (stt_inc::re_dim_0)
      int64
      0 1 2 3 4 5 ... 250 251 252 253 254

      array([  0,   1,   2, ..., 252, 253, 254], shape=(255,))

  • Data variables: (60)
    • age::raw
      (chain, draw, age::raw_dim_0)
      float64
      -0.8859 0.07228 ... 0.1329 0.4545

      array([[[-8.85887083e-01,  7.22776648e-02,  2.01756908e-01,
                3.65421054e-01],
              [-8.91911421e-01, -7.40482612e-02,  7.68908288e-02,
                6.92803520e-01],
              [-1.04584993e+00, -1.07040238e-01,  7.63997853e-03,
                5.70658800e-01],
              [-9.50091009e-01, -2.51292842e-01,  3.49065724e-01,
                7.22963960e-01],
              [-9.47188709e-01, -1.58388576e-01,  3.60813157e-01,
                6.88523368e-01],
              [-9.67711777e-01, -2.40692376e-01,  3.75508335e-01,
                6.54228571e-01],
              [-9.21541639e-01,  7.00852772e-02,  2.64886051e-01,
                7.07767690e-01],
              [-8.52767202e-01,  1.25852884e-01,  1.00672623e-02,
                3.02717699e-01],
              [-9.32038887e-01, -2.08406750e-01,  3.55297744e-01,
                7.62182052e-01],
              [-9.92365125e-01, -2.62647111e-01,  3.81975513e-01,
                6.43577518e-01],
      ...
              [-9.24933415e-01,  1.10989820e-01,  3.49358776e-02,
                5.45168690e-01],
              [-1.41121599e+00,  8.16080187e-02,  2.48402525e-01,
                6.57516526e-01],
              [-9.62366438e-01,  1.78312888e-01,  3.72443936e-01,
                6.01474498e-01],
              [-8.20846734e-01,  7.25525533e-02,  8.32374050e-02,
                5.09741869e-01],
              [-8.62108832e-01,  1.77805002e-01,  1.41091214e-01,
                6.15790261e-01],
              [-1.19387044e+00,  7.03857281e-02, -4.93975683e-02,
                5.09430866e-01],
              [-8.96502124e-01, -2.50651638e-01,  3.73269716e-01,
                8.47523092e-01],
              [-9.79552085e-01, -2.33984085e-01,  3.87559459e-01,
                7.12294274e-01],
              [-9.23521010e-01,  7.04913598e-02,  1.51992810e-01,
                3.37840348e-01],
              [-1.01296053e+00, -7.32521995e-03,  1.32908574e-01,
                4.54477596e-01]]])

    • age::raw_slope
      (chain, draw, age::raw_slope_dim_0)
      float64
      -1.031 0.6323 ... 0.5181 -0.245

      array([[[-1.03137399,  0.63234723,  0.53263136, -0.20713437],
              [-0.99058246,  0.71769518,  0.48856251, -0.35524308],
              [-0.93355158,  0.92592091,  0.48151317, -0.47178584],
              [-1.15213717,  1.40421803,  1.03775195, -0.22308838],
              [-1.25714628,  1.45579521,  0.95512065,  0.13252548],
              [-1.14575077,  1.39169608,  0.8961282 , -0.09733699],
              [-1.02303913,  0.78667418,  0.50429769, -0.30500008],
              [-0.91339651,  0.66174733,  0.67538606, -0.20962885],
              [-1.36752002,  1.42095902,  0.9534008 , -0.04494883],
              [-1.16014874,  1.26179693,  0.97717336,  0.11128438],
              [-1.06876344,  0.7688004 ,  0.55151724, -0.34264463],
              [-0.87083281,  0.66012971,  0.66349304, -0.55222437],
              [-1.27443843,  1.32588172,  1.00094047, -0.20320793],
              [-1.10128556,  0.69332162,  0.43301452, -0.36286608],
              [-1.08667771,  1.5094396 ,  1.01056012,  0.08766137],
              [-0.90331128,  0.65519271,  0.55702122, -0.39245324],
              [-1.07196   ,  0.65286556,  0.73725927, -0.3458026 ],
              [-1.08094712,  0.75754133,  0.59253456, -0.55546668],
              [-1.03881631,  0.78145425,  0.61099078, -0.43423739],
              [-1.0141298 ,  0.84981269,  0.69945213, -0.24284455],
      ...
              [-1.01664163,  0.61304766,  0.6020113 , -0.39076608],
              [-1.2564663 ,  1.3958524 ,  0.8666685 ,  0.03412074],
              [-1.23930617,  1.41501057,  1.01700011,  0.20671039],
              [-0.95069041,  0.77662029,  0.53790962, -0.5336289 ],
              [-1.32116463,  1.26295269,  1.12799919,  0.07352533],
              [-1.08340041,  1.57202441,  0.90652382,  0.07031077],
              [-0.91730039,  0.60558577,  0.76028255, -0.23707173],
              [-1.03011437,  0.77093806,  0.63953387, -0.30001742],
              [-1.32627344,  0.6052258 ,  0.52037789, -0.37548512],
              [-0.76485909,  0.90591923,  0.77500241, -0.35485785],
              [-1.03739044,  0.80168149,  0.5848585 , -0.23715185],
              [-0.88781834,  0.88182483,  0.53979263, -0.43751482],
              [-1.00811671,  0.96168924,  0.54458989, -0.30648614],
              [-1.00774837,  0.62881486,  0.51550716, -0.25431493],
              [-1.02415846,  0.50908126,  0.48247488, -0.33718953],
              [-1.10649772,  0.8896104 ,  0.63929109, -0.23691085],
              [-1.3721816 ,  1.48971497,  0.90415624, -0.00688705],
              [-0.99847252,  1.49788007,  0.8183955 , -0.07861755],
              [-1.02999106,  0.72908101,  0.50298372, -0.58805692],
              [-0.84384968,  0.6929165 ,  0.51812218, -0.24495336]]])

    • age::re
      (chain, draw, age::re_dim_0)
      float64
      -0.13 0.0106 ... 0.018 0.06155

      array([[[-1.29980523e-01,  1.06048376e-02,  2.96024954e-02,
                5.36158845e-02],
              [-1.32596617e-01, -1.10084350e-02,  1.14310273e-02,
                1.02996106e-01],
              [-1.25257772e-01, -1.28198333e-02,  9.15013388e-04,
                6.83457997e-02],
              [-5.62942522e-01, -1.48894606e-01,  2.06826438e-01,
                4.28366494e-01],
              [-5.34122431e-01, -8.93157724e-02,  2.03463575e-01,
                3.88260303e-01],
              [-5.62362165e-01, -1.39872521e-01,  2.18217537e-01,
                3.80189023e-01],
              [-1.12262406e-01,  8.53780398e-03,  3.22684773e-02,
                8.62204166e-02],
              [-1.50496957e-01,  2.22106056e-02,  1.77667755e-03,
                5.34238328e-02],
              [-5.35702089e-01, -1.19784628e-01,  2.04212234e-01,
                4.38074552e-01],
              [-5.65551634e-01, -1.49683316e-01,  2.17688903e-01,
                3.66776610e-01],
      ...
              [-1.16907113e-01,  1.40285768e-02,  4.41572607e-03,
                6.89066875e-02],
              [-1.78820047e-01,  1.03408336e-02,  3.14759409e-02,
                8.33161874e-02],
              [-1.35238651e-01,  2.50578090e-02,  5.23384996e-02,
                8.45235209e-02],
              [-1.06227947e-01,  9.38921786e-03,  1.07719728e-02,
                6.59670438e-02],
              [-1.21233263e-01,  2.50036650e-02,  1.98408224e-02,
                8.65949398e-02],
              [-1.54768927e-01,  9.12454420e-03, -6.40371717e-03,
                6.60407242e-02],
              [-5.34867676e-01, -1.49542824e-01,  2.22698754e-01,
                5.05645993e-01],
              [-5.49119723e-01, -1.31167375e-01,  2.17259037e-01,
                3.99299681e-01],
              [-1.12788659e-01,  8.60903636e-03,  1.85627235e-02,
                4.12600899e-02],
              [-1.37178380e-01, -9.92004901e-04,  1.79989076e-02,
                6.15468212e-02]]])

    • age::re_slope
      (chain, draw, age::re_slope_dim_0)
      float64
      -0.136 0.08336 ... 0.05792 -0.02738

      array([[[-0.13596452,  0.08336141,  0.07021601, -0.02730622],
              [-0.14518302,  0.10518776,  0.07160533, -0.05206559],
              [-0.10541717,  0.10455551,  0.05437274, -0.05327433],
              [-0.39952424,  0.48693781,  0.35985912, -0.0773599 ],
              [-0.4487228 ,  0.51962808,  0.34091849,  0.04730333],
              [-0.42947262,  0.52166263,  0.33590422, -0.03648575],
              [-0.13794607,  0.10607474,  0.06799924, -0.04112605],
              [-0.12453501,  0.09022447,  0.09208401, -0.02858138],
              [-0.52689119,  0.54748067,  0.36733537, -0.01731831],
              [-0.42557501,  0.46286242,  0.35845452,  0.04082222],
              [-0.10747884,  0.07731344,  0.05546263, -0.03445762],
              [-0.14147776,  0.10724639,  0.1077928 , -0.0897158 ],
              [-0.41917353,  0.43609366,  0.32921775, -0.0668368 ],
              [-0.12657164,  0.07968402,  0.04976671, -0.04170449],
              [-0.41770245,  0.58020571,  0.388444  ,  0.0336957 ],
              [-0.11761477,  0.08530873,  0.07252641, -0.05109899],
              [-0.14323151,  0.08723359,  0.09850998, -0.04620492],
              [-0.1567798 ,  0.10987325,  0.08594079, -0.08056449],
              [-0.12974265,  0.09759949,  0.07630951, -0.05423395],
              [-0.1809639 ,  0.15164273,  0.12481201, -0.0433338 ],
      ...
              [-0.16651056,  0.10040796,  0.09860037, -0.06400159],
              [-0.4246612 ,  0.47177099,  0.29291711,  0.01153215],
              [-0.46774912,  0.53406492,  0.38384454,  0.07801833],
              [-0.08759285,  0.07155472,  0.04956086, -0.04916645],
              [-0.41809815,  0.39967629,  0.35696866,  0.02326796],
              [-0.36286161,  0.52651569,  0.30362061,  0.02354908],
              [-0.12621261,  0.08332337,  0.10460831, -0.03261902],
              [-0.12175808,  0.0911238 ,  0.07559201, -0.03546164],
              [-0.17880562,  0.08159537,  0.07015634, -0.05062218],
              [-0.07646532,  0.09056753,  0.07747938, -0.03547623],
              [-0.12326285,  0.09525588,  0.06949295, -0.02817841],
              [-0.12561666,  0.12476865,  0.0763748 , -0.0619036 ],
              [-0.1486014 ,  0.14175776,  0.08027525, -0.04517758],
              [-0.11606465,  0.07242202,  0.05937212, -0.02929002],
              [-0.1142934 ,  0.05681213,  0.05384293, -0.03762947],
              [-0.14758648,  0.11865769,  0.08526969, -0.03159956],
              [-0.4704028 ,  0.51069486,  0.30995724, -0.00236098],
              [-0.39534299,  0.59308231,  0.32404189, -0.03112845],
              [-0.11736534,  0.08307727,  0.05731395, -0.06700786],
              [-0.09433411,  0.07746126,  0.05792097, -0.02738338]]])

    • age::sigma
      (chain, draw)
      float64
      0.1467 0.1487 ... 0.1221 0.1354

      array([[0.14672358, 0.14866568, 0.11976649, 0.59251431, 0.56390287,
              0.58112568, 0.12182022, 0.1764807 , 0.57476367, 0.56990277,
              0.12186945, 0.16790577, 0.58047166, 0.11431637, 0.56956333,
              0.1127026 , 0.13359683, 0.12923386, 0.13923011, 0.14062886,
              0.12676084, 0.5825825 , 0.55752913, 0.10463412, 0.12013148,
              0.14562966, 0.11209222, 0.57481178, 0.13431207, 0.54235868,
              0.11640313, 0.12083542, 0.56162726, 0.11818186, 0.12505573,
              0.55060127, 0.10983509, 0.13976321, 0.1440229 , 0.1278079 ,
              0.12601058, 0.58805672, 0.14400491, 0.58792081, 0.13608817,
              0.57733744, 0.5482017 , 0.14433135, 0.1360129 , 0.1020232 ,
              0.56524204, 0.12215858, 0.12075708, 0.54254767, 0.11599165,
              0.14137225, 0.60263441, 0.12656809, 0.54754596, 0.14048337,
              0.14621289, 0.54683555, 0.60721294, 0.13630068, 0.53347098,
              0.56880092, 0.59372534, 0.12707039, 0.1254517 , 0.58801852,
              0.16014268, 0.57055468, 0.11842695, 0.11300136, 0.13250709,
              0.15770281, 0.58403745, 0.13539799, 0.13534781, 0.15640889,
              0.12654919, 0.16401109, 0.12382677, 0.11658163, 0.10391641,
              0.13337872, 0.5714683 , 0.56593384, 0.11922395, 0.59360565,
              0.55204023, 0.10740545, 0.15979162, 0.12070251, 0.57639432,
              0.53906084, 0.11968519, 0.1289228 , 0.13451294, 0.12349985,
              0.56859998, 0.11772506, 0.12488368, 0.55357056, 0.15018695,
              0.15609545, 0.10219238, 0.57825008, 0.12562982, 0.54467029,
              0.1270177 , 0.14617486, 0.14972546, 0.11629263, 0.1381411 ,
              0.14100599, 0.13480475, 0.10664324, 0.14139862, 0.14355371,
              0.58270645, 0.10947933, 0.11973788, 0.12368264, 0.54779996,
              0.1420837 , 0.14763616, 0.1291553 , 0.56611398, 0.15539857,
              0.12342113, 0.11329624, 0.0938393 , 0.12193942, 0.55570524,
              0.13696092, 0.12167452, 0.55665572, 0.13105403, 0.15202957,
              0.14613261, 0.53833676, 0.56065326, 0.55954743, 0.59515982,
              0.15344672, 0.1224905 , 0.11659841, 0.11652971, 0.12387154,
              0.13122936, 0.12343318, 0.58002957, 0.53530191, 0.14650174,
              0.13209454, 0.14564589, 0.13887107, 0.12862783, 0.55792747,
              0.10153532, 0.15205379, 0.15507863, 0.13312759, 0.13153898,
              0.14899253, 0.14668619, 0.15586279, 0.13271571, 0.12224716,
              0.57808932, 0.12573901, 0.13942546, 0.14979773, 0.16615441,
              0.54460484, 0.11815175, 0.55877446, 0.15804358, 0.56439248,
              0.14301916, 0.5667644 , 0.60474802, 0.16097837, 0.59190858,
              0.57563638, 0.14950043, 0.12425062, 0.12414977, 0.13713548,
              0.12639517, 0.12671345, 0.14052719, 0.12941265, 0.14062408,
              0.12963628, 0.59661618, 0.56058247, 0.12212896, 0.13542322]])

    • age::sigma_slope
      (chain, draw)
      float64
      0.1318 0.1466 ... 0.1139 0.1118

      array([[0.13182853, 0.14656328, 0.11292057, 0.34676795, 0.35693762,
              0.37483948, 0.13483948, 0.13634277, 0.38528956, 0.36682798,
              0.10056373, 0.1624626 , 0.32890842, 0.11493081, 0.38438485,
              0.13020403, 0.13361647, 0.14503929, 0.1248947 , 0.17844254,
              0.11467326, 0.35983926, 0.33724538, 0.12530124, 0.13011092,
              0.10437084, 0.10460433, 0.335114  , 0.13365966, 0.34418369,
              0.11036171, 0.11256844, 0.37340251, 0.13681179, 0.14956912,
              0.35106072, 0.14986452, 0.14967963, 0.12193255, 0.09799216,
              0.10571877, 0.3402496 , 0.13569081, 0.3470864 , 0.09373569,
              0.36098662, 0.31542051, 0.12494627, 0.12907778, 0.11884953,
              0.36160802, 0.13398122, 0.12846661, 0.36454977, 0.0981906 ,
              0.13985523, 0.36336007, 0.10183961, 0.34400621, 0.13112066,
              0.12699897, 0.35804495, 0.35453186, 0.1214378 , 0.32428615,
              0.35923676, 0.37534678, 0.11620439, 0.11232038, 0.36298442,
              0.11756864, 0.33977383, 0.11965891, 0.13427061, 0.10434382,
              0.12397527, 0.34122445, 0.10908923, 0.12002819, 0.11732381,
              0.10006849, 0.09437222, 0.11439806, 0.1077383 , 0.12639857,
              0.11830046, 0.33488542, 0.35032628, 0.12395683, 0.37081037,
              0.34594437, 0.14477002, 0.13854471, 0.13400194, 0.3364306 ,
              0.34925328, 0.10524588, 0.13027844, 0.13898546, 0.12235664,
              0.34960363, 0.14210035, 0.13047626, 0.35745904, 0.12759701,
              0.15039485, 0.11132616, 0.37028287, 0.13148771, 0.36079488,
              0.15674838, 0.1093896 , 0.13982592, 0.13936718, 0.13852452,
              0.12885043, 0.11839271, 0.10786432, 0.11493197, 0.12137293,
              0.36344434, 0.10841017, 0.10918821, 0.13530404, 0.39120797,
              0.11506997, 0.09529128, 0.17969513, 0.34539058, 0.12235475,
              0.10134786, 0.11995945, 0.11197438, 0.12780113, 0.33545605,
              0.12191145, 0.12803261, 0.31082083, 0.13666195, 0.09725252,
              0.1134696 , 0.33997013, 0.3399715 , 0.37923702, 0.36713523,
              0.13052043, 0.13655807, 0.14213001, 0.11627549, 0.11196337,
              0.11191715, 0.08248168, 0.34529235, 0.33332339, 0.10349647,
              0.1171675 , 0.10761315, 0.12035825, 0.12087844, 0.3713693 ,
              0.15227827, 0.16476452, 0.12994879, 0.12050294, 0.11331298,
              0.10424816, 0.15327524, 0.10795288, 0.1205453 , 0.13707532,
              0.35647859, 0.12841188, 0.09090039, 0.13874771, 0.14958017,
              0.33022993, 0.09808628, 0.35985496, 0.12139794, 0.38510399,
              0.16378491, 0.33798057, 0.37742822, 0.09213604, 0.31646181,
              0.33492844, 0.13759136, 0.11819861, 0.13481807, 0.09997308,
              0.11882011, 0.14148915, 0.14740496, 0.11517225, 0.11159738,
              0.13338164, 0.34281381, 0.39594779, 0.11394792, 0.11179018]])

    • b_0
      (chain, draw)
      float64
      0.69 0.68 0.653 ... 0.6649 0.6596

      array([[0.69004983, 0.67997229, 0.65297685, 0.75199732, 0.72479312,
              0.77144118, 0.68303885, 0.67611082, 0.74907828, 0.7259487 ,
              0.7157988 , 0.69172425, 0.76411321, 0.6456164 , 0.73842283,
              0.68741064, 0.68008967, 0.6862211 , 0.6602593 , 0.67225422,
              0.67592667, 0.74872534, 0.77066057, 0.67224663, 0.66624076,
              0.6794052 , 0.676817  , 0.73523315, 0.68175437, 0.75753986,
              0.69556823, 0.73145195, 0.74636146, 0.68628187, 0.69303923,
              0.75316904, 0.66152213, 0.6961064 , 0.686665  , 0.68846643,
              0.66671476, 0.77679521, 0.68352724, 0.79023461, 0.69371346,
              0.74149102, 0.76702361, 0.68863384, 0.65373064, 0.68263435,
              0.75131399, 0.6895278 , 0.66778182, 0.73341138, 0.67535767,
              0.69067266, 0.75563448, 0.67471153, 0.76225261, 0.67672479,
              0.6958324 , 0.71799687, 0.74013688, 0.66407328, 0.78948169,
              0.73019733, 0.749948  , 0.72158271, 0.67582356, 0.73941078,
              0.65864176, 0.77252022, 0.67015403, 0.74141999, 0.67854663,
              0.70907845, 0.75248709, 0.70003379, 0.6937228 , 0.67565895,
              0.68540749, 0.69664184, 0.65365429, 0.67294297, 0.68938859,
              0.70855827, 0.71377813, 0.74952413, 0.67274003, 0.73488953,
              0.7667333 , 0.71168714, 0.67249398, 0.70140419, 0.71576981,
              0.7555608 , 0.70113392, 0.69595602, 0.66687269, 0.66335187,
              0.74866117, 0.66880916, 0.70405903, 0.77306808, 0.67190767,
              0.678023  , 0.69548746, 0.76089611, 0.68002341, 0.72481534,
              0.64853173, 0.69479371, 0.69246963, 0.675336  , 0.68539942,
              0.65045129, 0.66408246, 0.67101431, 0.66353105, 0.69073656,
              0.74838396, 0.70166674, 0.69004154, 0.66179192, 0.74621572,
              0.70529685, 0.69425932, 0.68014214, 0.76372437, 0.68905463,
              0.68353788, 0.65727134, 0.6715989 , 0.69360675, 0.75664285,
              0.68120219, 0.6754931 , 0.76779695, 0.68479707, 0.66929835,
              0.65877529, 0.77030394, 0.7576175 , 0.75667749, 0.74175881,
              0.65216735, 0.65854499, 0.6568266 , 0.66518296, 0.68542399,
              0.67731082, 0.7108863 , 0.75523707, 0.7679804 , 0.69390609,
              0.69994898, 0.69188336, 0.64450936, 0.64367043, 0.7744048 ,
              0.70754606, 0.71093488, 0.67731857, 0.68732256, 0.66487393,
              0.67965034, 0.65395337, 0.68350086, 0.68035126, 0.6817718 ,
              0.72927156, 0.67202311, 0.68623577, 0.69959241, 0.64779036,
              0.73071992, 0.69428896, 0.77004901, 0.67073984, 0.76544487,
              0.67914324, 0.76140397, 0.7641819 , 0.6813688 , 0.74266988,
              0.73868956, 0.68153754, 0.6900444 , 0.65724835, 0.71416318,
              0.68458525, 0.68523095, 0.71286971, 0.6791119 , 0.69245117,
              0.66227631, 0.79884659, 0.73107604, 0.66487052, 0.65961762]])

    • b_z_inc
      (chain, draw)
      float64
      0.9592 0.9105 ... 0.9332 0.9928

      array([[0.95915771, 0.91052944, 0.91019375, 0.88686459, 0.88082387,
              0.87242299, 0.90380609, 0.91274328, 0.90037276, 0.81011468,
              0.93408196, 0.98623252, 0.93413836, 0.9303749 , 0.87929504,
              0.92792662, 0.90597933, 0.93112465, 0.93803682, 0.93259375,
              0.89777935, 0.92055723, 0.90032364, 0.91123194, 0.90918865,
              0.93965361, 0.90515977, 0.91333432, 0.92274939, 0.90117284,
              0.8883211 , 0.95093843, 0.86110687, 0.96817112, 0.92333727,
              0.87966029, 0.96014101, 0.9086561 , 0.97319403, 0.97334971,
              0.91856637, 0.90803543, 0.92545888, 0.86327922, 0.93112304,
              0.85944114, 0.89476509, 0.93274424, 0.90935795, 1.01196049,
              0.89915738, 0.91597996, 0.9682803 , 0.90397021, 0.96716624,
              0.96318581, 0.9133999 , 0.93217398, 0.92550742, 0.9478251 ,
              0.93273122, 0.88348167, 0.9520683 , 0.90349135, 0.92417165,
              0.87652916, 0.86627136, 0.92720653, 0.93409055, 0.90062343,
              0.96593789, 0.90962192, 0.89921101, 1.00021695, 0.94888681,
              0.9364095 , 0.93748858, 0.93561875, 0.9194251 , 0.91125288,
              0.92687959, 0.93065034, 0.91485593, 0.95409561, 0.91617672,
              0.9408208 , 0.88616706, 0.92259584, 0.93476219, 0.89639599,
              0.91857148, 0.93928676, 0.9355616 , 0.95545805, 0.90309995,
              0.86113279, 0.93575084, 0.89107424, 0.92748767, 0.91609904,
              0.91196899, 0.92548239, 0.95865633, 0.93065836, 0.94064639,
              0.95511447, 0.91495776, 0.92838656, 0.92894019, 0.89645109,
              0.91419471, 0.96391874, 0.95044959, 0.92568336, 0.93983212,
              0.920147  , 0.89802597, 0.88817886, 0.93015914, 0.92982882,
              0.89875166, 0.96094036, 0.94426153, 0.88180291, 0.88008867,
              0.9025565 , 0.9949259 , 0.90845888, 0.8727789 , 0.93727392,
              0.93093644, 0.94400582, 0.91990658, 0.94385798, 0.88391715,
              0.99324651, 0.95249433, 0.89229467, 0.88673716, 0.95515731,
              0.95597025, 0.90868554, 0.98043827, 0.85459278, 0.89825078,
              0.93594412, 0.89195914, 0.9641802 , 0.95143985, 0.88210308,
              0.95667313, 0.92246665, 0.88359989, 0.90033297, 0.92486333,
              0.94675992, 0.94566071, 0.90070662, 0.92733966, 0.86231851,
              0.94399285, 0.96547956, 0.93255589, 0.96045309, 0.89379946,
              0.93739083, 0.95097915, 0.9139472 , 0.97148   , 0.93803882,
              0.88485607, 0.92641359, 0.92205367, 0.95717377, 0.89844807,
              0.85640133, 0.92522197, 0.93759387, 0.96133503, 0.8930921 ,
              0.84684713, 0.92316067, 0.91961146, 0.9393664 , 0.90252803,
              0.87479328, 0.89472335, 0.95785863, 0.85936654, 0.91671983,
              0.95001139, 0.93538909, 0.93694577, 0.92638928, 0.91172428,
              0.89660185, 0.95057809, 0.89699854, 0.93324577, 0.9927605 ]])

    • b_z_inc_z_incstt
      (chain, draw)
      float64
      -0.2261 -0.168 ... 0.01207 -0.1852

      array([[-2.26077835e-01, -1.67974701e-01, -6.99938451e-02,
              -2.50349035e-02, -7.00397320e-02, -3.25493909e-02,
              -8.68708520e-02, -6.08867059e-02, -9.44306357e-04,
              -2.07879111e-02, -8.72811573e-02, -1.10438240e-01,
              -1.31754032e-01, -1.35797732e-01, -8.57858009e-02,
              -1.57473444e-01, -9.35675072e-02, -1.99628092e-01,
              -1.09776317e-01, -1.78576781e-01, -1.72385089e-01,
              -5.71805539e-02, -6.98977680e-02, -1.89404477e-01,
              -1.81696373e-01, -1.53358229e-01, -7.34270846e-02,
               6.14951161e-02, -6.28021232e-02, -2.94740512e-02,
              -1.90877716e-01, -1.73579300e-01,  4.26027419e-02,
              -5.66051442e-02, -9.63130222e-02, -8.33190008e-02,
              -9.89754202e-02, -1.49006701e-01, -1.68435141e-01,
              -1.52746775e-02, -9.55109239e-02, -1.62485109e-01,
              -1.35702316e-01, -1.10272127e-01, -6.55846543e-02,
              -7.76515011e-02, -3.92060378e-02, -1.86731902e-01,
              -1.64249301e-01, -1.52987646e-01,  2.14095260e-03,
              -1.35365789e-01, -1.74214307e-01,  1.70567532e-02,
              -1.73813602e-01, -2.06941212e-01, -3.09289348e-02,
              -1.13025643e-01, -1.99287816e-02, -1.03797942e-01,
      ...
              -8.80971051e-02, -2.06101137e-02, -9.30946449e-02,
              -9.32702560e-02, -2.83666542e-01, -1.33183162e-01,
              -2.19651250e-01, -1.49094904e-01, -1.80008502e-01,
              -1.60428846e-01, -1.02883220e-01, -8.67297808e-02,
              -2.71341270e-04, -1.16145579e-01, -1.06717451e-01,
              -1.07164770e-01, -1.45557895e-01, -1.25753932e-01,
              -4.42757771e-02, -1.67540165e-01, -1.05537194e-01,
              -1.06905330e-01, -8.85140540e-02, -1.15300230e-01,
              -1.34713963e-01, -1.57200751e-01, -1.72700970e-01,
              -5.38161273e-02, -9.85015428e-02, -1.11137383e-01,
              -6.86831391e-02, -1.69566919e-01, -2.23413389e-01,
              -2.85712069e-01, -4.23107483e-02, -1.57856727e-02,
               9.08644736e-03, -4.53459323e-02,  1.86321102e-02,
              -1.36707732e-01, -1.97785818e-02, -1.23176594e-01,
              -1.58338440e-01,  5.09143433e-02,  5.86211615e-02,
              -1.52127080e-01, -1.00920344e-01, -8.35471915e-02,
              -2.09611964e-01, -1.16312416e-01, -1.02498218e-01,
              -9.94450456e-02, -1.50517737e-01, -2.10371459e-01,
              -8.43304153e-02, -1.28605903e-01, -3.91217120e-02,
               1.20655935e-02, -1.85187363e-01]])

    • b_z_inc_z_trnprv
      (chain, draw)
      float64
      0.1436 0.1001 ... 0.1081 0.1812

      array([[ 0.14358085,  0.10010962,  0.20840373,  0.0393697 ,  0.16002006,
              -0.00255391,  0.15961656,  0.04489029,  0.09609323,  0.05445188,
               0.177183  ,  0.16621232,  0.15201709,  0.19411498,  0.08244564,
               0.20784112,  0.13924983,  0.16530496,  0.11868409,  0.14034506,
               0.0975322 ,  0.0396544 ,  0.06532265,  0.07913373,  0.10006717,
               0.07966838,  0.19346292,  0.13517618,  0.18230419,  0.0193711 ,
               0.15640207,  0.15276394,  0.08472338,  0.12455547,  0.0556782 ,
               0.09654335,  0.19712289,  0.14451922,  0.20226221,  0.14864479,
               0.16163807,  0.07465561,  0.16711406,  0.14270578,  0.06343072,
               0.05339725,  0.08820207,  0.20561177,  0.09440738,  0.17830119,
               0.07052273,  0.17992181,  0.07555226,  0.04796211,  0.22531545,
               0.17538129,  0.01990938,  0.15546796,  0.04622114,  0.25599635,
               0.12275979,  0.05977568,  0.13079099,  0.16155263,  0.14037535,
               0.09005847,  0.18145167,  0.04004655,  0.1058549 ,  0.18182027,
               0.18674961,  0.09997833,  0.1352157 ,  0.07297069,  0.14079509,
               0.07188038,  0.11323012,  0.08914618,  0.09629087,  0.03741893,
               0.22585903,  0.13489344,  0.15828225,  0.16885864,  0.10266353,
               0.14764044,  0.02916438,  0.14890032,  0.14259504,  0.09309526,
               0.03157115,  0.22228549,  0.09439994,  0.06472328,  0.07234776,
               0.04869488,  0.25961146,  0.09391459,  0.19861325,  0.09844495,
               0.11318379,  0.22223947,  0.132487  ,  0.16446081,  0.10083744,
               0.15808635,  0.11294836,  0.12022444,  0.15215411,  0.13518498,
               0.12613787,  0.17639049,  0.14802601,  0.02935844,  0.1822543 ,
               0.17842486,  0.10096909,  0.10236263,  0.20569747,  0.14314   ,
               0.08277029,  0.15892764,  0.12556761,  0.17571107,  0.0968234 ,
               0.20227108,  0.05861157,  0.08918276,  0.04613514,  0.28958975,
               0.09307726,  0.09624832,  0.13937369,  0.1692238 ,  0.03570593,
               0.16229958,  0.22509302,  0.12328923,  0.14284406,  0.21804085,
               0.09826131,  0.00310489,  0.18958159,  0.11498195,  0.1113331 ,
               0.16836071,  0.11477756,  0.06751396,  0.07023632,  0.14392304,
               0.01718503,  0.12456433,  0.1023657 ,  0.04564267,  0.19994542,
               0.18205398,  0.14141663,  0.15928273,  0.20810519,  0.13806601,
               0.17269854,  0.08662185,  0.22155401,  0.2285728 ,  0.17384966,
               0.14967212,  0.11303977,  0.17893042,  0.23938932,  0.20592558,
               0.13876541,  0.11841973,  0.00457813,  0.03197264,  0.05421373,
               0.15229564,  0.09228422,  0.02516519,  0.20065156,  0.12557037,
               0.01937068,  0.12919623,  0.1407686 ,  0.04191161,  0.16050205,
               0.00200836,  0.16757749,  0.12752217, -0.00596821,  0.00030235,
               0.10053319,  0.11329044,  0.12162344,  0.06470924,  0.15594185,
               0.04877175,  0.16552963,  0.09798741,  0.10814654,  0.18123574]])

    • b_z_incstt
      (chain, draw)
      float64
      -0.02899 -0.03946 ... -0.05426

      array([[-0.02899181, -0.03945569,  0.00371006, -0.06967235, -0.05600125,
              -0.10091183,  0.00022027, -0.01358779, -0.09593672, -0.07902689,
               0.0032761 , -0.04309491, -0.07394473, -0.03272402, -0.1254751 ,
              -0.00719619, -0.06246559, -0.03318726,  0.02994016, -0.00409185,
              -0.00757986, -0.10773338, -0.06854154,  0.02338163, -0.08048688,
              -0.08038147, -0.0337538 , -0.08212846, -0.00025512, -0.04866164,
               0.01741605, -0.02001553, -0.05552975, -0.01205426, -0.06102488,
              -0.11430763, -0.05519058, -0.04106687, -0.03769852, -0.05925999,
               0.00780767, -0.0848872 , -0.04715282, -0.06101517, -0.03185638,
              -0.09803251, -0.06811367, -0.00626188, -0.00642537, -0.0302619 ,
              -0.09707761, -0.03657568, -0.01170007, -0.07424561, -0.00868867,
              -0.03217261, -0.1296183 ,  0.00585004, -0.08435326,  0.0020591 ,
              -0.04101363, -0.10981509, -0.05000566, -0.0277691 , -0.09282189,
              -0.08655527, -0.11181998, -0.05165455, -0.01777763, -0.10590029,
              -0.06000398, -0.10692454,  0.00610054, -0.00442238, -0.02952813,
              -0.02390837, -0.12291271, -0.02027694, -0.01793207, -0.04778801,
              -0.00542766, -0.04176686, -0.03305156, -0.04560834, -0.02563358,
              -0.01801394, -0.08899123, -0.11710457, -0.0152307 , -0.12423249,
              -0.14081105, -0.0272856 , -0.05135053, -0.0300924 , -0.09211127,
              -0.12887611, -0.03704632, -0.05485466, -0.00947002, -0.00818145,
              -0.09975723, -0.04444652, -0.00550742, -0.08053623, -0.03053587,
              -0.01290304, -0.02881425, -0.10693316, -0.06966321, -0.07133025,
              -0.02214346,  0.03104769, -0.0006604 , -0.01347952, -0.00819464,
              -0.04528761, -0.05445053, -0.04565009,  0.00521983, -0.06078224,
              -0.1105146 , -0.04333589, -0.01849423, -0.04176805, -0.09605983,
              -0.0378094 , -0.01166691, -0.04212076, -0.03461383, -0.01973402,
              -0.01435145, -0.05209701, -0.04446907, -0.04506649, -0.12435443,
              -0.04980111,  0.00511712, -0.07232625, -0.04931347, -0.00255618,
              -0.04053256, -0.06672644, -0.11412025, -0.08658023, -0.11765138,
              -0.04218894, -0.03909829, -0.05037423, -0.04330837, -0.01172795,
              -0.05345805, -0.022226  , -0.09195374, -0.13466521, -0.01376304,
              -0.01888408, -0.05162816, -0.01471167, -0.03083992, -0.07771789,
              -0.01982523, -0.06083102, -0.02969862, -0.00367666, -0.0170963 ,
              -0.03334146, -0.01059159, -0.05023086,  0.01287904, -0.01097678,
              -0.06042015, -0.03099932, -0.0303348 , -0.004711  , -0.01805282,
              -0.07788312, -0.00022206, -0.11160741,  0.01259595, -0.11404607,
              -0.01515564, -0.08800333, -0.07892355, -0.06290811, -0.09119765,
              -0.02167654,  0.00260505, -0.03017819,  0.00747   , -0.08517093,
               0.00155484, -0.01940995, -0.03944381,  0.00420039, -0.06069636,
              -0.0101743 , -0.10072712, -0.07974705, -0.05701313, -0.05425728]])

    • b_z_trnprv
      (chain, draw)
      float64
      0.3379 0.3925 ... 0.3537 0.362

      array([[0.33790069, 0.39249947, 0.34740413, 0.2863036 , 0.25992868,
              0.26504476, 0.37571269, 0.38082747, 0.31367328, 0.28850043,
              0.33887616, 0.35693217, 0.28282619, 0.35184067, 0.30842205,
              0.34721854, 0.32323301, 0.35785302, 0.31781243, 0.31971215,
              0.34296884, 0.27299773, 0.29728741, 0.35545181, 0.32590306,
              0.35419874, 0.33414375, 0.28811296, 0.33524052, 0.25317102,
              0.30256384, 0.33060587, 0.31702256, 0.33454809, 0.32458919,
              0.28043475, 0.39614986, 0.36795692, 0.3596813 , 0.37640289,
              0.34371128, 0.31385645, 0.3451538 , 0.28215285, 0.32911967,
              0.2577037 , 0.2948316 , 0.36895591, 0.32832424, 0.38144076,
              0.25401879, 0.30257564, 0.28305635, 0.25345259, 0.36506952,
              0.34232382, 0.3097377 , 0.34545691, 0.29299704, 0.35872749,
              0.33181895, 0.31139864, 0.29759138, 0.33967016, 0.27040172,
              0.27574815, 0.28689788, 0.30818506, 0.36162778, 0.25878715,
              0.30901269, 0.27975445, 0.30083127, 0.32573816, 0.30551949,
              0.35256807, 0.31187917, 0.32975752, 0.34514069, 0.2994743 ,
              0.33032726, 0.29559892, 0.35298218, 0.33516433, 0.34603643,
              0.36549278, 0.25552706, 0.2873392 , 0.32481038, 0.27394027,
              0.26987403, 0.34510444, 0.3061773 , 0.3253406 , 0.27436595,
              0.27029211, 0.34137578, 0.33965213, 0.35427248, 0.31692431,
              0.30126879, 0.35252243, 0.32141459, 0.28967186, 0.36215944,
              0.35666542, 0.3847418 , 0.32421482, 0.38134975, 0.29732319,
              0.30386957, 0.31626732, 0.28708469, 0.33222634, 0.33867798,
              0.33479117, 0.34121022, 0.32816609, 0.32899477, 0.35426815,
              0.247691  , 0.33293422, 0.34026962, 0.37576646, 0.30844882,
              0.35854391, 0.32572774, 0.34800998, 0.24300954, 0.38788753,
              0.315167  , 0.36978964, 0.3690562 , 0.31540031, 0.28070379,
              0.30808595, 0.34117409, 0.32714233, 0.31626696, 0.33051296,
              0.34183336, 0.27863148, 0.28708585, 0.25175495, 0.23548561,
              0.31966053, 0.32233501, 0.34519208, 0.33032394, 0.34538619,
              0.3245483 , 0.30919201, 0.31112477, 0.26531486, 0.35060525,
              0.3229617 , 0.3235779 , 0.36182978, 0.36851737, 0.27283963,
              0.30628755, 0.30618451, 0.35476553, 0.38603793, 0.32935991,
              0.32845536, 0.35971326, 0.31714148, 0.32120276, 0.31801533,
              0.2605801 , 0.33000362, 0.33741134, 0.3798856 , 0.33406975,
              0.29087562, 0.35395211, 0.27203572, 0.33280543, 0.28434978,
              0.32345017, 0.24905026, 0.28260638, 0.3349196 , 0.24497633,
              0.25906243, 0.34779931, 0.35365821, 0.33554885, 0.34402324,
              0.30177446, 0.35691157, 0.3199965 , 0.31600201, 0.35066214,
              0.31643443, 0.29994683, 0.27720453, 0.35372735, 0.36199571]])

    • eth::raw
      (chain, draw, eth::raw_dim_0)
      float64
      0.7248 2.805 ... -0.7377 -2.447

      array([[[ 0.72483365,  2.80502317, -0.99211121, -2.49439636],
              [ 0.88683817,  2.78966689, -0.92644418, -2.42097068],
              [ 0.69520845,  2.81095399, -0.95203104, -2.61550443],
              [ 0.58861759,  1.14399628, -0.84941612, -1.31528339],
              [ 0.68748776,  0.91750026, -1.0826668 , -1.36420188],
              [ 0.57921418,  1.16447018, -0.93057325, -1.31529206],
              [ 0.74529863,  2.99901931, -0.83095941, -2.5828004 ],
              [ 0.87648944,  2.88065668, -0.96926652, -2.31039605],
              [ 0.70573776,  1.06942475, -0.98642827, -1.42980711],
              [ 0.64440842,  0.95618847, -0.99153108, -1.36065023],
              [ 0.63039251,  3.02282639, -0.73512675, -2.42569019],
              [ 0.6559407 ,  2.76712002, -0.90329916, -2.40968232],
              [ 0.60072485,  1.21394461, -0.96815382, -1.33112404],
              [ 0.78877204,  2.94337561, -0.83310817, -2.50909393],
              [ 0.65573991,  1.18952917, -0.94789414, -1.14412803],
              [ 0.87333541,  2.70238136, -0.90716034, -2.4394575 ],
              [ 0.81377451,  2.5707822 , -0.82871521, -2.43109192],
              [ 0.75442668,  2.99190976, -0.88721464, -2.39948551],
              [ 0.87436077,  2.85908767, -0.79851685, -2.41769638],
              [ 0.75403566,  2.69030871, -0.9002777 , -2.50921384],
      ...
              [ 0.93817091,  2.69758938, -1.026331  , -2.35061194],
              [ 0.61953819,  1.25391476, -0.98033322, -1.32096266],
              [ 0.65053572,  1.05143943, -0.92901256, -1.19753967],
              [ 0.73932154,  2.87481517, -0.86275206, -2.40365712],
              [ 0.75671757,  0.94085074, -0.84402222, -1.32271811],
              [ 0.65403286,  0.99020161, -0.97621072, -1.34639613],
              [ 0.86096351,  2.78706704, -0.77629769, -2.49372222],
              [ 0.76594116,  2.87651386, -0.80229936, -2.36740512],
              [ 0.78520859,  2.73653107, -0.79058362, -2.48119395],
              [ 0.73432791,  2.84123168, -0.70661887, -2.50782366],
              [ 0.59888753,  2.8832999 , -0.66136754, -2.63567541],
              [ 0.66237262,  2.86972964, -0.84200589, -2.31509542],
              [ 0.53368878,  2.9065482 , -0.7825328 , -2.30778587],
              [ 0.80502505,  2.69571689, -1.07934891, -2.41754247],
              [ 0.81429956,  2.67669607, -0.78187919, -2.47734385],
              [ 0.85028599,  2.95633448, -0.79977171, -2.48429558],
              [ 0.59964593,  1.11787853, -0.90511825, -1.31271362],
              [ 0.67456189,  1.09890708, -0.98997255, -1.39478021],
              [ 0.77672316,  2.52842004, -0.67827878, -2.6054488 ],
              [ 0.82202933,  2.81320826, -0.73772543, -2.4465425 ]]])

    • eth::raw_slope
      (chain, draw, eth::raw_slope_dim_0)
      float64
      0.9191 -0.5902 ... 2.785 -1.945

      array([[[ 0.91911629, -0.59022633,  2.83885952, -1.99009123],
              [ 1.14503128, -0.96054566,  2.79806549, -1.91635645],
              [ 1.13294421, -0.65423081,  2.64233575, -2.05619791],
              [ 0.802714  , -1.44938616,  2.51319013, -1.59665928],
              [ 0.80252852, -1.12321901,  2.29565991, -1.88549007],
              [ 0.61471793, -1.34171776,  2.32179521, -1.64096405],
              [ 1.16237206, -0.70701028,  2.72878171, -2.00375422],
              [ 0.94356499, -0.56799346,  2.65694716, -1.80704089],
              [ 0.84646729, -1.28475486,  2.45115354, -1.61820048],
              [ 0.72143024, -1.16661894,  2.1918059 , -1.70090915],
              [ 1.08115528, -0.67472935,  2.96145948, -1.97969081],
              [ 0.90275222, -0.59235216,  2.76694959, -1.78817009],
              [ 0.33000765, -1.07954967,  2.45046204, -1.65768005],
              [ 0.84980863, -0.76136866,  2.6355892 , -2.0438312 ],
              [ 0.86452375, -1.1944162 ,  2.39894613, -1.60821912],
              [ 0.91220692, -0.75860515,  2.89656396, -2.05907476],
              [ 0.71591618, -0.78705257,  2.90841543, -1.87755856],
              [ 1.05417925, -0.78518703,  2.8352913 , -1.9247722 ],
              [ 0.99099968, -0.69321855,  2.69019796, -1.83349004],
              [ 0.99342331, -0.76795664,  3.03792844, -1.92829792],
      ...
              [ 1.12335358, -0.85054796,  2.79028336, -2.03450281],
              [ 0.56981979, -1.1443041 ,  2.3484763 , -1.52819873],
              [ 0.79404936, -1.0864948 ,  2.27899736, -1.62710795],
              [ 0.87731982, -1.03610903,  3.05637906, -1.96888532],
              [ 0.74134967, -1.19418397,  2.59684913, -1.63982077],
              [ 0.65989484, -0.99539677,  2.46899717, -1.60308701],
              [ 1.04555216, -0.90043756,  2.79349935, -1.91179068],
              [ 0.93553821, -0.95771074,  2.72755003, -1.79865951],
              [ 0.94932122, -0.52233155,  2.75082713, -1.89742027],
              [ 0.9916671 , -0.85196692,  2.7482332 , -1.74131063],
              [ 0.9223337 , -0.73022598,  2.72981436, -1.80950173],
              [ 0.92454335, -0.79213763,  2.87938011, -2.00713067],
              [ 0.91294927, -0.57545903,  2.76975201, -1.96506986],
              [ 1.0362263 , -0.64548978,  2.68875086, -1.96755672],
              [ 1.29672969, -0.83384666,  2.76239313, -1.99660812],
              [ 1.036476  , -0.86896001,  2.62081257, -1.77738876],
              [ 0.63231873, -1.11437718,  2.50462187, -1.59242895],
              [ 0.66084999, -1.22885632,  2.4657357 , -1.72891134],
              [ 1.01084007, -0.5275863 ,  2.66590771, -1.76098642],
              [ 0.86603785, -0.91085717,  2.78452935, -1.94493131]]])

    • eth::re
      (chain, draw, eth::re_dim_0)
      float64
      0.1169 0.4523 ... -0.116 -0.3846

      array([[[ 0.11686696,  0.45226176, -0.15996088, -0.40217853],
              [ 0.14141032,  0.44482489, -0.14772568, -0.38603462],
              [ 0.12139707,  0.49084784, -0.16624334, -0.45671851],
              [ 0.19423679,  0.37750513, -0.28029719, -0.43402783],
              [ 0.20269287,  0.27050774, -0.319204  , -0.40220934],
              [ 0.18724974,  0.37645269, -0.30083793, -0.42521074],
              [ 0.11408731,  0.45907777, -0.12719991, -0.39536466],
              [ 0.13988984,  0.45975978, -0.15469728, -0.3687448 ],
              [ 0.21422772,  0.32462544, -0.29943173, -0.43402003],
              [ 0.20252208,  0.30050706, -0.31161439, -0.42761967],
              [ 0.09605015,  0.46057485, -0.11200805, -0.36959181],
              [ 0.10129526,  0.42731934, -0.1394942 , -0.37212114],
              [ 0.19704885,  0.39819626, -0.31757234, -0.43663328],
              [ 0.13296707,  0.49617887, -0.14044102, -0.42296994],
              [ 0.24074653,  0.43672044, -0.34800723, -0.420052  ],
              [ 0.14302556,  0.4425672 , -0.14856505, -0.39950833],
              [ 0.12926322,  0.40835339, -0.13163646, -0.38616442],
              [ 0.11363513,  0.45065488, -0.13363625, -0.36142128],
              [ 0.14767613,  0.48288877, -0.13486639, -0.4083395 ],
              [ 0.11596729,  0.41375735, -0.13845865, -0.38590578],
      ...
              [ 0.13283622,  0.38195342, -0.14531887, -0.33282466],
              [ 0.20093071,  0.40667386, -0.31794497, -0.42841906],
              [ 0.20651486,  0.33378316, -0.29491831, -0.38016319],
              [ 0.11553133,  0.44923783, -0.1348194 , -0.37561153],
              [ 0.24311558,  0.30227324, -0.27116451, -0.42495825],
              [ 0.21961   ,  0.33248816, -0.32779032, -0.45209052],
              [ 0.13689357,  0.44314486, -0.12343167, -0.39650291],
              [ 0.12413744,  0.4662017 , -0.13003008, -0.38368954],
              [ 0.12434354,  0.43334978, -0.12519472, -0.39291527],
              [ 0.11428887,  0.44220187, -0.10997631, -0.39031111],
              [ 0.10034684,  0.48311248, -0.11081571, -0.44162166],
              [ 0.10138714,  0.43925981, -0.12888299, -0.35436382],
              [ 0.08493669,  0.4625778 , -0.12454027, -0.36728464],
              [ 0.12010399,  0.40218172, -0.16103115, -0.36068008],
              [ 0.13242117,  0.43528359, -0.12714898, -0.40286498],
              [ 0.13579588,  0.47214471, -0.12772844, -0.39675721],
              [ 0.20439224,  0.38103436, -0.30851398, -0.44744485],
              [ 0.22063874,  0.35943547, -0.32380467, -0.45621098],
              [ 0.12925803,  0.42076587, -0.11287546, -0.43358458],
              [ 0.12921691,  0.44221545, -0.11596496, -0.38457832]]])

    • eth::re_slope
      (chain, draw, eth::re_slope_dim_0)
      float64
      0.1336 -0.08579 ... 0.4654 -0.3251

      array([[[ 0.13358985, -0.08578702,  0.41261679, -0.28925174],
              [ 0.16819333, -0.14109429,  0.41100708, -0.28149308],
              [ 0.15071858, -0.08703406,  0.35151694, -0.27354147],
              [ 0.15257495, -0.27549042,  0.47769175, -0.30348319],
              [ 0.15231495, -0.21318002,  0.43570206, -0.35785436],
              [ 0.12205717, -0.26640882,  0.46101106, -0.32582658],
              [ 0.17641239, -0.10730245,  0.41414528, -0.30410837],
              [ 0.1678259 , -0.10102538,  0.47257427, -0.32140686],
              [ 0.13047208, -0.19802848,  0.37781388, -0.24942485],
              [ 0.13264929, -0.21450608,  0.40300708, -0.31274595],
              [ 0.19689004, -0.12287549,  0.53931371, -0.36052305],
              [ 0.15571185, -0.10217228,  0.47725925, -0.30843378],
              [ 0.0536507 , -0.17550681,  0.39838166, -0.26949584],
              [ 0.14304641, -0.12815951,  0.44364291, -0.3440336 ],
              [ 0.15163874, -0.20950236,  0.42077869, -0.282084  ],
              [ 0.14298426, -0.11890789,  0.45402315, -0.32275055],
              [ 0.10342594, -0.11370277,  0.42016874, -0.27124441],
              [ 0.15527864, -0.11565658,  0.41763312, -0.28351535],
              [ 0.13372984, -0.09354595,  0.3630271 , -0.24741918],
              [ 0.15887273, -0.12281508,  0.4858392 , -0.30838209],
      ...
              [ 0.1621893 , -0.12280174,  0.40285989, -0.29374063],
              [ 0.08908718, -0.17890362,  0.36716718, -0.23892275],
              [ 0.12455682, -0.17043064,  0.35748996, -0.25523275],
              [ 0.13413061, -0.15840739,  0.46727999, -0.30101656],
              [ 0.14208006, -0.22886599,  0.49768752, -0.31427252],
              [ 0.12975475, -0.19572431,  0.48547754, -0.3152141 ],
              [ 0.16160411, -0.13917471,  0.4317728 , -0.2954929 ],
              [ 0.13751992, -0.14077918,  0.4009376 , -0.26439487],
              [ 0.13950071, -0.0767555 ,  0.40422813, -0.27882183],
              [ 0.15456835, -0.13279368,  0.42835934, -0.27141317],
              [ 0.15704035, -0.1243313 ,  0.46478949, -0.30809325],
              [ 0.14562177, -0.12476699,  0.45352167, -0.31613653],
              [ 0.17966598, -0.1132488 ,  0.5450798 , -0.3867205 ],
              [ 0.16556014, -0.10313131,  0.42958759, -0.31436083],
              [ 0.18214928, -0.11712893,  0.38802837, -0.28045994],
              [ 0.17084125, -0.14322976,  0.43198577, -0.29296511],
              [ 0.09257554, -0.16315201,  0.3666928 , -0.23314187],
              [ 0.09066605, -0.16859431,  0.33828935, -0.23719992],
              [ 0.18696914, -0.09758453,  0.49309727, -0.3257193 ],
              [ 0.14476249, -0.15225427,  0.4654478 , -0.32510485]]])

    • eth::sigma
      (chain, draw)
      float64
      0.1612 0.1595 ... 0.1664 0.1572

      array([[0.16123281, 0.15945448, 0.17461967, 0.32998808, 0.29483124,
              0.32328238, 0.15307596, 0.15960242, 0.30355145, 0.31427597,
              0.15236563, 0.15442747, 0.32801848, 0.16857477, 0.36713723,
              0.16376933, 0.15884402, 0.15062449, 0.16889611, 0.15379549,
              0.16665578, 0.33970013, 0.32478709, 0.15829829, 0.17717706,
              0.14942372, 0.16179923, 0.32256654, 0.166984  , 0.3074722 ,
              0.17350895, 0.15687854, 0.33657705, 0.15511033, 0.15690212,
              0.3229872 , 0.16798839, 0.16222412, 0.15480809, 0.16204996,
              0.15688682, 0.30688192, 0.15633362, 0.33146067, 0.1590213 ,
              0.31049279, 0.33219811, 0.16893639, 0.15696707, 0.16420979,
              0.31803495, 0.15830598, 0.16562911, 0.29685138, 0.15060909,
              0.16944443, 0.2995654 , 0.15649907, 0.32801146, 0.16341848,
              0.1536939 , 0.3277928 , 0.3376816 , 0.15525422, 0.30581051,
              0.28992764, 0.32885571, 0.15674466, 0.15596395, 0.29929815,
              0.1537264 , 0.33349052, 0.1720199 , 0.15890737, 0.16130976,
              0.15741747, 0.33704828, 0.15704254, 0.16985428, 0.15963194,
              0.16189543, 0.16970023, 0.15192061, 0.15377197, 0.16313176,
              0.1537901 , 0.30476827, 0.33055592, 0.17033312, 0.32605889,
              0.32214186, 0.14954439, 0.15756272, 0.16424151, 0.34799435,
              0.30498308, 0.16018939, 0.15545912, 0.15449971, 0.14705834,
              0.29639383, 0.15995831, 0.17036022, 0.30578297, 0.16105494,
              0.15814503, 0.15345993, 0.34171321, 0.15292459, 0.323185  ,
              0.1600565 , 0.16984072, 0.15334224, 0.17217781, 0.17344867,
              0.14998369, 0.16345401, 0.15889232, 0.15615819, 0.16059451,
              0.29879262, 0.14850845, 0.16502425, 0.16095603, 0.32326978,
              0.1499444 , 0.15789336, 0.15389026, 0.32078969, 0.1637198 ,
              0.15816901, 0.16553308, 0.14905016, 0.16906467, 0.32161382,
              0.16711672, 0.17269874, 0.30789524, 0.1578043 , 0.15993157,
              0.15741638, 0.35185162, 0.32376889, 0.306095  , 0.31752982,
              0.15997573, 0.16062013, 0.14857769, 0.15495093, 0.14727482,
              0.15849784, 0.1614661 , 0.3043599 , 0.31668087, 0.15666548,
              0.17363945, 0.1623074 , 0.16417639, 0.17100048, 0.2836507 ,
              0.16391016, 0.16156258, 0.15627972, 0.15031797, 0.15626455,
              0.1689839 , 0.15443203, 0.16032705, 0.17741288, 0.15399658,
              0.31873078, 0.16313241, 0.15530559, 0.15294415, 0.16836762,
              0.30187757, 0.17397107, 0.3235932 , 0.16250401, 0.31016314,
              0.14159064, 0.32432337, 0.31745353, 0.15626668, 0.32127651,
              0.33577824, 0.15900043, 0.16207177, 0.15835734, 0.15563738,
              0.1675554 , 0.15306662, 0.15915023, 0.14919286, 0.16261973,
              0.15970612, 0.34085489, 0.3270845 , 0.16641455, 0.15719258]])

    • eth::sigma_slope
      (chain, draw)
      float64
      0.1453 0.1469 ... 0.185 0.1672

      array([[0.14534597, 0.14688973, 0.13303266, 0.19007386, 0.18979382,
              0.19855802, 0.1517693 , 0.17786363, 0.15413717, 0.18386987,
              0.18211078, 0.17248571, 0.1625741 , 0.16832779, 0.17540147,
              0.15674543, 0.14446655, 0.14729813, 0.13494438, 0.1599245 ,
              0.14776513, 0.19573235, 0.17606072, 0.12447009, 0.16443026,
              0.18144573, 0.18480588, 0.18125727, 0.14317762, 0.17024227,
              0.12088829, 0.15993301, 0.17000364, 0.16884601, 0.16998303,
              0.17234334, 0.15248259, 0.14139982, 0.15987613, 0.12740531,
              0.18422211, 0.17007984, 0.18664243, 0.18205845, 0.17367222,
              0.15237028, 0.18477035, 0.15895701, 0.15540984, 0.1600255 ,
              0.20914885, 0.16930193, 0.14088314, 0.19196669, 0.17539034,
              0.14055354, 0.15322213, 0.12950133, 0.18297722, 0.13037772,
              0.15826892, 0.18686311, 0.17752953, 0.13180062, 0.15669153,
              0.17267466, 0.16425012, 0.13580016, 0.18771008, 0.22284211,
              0.19478283, 0.22335673, 0.19047898, 0.18672483, 0.16176591,
              0.14867385, 0.14607743, 0.16190043, 0.11945244, 0.15222918,
              0.16176372, 0.15556104, 0.15955401, 0.15330361, 0.14665305,
              0.16849178, 0.17254348, 0.20769219, 0.14122554, 0.17090924,
              0.20515388, 0.14800597, 0.19178341, 0.14631529, 0.18895351,
              0.20061676, 0.17197846, 0.15672533, 0.12910574, 0.17217529,
              0.18077138, 0.20069862, 0.18239199, 0.18432682, 0.16581709,
              0.16367726, 0.14910558, 0.15094722, 0.13972285, 0.21605996,
              0.14951551, 0.16264082, 0.16634578, 0.18295246, 0.16072304,
              0.15719618, 0.1608842 , 0.14292159, 0.15795091, 0.14141727,
              0.13806724, 0.14623834, 0.19572119, 0.14966528, 0.14857477,
              0.14550934, 0.16008479, 0.15387463, 0.17548274, 0.16737159,
              0.12762019, 0.15568174, 0.16374631, 0.17872883, 0.19267182,
              0.17843003, 0.18571111, 0.21538297, 0.15079783, 0.17709289,
              0.1683122 , 0.14106973, 0.21792481, 0.19674262, 0.16192431,
              0.15708388, 0.15605102, 0.15519007, 0.18933619, 0.16740629,
              0.16494412, 0.15737122, 0.16857907, 0.18731053, 0.17467024,
              0.15959427, 0.20289401, 0.15698966, 0.17793779, 0.19975546,
              0.15830336, 0.14314078, 0.16624405, 0.15624767, 0.15209037,
              0.15627701, 0.14351986, 0.15585014, 0.15887543, 0.17178672,
              0.19559642, 0.15926983, 0.17383464, 0.15888034, 0.14696297,
              0.18161602, 0.17193   , 0.15766225, 0.16296765, 0.16552236,
              0.14437956, 0.15634272, 0.15686282, 0.15288679, 0.19165053,
              0.19662944, 0.15456342, 0.14699551, 0.14694785, 0.15586717,
              0.17026414, 0.1575067 , 0.19679733, 0.15977218, 0.14046819,
              0.16482894, 0.14640645, 0.13719611, 0.18496412, 0.16715493]])

    • eth_age::raw
      (chain, draw, eth_age::raw_dim_0)
      float64
      -0.9826 0.3169 ... -0.2987 -0.8251

      array([[[-0.98255068,  0.31690358,  0.83796889, ..., -0.35026943,
               -0.25273914, -0.91881068],
              [-0.96384363,  0.36426928,  0.79266569, ..., -0.38901953,
               -0.31053314, -0.7375492 ],
              [-0.88632493,  0.54220242,  0.84307812, ..., -0.30724001,
               -0.10388991, -0.79207605],
              ...,
              [-0.81121643, -0.72727063, -0.01062811, ..., -0.36059573,
               -0.11198346, -0.99950846],
              [-0.93600106,  0.55135234,  0.81884801, ..., -0.35401152,
               -0.16332173, -0.9280872 ],
              [-1.06771948,  0.68180709,  0.73707954, ..., -0.35140446,
               -0.29867313, -0.82511299]]], shape=(1, 200, 16))

    • eth_age::re
      (chain, draw, eth_age::re_dim_0)
      float64
      -0.1255 0.04049 ... -0.09199

      array([[[-0.12554953,  0.04049368,  0.10707499, ..., -0.04475715,
               -0.0322948 , -0.11740489],
              [-0.11157439,  0.04216776,  0.09175886, ..., -0.04503284,
               -0.03594727, -0.08537858],
              [-0.10785641,  0.06598033,  0.10259373, ..., -0.03738787,
               -0.01264231, -0.09638732],
              ...,
              [-0.0975303 , -0.08743773, -0.00127779, ..., -0.04335342,
               -0.01346346, -0.12016813],
              [-0.10719012,  0.06314045,  0.09377385, ..., -0.04054113,
               -0.01870348, -0.10628383],
              [-0.11903999,  0.07601464,  0.08217696, ..., -0.03917806,
               -0.03329905, -0.0919918 ]]], shape=(1, 200, 16))

    • eth_age::sigma
      (chain, draw)
      float64
      0.1278 0.1158 ... 0.1145 0.1115

      array([[0.12777919, 0.11575985, 0.12168947, 0.10754056, 0.10133078,
              0.12377244, 0.11070179, 0.12153222, 0.10760528, 0.11623198,
              0.11000128, 0.12528442, 0.11330399, 0.1240725 , 0.11749534,
              0.09984206, 0.11252773, 0.1232576 , 0.12085866, 0.12749506,
              0.11066216, 0.13030454, 0.1295455 , 0.10770559, 0.13200343,
              0.1497475 , 0.10881813, 0.10758722, 0.10143986, 0.12386561,
              0.10486608, 0.12023688, 0.11964355, 0.11881189, 0.12557406,
              0.12301727, 0.14108712, 0.12671294, 0.1237242 , 0.11153279,
              0.11781955, 0.12810337, 0.12652737, 0.14717893, 0.11049351,
              0.11601998, 0.12709132, 0.11058949, 0.14158878, 0.12555132,
              0.1231467 , 0.10928656, 0.14865134, 0.11027329, 0.1273098 ,
              0.12853516, 0.11781505, 0.12426138, 0.10651821, 0.13185856,
              0.11469593, 0.1190756 , 0.12972362, 0.11927421, 0.10951694,
              0.12702985, 0.10469949, 0.14478967, 0.11657283, 0.10656351,
              0.10999425, 0.12039024, 0.12983993, 0.12577304, 0.1221648 ,
              0.12536846, 0.11430276, 0.12253605, 0.1223182 , 0.12802312,
              0.11208688, 0.114143  , 0.11671034, 0.1150549 , 0.14157937,
              0.10585312, 0.09466397, 0.10649678, 0.12511344, 0.13341729,
              0.12472907, 0.12691236, 0.129664  , 0.11529394, 0.10714353,
              0.12119541, 0.1157863 , 0.12510325, 0.12835785, 0.13819012,
              0.12341309, 0.11819069, 0.13019568, 0.10718555, 0.11945083,
              0.1296828 , 0.12684271, 0.12178364, 0.12862145, 0.12302605,
              0.10947929, 0.11530497, 0.10750897, 0.12100244, 0.0995087 ,
              0.12149967, 0.12014659, 0.12023331, 0.12197894, 0.12553815,
              0.12828378, 0.14001008, 0.11873079, 0.10871373, 0.12502075,
              0.12601093, 0.13416846, 0.14720389, 0.11035841, 0.10352462,
              0.13279496, 0.11243375, 0.12999756, 0.1313648 , 0.10292046,
              0.16583748, 0.10184634, 0.10565603, 0.11748012, 0.10523359,
              0.13915124, 0.11355718, 0.11667103, 0.11768821, 0.13755398,
              0.11874012, 0.11549092, 0.16917282, 0.1526263 , 0.13018782,
              0.13051071, 0.1274412 , 0.11394362, 0.11016862, 0.11490144,
              0.11895266, 0.11474442, 0.12830929, 0.11529117, 0.11273974,
              0.11681038, 0.11068268, 0.13394061, 0.11120398, 0.13681039,
              0.13299969, 0.12934356, 0.1315771 , 0.12861347, 0.11168289,
              0.13802093, 0.10553087, 0.12566145, 0.1364385 , 0.11528716,
              0.11756576, 0.09226645, 0.13624948, 0.12373424, 0.12493492,
              0.12295046, 0.11406878, 0.12491144, 0.14332498, 0.11479346,
              0.10854945, 0.11842336, 0.11804252, 0.13257842, 0.11394364,
              0.11986715, 0.11728225, 0.11249342, 0.13876817, 0.11662077,
              0.14020273, 0.11265718, 0.12022722, 0.11451923, 0.11148995]])

    • eth_inc::raw
      (chain, draw, eth_inc::raw_dim_0)
      float64
      -0.8781 -0.09956 ... -0.2629

      array([[[-0.87812581, -0.09956393,  1.02011659, ..., -0.45749041,
                0.24347643, -0.15729544],
              [-0.53865125, -0.16936506,  0.94531824, ..., -0.28682818,
                0.06098147, -0.22180188],
              [-0.86131835, -0.10531612,  0.79135177, ..., -0.33837629,
                0.30851018, -0.2441858 ],
              ...,
              [-0.86574514, -1.35358141,  0.51323318, ..., -0.08941142,
                0.57676144, -0.89667003],
              [-0.55151376, -0.29943438,  0.86279157, ..., -0.43573501,
                0.07500069, -0.19759462],
              [-0.5832075 , -0.13060473,  1.0432996 , ..., -0.39902442,
                0.01288381, -0.26293527]]], shape=(1, 200, 20))

    • eth_inc::re
      (chain, draw, eth_inc::re_dim_0)
      float64
      -0.06263 -0.007101 ... -0.01858

      array([[[-0.06262982, -0.00710111,  0.07275691, ..., -0.0326292 ,
                0.01736526, -0.01121865],
              [-0.04499104, -0.01414628,  0.07895805, ..., -0.02395743,
                0.0050935 , -0.01852608],
              [-0.05747195, -0.00702728,  0.05280339, ..., -0.02257835,
                0.02058551, -0.01629343],
              ...,
              [-0.02338898, -0.03656837,  0.01386551, ..., -0.00241554,
                0.01558179, -0.02422445],
              [-0.03917547, -0.02126961,  0.06128635, ..., -0.0309514 ,
                0.0053275 , -0.01403566],
              [-0.04120533, -0.00922761,  0.07371219, ..., -0.02819225,
                0.00091028, -0.01857715]]], shape=(1, 200, 20))

    • eth_inc::sigma
      (chain, draw)
      float64
      0.07132 0.08353 ... 0.07103 0.07065

      array([[0.07132215, 0.08352536, 0.06672556, 0.02115253, 0.02111952,
              0.02348953, 0.06235542, 0.07999717, 0.02126815, 0.02319741,
              0.07029773, 0.09027566, 0.02242506, 0.06717046, 0.02009719,
              0.0654602 , 0.07768641, 0.07414331, 0.07167909, 0.08390197,
              0.06767802, 0.02385933, 0.02473879, 0.06652377, 0.08183736,
              0.06819581, 0.06127243, 0.02291855, 0.07895327, 0.02240073,
              0.06739207, 0.07198861, 0.02105163, 0.07505935, 0.06630889,
              0.02112686, 0.07456832, 0.07927598, 0.06480195, 0.07413366,
              0.07243796, 0.02500105, 0.07214384, 0.02684667, 0.06572651,
              0.02836836, 0.02236816, 0.07750703, 0.0640517 , 0.04524853,
              0.02530847, 0.06519509, 0.06948126, 0.02247212, 0.06826185,
              0.06339945, 0.02515748, 0.06668069, 0.02384526, 0.07680515,
              0.0775203 , 0.02103965, 0.02214553, 0.0691906 , 0.01857206,
              0.02248781, 0.02576437, 0.08925347, 0.0692041 , 0.01969778,
              0.0531888 , 0.02074406, 0.08105072, 0.07357867, 0.06900605,
              0.06819543, 0.01951647, 0.07189433, 0.06564563, 0.07022918,
              0.06817288, 0.07081503, 0.06670586, 0.06851503, 0.05521554,
              0.08164191, 0.0209474 , 0.03017593, 0.08202945, 0.03381779,
              0.02328505, 0.06963935, 0.06908726, 0.06374038, 0.02795274,
              0.02407164, 0.06553682, 0.07478041, 0.08173834, 0.0727764 ,
              0.01955994, 0.0583554 , 0.0603819 , 0.02278976, 0.07580335,
              0.08834921, 0.07164868, 0.02662418, 0.06739381, 0.02518583,
              0.0638793 , 0.0588516 , 0.05874728, 0.0645377 , 0.07065112,
              0.09186435, 0.08002123, 0.08990957, 0.08284284, 0.06442   ,
              0.02801835, 0.06349193, 0.06235737, 0.05835808, 0.02670013,
              0.07418114, 0.09125479, 0.06588183, 0.02562203, 0.07767654,
              0.07582824, 0.07649767, 0.06893121, 0.06516008, 0.01909742,
              0.07110876, 0.07609497, 0.02052944, 0.08779142, 0.07175908,
              0.0808063 , 0.02512182, 0.0190098 , 0.02206436, 0.02467933,
              0.07555114, 0.08358826, 0.08277425, 0.06818438, 0.08637619,
              0.07522803, 0.05815354, 0.0273189 , 0.02414929, 0.08559394,
              0.06082944, 0.09098417, 0.07084437, 0.06274756, 0.01844737,
              0.05411026, 0.08787207, 0.0687994 , 0.07182681, 0.07383321,
              0.10278567, 0.06085116, 0.07989737, 0.06206953, 0.07460212,
              0.02529738, 0.07010526, 0.06302447, 0.06891014, 0.06442542,
              0.02485413, 0.08097279, 0.02708063, 0.07283906, 0.02329317,
              0.07609844, 0.02395219, 0.02276989, 0.08094165, 0.02464959,
              0.02147791, 0.06921519, 0.0667054 , 0.06851155, 0.06107342,
              0.0739719 , 0.08222819, 0.07808471, 0.06702038, 0.06303422,
              0.07385667, 0.02266453, 0.02701601, 0.07103262, 0.07065295]])

    • inc::raw
      (chain, draw, inc::raw_dim_0)
      float64
      -0.03539 0.06979 ... 0.7856 0.04342

      array([[[-3.53858414e-02,  6.97906385e-02,  7.65342735e-01,
                8.76537694e-01,  1.78414568e-01],
              [-1.02681728e-02,  2.46928751e-02,  7.75147670e-01,
                7.91625107e-01,  5.85263271e-02],
              [-1.90321902e-01,  1.23176029e-01,  6.07156021e-01,
                1.07312285e+00,  2.70319099e-01],
              [ 2.76932636e-01, -6.96440317e-01, -2.20485483e-01,
                1.53975568e+00, -9.96217695e-01],
              [ 4.06397963e-01, -8.56972339e-01, -2.03991061e-01,
                1.50830356e+00, -8.94985447e-01],
              [ 3.32869595e-01, -9.45882909e-01, -1.39307469e-01,
                1.32579555e+00, -9.67430586e-01],
              [-2.73274992e-02, -1.27256101e-01,  6.73003917e-01,
                9.46972626e-01,  1.40208719e-01],
              [ 4.02295719e-02, -7.05601077e-02,  9.93232018e-01,
                9.76172299e-01,  4.84381731e-02],
              [ 2.52164838e-01, -8.00135507e-01, -1.96266115e-01,
                1.33674091e+00, -8.78844415e-01],
              [ 3.26857885e-01, -6.65028492e-01, -2.15908114e-01,
                1.44551542e+00, -1.08228413e+00],
      ...
              [ 7.86226004e-03, -1.47248454e-01,  8.17695118e-01,
                9.19867074e-01,  1.14853448e-01],
              [-7.19432003e-02, -5.74635499e-02,  5.84364656e-01,
                9.85206624e-01,  1.48024056e-01],
              [-1.85910551e-01, -1.52184877e-01,  8.28689779e-01,
                7.06520976e-01,  1.82986488e-01],
              [-2.16821029e-01, -1.13654654e-01,  6.62043191e-01,
                9.80797631e-01,  2.06707377e-01],
              [-1.47196142e-01, -5.06203169e-02,  8.96146606e-01,
                9.91960371e-01,  1.49012996e-01],
              [-2.78389207e-01,  3.40639683e-02,  7.46825169e-01,
                9.63080772e-01,  1.89704081e-02],
              [ 4.62630228e-01, -8.49553063e-01, -3.63039684e-01,
                1.22818439e+00, -8.36798728e-01],
              [ 2.57879927e-01, -8.47210118e-01, -2.08820837e-01,
                1.38089946e+00, -8.16247235e-01],
              [-1.07646949e-01, -5.67639227e-02,  6.57785020e-01,
                9.05067481e-01,  2.64472840e-01],
              [ 7.33427885e-02,  2.39559239e-02,  7.11214238e-01,
                7.85594906e-01,  4.34163750e-02]]])

    • inc::re
      (chain, draw, inc::re_dim_0)
      float64
      -0.001422 0.002804 ... 0.002137

      array([[[-1.42165447e-03,  2.80389470e-03,  3.07482563e-02,
                3.52156027e-02,  7.16794793e-03],
              [-3.76234231e-04,  9.04767094e-04,  2.84020432e-02,
                2.90057900e-02,  2.14445239e-03],
              [-6.85004885e-03,  4.43334059e-03,  2.18527051e-02,
                3.86237415e-02,  9.72930079e-03],
              [ 2.64769042e-04, -6.65850866e-04, -2.10801193e-04,
                1.47212565e-03, -9.52461251e-04],
              [ 4.72781159e-04, -9.96954743e-04, -2.37312042e-04,
                1.75467786e-03, -1.04117711e-03],
              [ 2.60902635e-04, -7.41381450e-04, -1.09188963e-04,
                1.03915634e-03, -7.58270483e-04],
              [-1.30023354e-03, -6.05480395e-03,  3.20213079e-02,
                4.50566501e-02,  6.67108534e-03],
              [ 1.81806889e-03, -3.18877707e-03,  4.48864889e-02,
                4.41155201e-02,  2.18903487e-03],
              [ 3.75883248e-04, -1.19270210e-03, -2.92559205e-04,
                1.99257960e-03, -1.31002758e-03],
              [ 3.57538291e-04, -7.27451169e-04, -2.36174257e-04,
                1.58119824e-03, -1.18387237e-03],
      ...
              [ 3.85553672e-04, -7.22084769e-03,  4.00985663e-02,
                4.51089288e-02,  5.63224422e-03],
              [-3.04128702e-03, -2.42918230e-03,  2.47031080e-02,
                4.16480794e-02,  6.25748698e-03],
              [-9.05570061e-03, -7.41292349e-03,  4.03654688e-02,
                3.44146280e-02,  8.91326954e-03],
              [-9.10888439e-03, -4.77475412e-03,  2.78131457e-02,
                4.12043622e-02,  8.68399900e-03],
              [-6.31993772e-03, -2.17340785e-03,  3.84764891e-02,
                4.25902995e-02,  6.39794524e-03],
              [-1.20660256e-02,  1.47641038e-03,  3.23691127e-02,
                4.17421256e-02,  8.22220922e-04],
              [ 6.12251306e-04, -1.12431039e-03, -4.80451788e-04,
                1.62539638e-03, -1.10743113e-03],
              [ 3.13052583e-04, -1.02846824e-03, -2.53497444e-04,
                1.67633886e-03, -9.90880941e-04],
              [-3.81780180e-03, -2.01318671e-03,  2.33289737e-02,
                3.20990822e-02,  9.37978173e-03],
              [ 3.61073335e-03,  1.17937230e-03,  3.50137351e-02,
                3.86755642e-02,  2.13742832e-03]]])

    • inc::sigma
      (chain, draw)
      float64
      0.04018 0.03664 ... 0.03547 0.04923

      array([[0.0401758 , 0.03664082, 0.03599191, 0.00095608, 0.00116335,
              0.0007838 , 0.04757968, 0.04519235, 0.00149063, 0.00109386,
              0.03750765, 0.04858911, 0.00111335, 0.04635107, 0.00100805,
              0.04191653, 0.04298834, 0.0394314 , 0.03798589, 0.04518853,
              0.04432877, 0.00115365, 0.00109179, 0.04152718, 0.04464613,
              0.04999708, 0.03961148, 0.00135593, 0.03454509, 0.00104652,
              0.04952253, 0.04494513, 0.00097411, 0.03554836, 0.05153522,
              0.00103283, 0.03572986, 0.03946072, 0.03471925, 0.03747289,
              0.04740912, 0.00105269, 0.04849305, 0.00143658, 0.05317001,
              0.00098077, 0.00116556, 0.04532871, 0.04564875, 0.04176176,
              0.0010629 , 0.04398953, 0.03695975, 0.00101209, 0.04641345,
              0.0438994 , 0.00119945, 0.0446081 , 0.00104854, 0.04591716,
              0.03216379, 0.00104998, 0.00131999, 0.03636512, 0.00097443,
              0.00110333, 0.00089642, 0.03836263, 0.0332652 , 0.00089874,
              0.04988791, 0.0010433 , 0.04296404, 0.03989892, 0.03248119,
              0.04842845, 0.00112991, 0.04936556, 0.03380824, 0.04594743,
              0.04468236, 0.04024362, 0.04043256, 0.02969417, 0.04017302,
              0.04052515, 0.00096889, 0.00101693, 0.03623478, 0.00092644,
              0.00121256, 0.04251615, 0.03952385, 0.0456523 , 0.00104221,
              0.00125832, 0.05564302, 0.03721912, 0.03761583, 0.0380734 ,
              0.00121124, 0.04659964, 0.04155797, 0.00102773, 0.04240769,
              0.05003714, 0.03768858, 0.00113947, 0.04550318, 0.00105058,
              0.02772022, 0.041101  , 0.03533216, 0.04515257, 0.04376775,
              0.0425581 , 0.0447814 , 0.05318387, 0.0456176 , 0.04337181,
              0.00098605, 0.03837009, 0.04186279, 0.03972323, 0.00119997,
              0.05930244, 0.04066971, 0.04559811, 0.00134627, 0.03485322,
              0.04532232, 0.04260645, 0.03781581, 0.0434224 , 0.0009054 ,
              0.04741035, 0.03699497, 0.00102995, 0.04214195, 0.04161747,
              0.0446158 , 0.001011  , 0.0009765 , 0.00115609, 0.00124114,
              0.03700882, 0.03815659, 0.03860405, 0.04374112, 0.03689942,
              0.03617743, 0.05530868, 0.00106849, 0.00106681, 0.03839926,
              0.03481781, 0.03981914, 0.04285561, 0.04854248, 0.00118015,
              0.03013781, 0.03606607, 0.04547585, 0.04542706, 0.04175977,
              0.03482528, 0.05367079, 0.04918724, 0.04514274, 0.03502166,
              0.00105885, 0.03880299, 0.03330559, 0.04802256, 0.03367928,
              0.00118888, 0.03944955, 0.00120303, 0.03799255, 0.00106708,
              0.04440492, 0.00125083, 0.0011419 , 0.04075659, 0.00110783,
              0.00109665, 0.06033065, 0.04234182, 0.05683572, 0.03904176,
              0.04903853, 0.04227345, 0.04870999, 0.04201107, 0.04293548,
              0.04334229, 0.00132341, 0.00121395, 0.03546595, 0.04923093]])

    • inc_age::raw
      (chain, draw, inc_age::raw_dim_0)
      float64
      2.732 -2.812 ... 1.853 -0.6695

      array([[[ 2.73220655, -2.81164949, -1.00297084, ...,  3.53658656,
                1.79795618, -0.73093361],
              [ 2.82627482, -2.91974802, -0.89595869, ...,  3.68803826,
                2.09388981, -0.90904612],
              [ 2.92506808, -2.92592207, -0.6729932 , ...,  3.73569873,
                2.05701409, -0.67487639],
              ...,
              [ 0.92390023,  0.45539292, -0.32515727, ..., -0.22308808,
               -0.61469273, -0.02678431],
              [ 2.65674341, -2.80627432, -0.97207829, ...,  3.53799546,
                1.74744467, -0.81741969],
              [ 3.00437208, -2.90522701, -0.99827333, ...,  3.55039581,
                1.85295088, -0.6695045 ]]], shape=(1, 200, 20))

    • inc_age::re
      (chain, draw, inc_age::re_dim_0)
      float64
      0.2028 -0.2087 ... 0.1711 -0.06181

      array([[[ 0.2027982 , -0.20869486, -0.07444557, ...,  0.26250336,
                0.13345341, -0.05425359],
              [ 0.23356593, -0.24129064, -0.07404284, ...,  0.30478285,
                0.17304097, -0.0751244 ],
              [ 0.24913197, -0.2492047 , -0.05731973, ...,  0.31817447,
                0.17519865, -0.05748013],
              ...,
              [ 0.02208092,  0.01088375, -0.00777116, ..., -0.00533173,
               -0.01469096, -0.00064014],
              [ 0.21851027, -0.2308088 , -0.07995092, ...,  0.29099097,
                0.1437228 , -0.06723065],
              [ 0.27736659, -0.26821342, -0.09216158, ...,  0.32777604,
                0.17106625, -0.06180932]]], shape=(1, 200, 20))

    • inc_age::sigma
      (chain, draw)
      float64
      0.07423 0.08264 ... 0.08225 0.09232

      array([[0.07422506, 0.08264091, 0.08517134, 0.02131471, 0.01834669,
              0.02322415, 0.08787863, 0.08947164, 0.02247292, 0.01655286,
              0.08284362, 0.07290859, 0.01910234, 0.08407261, 0.0204066 ,
              0.08928871, 0.08041209, 0.08158367, 0.09332391, 0.08263215,
              0.08166706, 0.0175751 , 0.01759501, 0.08448853, 0.08020603,
              0.08337653, 0.09568542, 0.01889757, 0.08759506, 0.02065887,
              0.09014336, 0.09619147, 0.01830125, 0.07714268, 0.08480592,
              0.0154657 , 0.09405201, 0.08457306, 0.08473553, 0.08104566,
              0.08056462, 0.01994706, 0.07944379, 0.02033161, 0.09114235,
              0.01934571, 0.01857653, 0.07870104, 0.08403553, 0.08159431,
              0.01869626, 0.09177569, 0.09534713, 0.02026863, 0.08069956,
              0.08623397, 0.01826549, 0.08801606, 0.02481904, 0.08242713,
              0.08295564, 0.01567355, 0.02487774, 0.08228112, 0.02135862,
              0.02410711, 0.01882327, 0.0868839 , 0.08471936, 0.0207845 ,
              0.08751133, 0.01869521, 0.08986763, 0.08399271, 0.08687182,
              0.08440504, 0.01781568, 0.0888734 , 0.07898819, 0.0827786 ,
              0.07870695, 0.08307959, 0.08744385, 0.08857669, 0.09321025,
              0.0885485 , 0.01699771, 0.02121218, 0.09802725, 0.01865027,
              0.01903655, 0.07959831, 0.07657361, 0.07822851, 0.0214378 ,
              0.02271149, 0.07214327, 0.09921709, 0.08988015, 0.08737279,
              0.01808172, 0.07794206, 0.08640528, 0.0189228 , 0.08681286,
              0.07858752, 0.0872804 , 0.02083164, 0.0842554 , 0.0181423 ,
              0.08781693, 0.08183273, 0.08117771, 0.09232791, 0.07414759,
              0.08416404, 0.08912973, 0.08865631, 0.0845735 , 0.07809979,
              0.01725652, 0.07180589, 0.08347143, 0.0934131 , 0.01752312,
              0.0923606 , 0.07405761, 0.07788453, 0.01946293, 0.08645003,
              0.08178511, 0.08017022, 0.0825192 , 0.07142852, 0.02234653,
              0.0761664 , 0.07953443, 0.01881299, 0.08707276, 0.0812862 ,
              0.08689871, 0.01611025, 0.01828062, 0.01843558, 0.01713233,
              0.07315624, 0.09235031, 0.08170686, 0.08683193, 0.08447494,
              0.07875971, 0.09147174, 0.01958121, 0.02132952, 0.07959155,
              0.07611116, 0.08092925, 0.08079571, 0.08596907, 0.01774   ,
              0.08368307, 0.08283584, 0.07789155, 0.08055524, 0.09248254,
              0.09060449, 0.07393047, 0.08926895, 0.07450349, 0.08586912,
              0.01798528, 0.09740303, 0.09083831, 0.089078  , 0.08401645,
              0.01650627, 0.08061977, 0.01871784, 0.08259657, 0.02153403,
              0.08943453, 0.01906011, 0.02092018, 0.08708739, 0.02075871,
              0.01721524, 0.08511266, 0.08698412, 0.0848049 , 0.0872093 ,
              0.09029822, 0.07367933, 0.08127817, 0.09563195, 0.0830609 ,
              0.08590827, 0.02295479, 0.02389968, 0.08224741, 0.09232099]])

    • reg::raw
      (chain, draw, reg::raw_dim_0)
      float64
      -0.007254 0.6457 ... 0.0975 1.446

      array([[[-7.25423536e-03,  6.45735990e-01,  4.53788948e-01,
                2.06916326e-01,  1.49365794e+00],
              [ 1.62018571e-02,  4.17941047e-01,  3.71404779e-01,
                1.83664837e-01,  1.53629331e+00],
              [ 3.16789916e-02,  5.64473569e-01,  3.15159008e-01,
                4.62591356e-01,  1.50961205e+00],
              [-1.39954235e+00,  3.45932694e-01, -6.29195476e-02,
               -4.51510734e-01,  3.94091063e-01],
              [-1.53734220e+00,  4.80779310e-01,  1.21368121e-01,
               -3.92161318e-01,  2.12165585e-01],
              [-1.27689262e+00,  4.06754570e-01,  1.83206925e-01,
               -3.09653537e-01,  4.09183501e-01],
              [-1.20977712e-01,  3.66016125e-01,  1.67404198e-01,
                1.98300289e-01,  1.33120040e+00],
              [-1.32509863e-01,  7.89748898e-01,  1.98690847e-01,
                4.54599003e-02,  1.30656705e+00],
              [-1.56508620e+00,  4.04233763e-01,  1.21046895e-01,
               -3.58395881e-01,  4.98300058e-01],
              [-1.59601469e+00,  3.64156549e-01,  1.42221605e-01,
               -5.74611033e-01,  6.08220451e-01],
      ...
              [-9.73592046e-02,  5.51334059e-01,  3.13001200e-01,
                7.10786238e-02,  1.59030160e+00],
              [-3.36478041e-02,  7.14359933e-01,  2.56879239e-01,
                1.69467381e-01,  1.56381066e+00],
              [-3.73619328e-02,  4.64091476e-01,  2.10627300e-01,
                8.97515853e-03,  1.51776341e+00],
              [-2.65554987e-03,  5.85624088e-01,  3.78404795e-01,
                1.31624072e-01,  1.29024542e+00],
              [-1.91297784e-03,  6.24182352e-01,  1.67560622e-01,
                1.62200791e-01,  1.23622488e+00],
              [ 5.80258841e-02,  7.10255504e-01,  3.19919855e-01,
                7.03658492e-02,  1.48066075e+00],
              [-1.49786962e+00,  4.29186068e-01, -8.01479641e-02,
               -4.33161338e-01,  4.55567463e-01],
              [-1.46144270e+00,  4.62713594e-01,  3.47252223e-02,
               -4.92020163e-01,  3.61054411e-01],
              [ 4.85846651e-02,  5.45737560e-01,  2.14699754e-01,
                4.39846841e-01,  1.43182749e+00],
              [ 1.10550228e-01,  6.23750659e-01,  3.95045772e-01,
                9.75010977e-02,  1.44598656e+00]]])

    • reg::raw_slope
      (chain, draw, reg::raw_slope_dim_0)
      float64
      -0.5649 1.586 ... -1.345 0.1972

      array([[[-5.64896693e-01,  1.58606010e+00, -1.91412027e-04,
               -1.35998734e+00,  4.80655591e-02],
              [-7.30689873e-01,  1.51916756e+00,  1.29907033e-01,
               -1.32675169e+00,  6.91833564e-02],
              [-6.01572098e-01,  1.50479220e+00, -1.24675514e-02,
               -1.33633844e+00,  1.30923749e-01],
              [ 5.23894009e-01,  1.28275840e+00,  4.42954099e-02,
               -1.77075146e+00,  3.84661423e-01],
              [ 6.27410270e-01,  1.25635324e+00, -9.24764759e-02,
               -1.52621370e+00,  4.31463166e-01],
              [ 5.31289085e-01,  1.09342689e+00, -8.22254982e-03,
               -1.64491097e+00,  3.08736074e-01],
              [-6.88316163e-01,  1.68322810e+00,  9.55917958e-02,
               -1.37337415e+00,  4.74960640e-02],
              [-6.50082695e-01,  1.44990639e+00, -8.77601295e-02,
               -1.28550689e+00,  1.46333116e-01],
              [ 4.90081972e-01,  1.19276828e+00, -3.47833474e-02,
               -1.82745795e+00,  4.84938780e-01],
              [ 7.09750713e-01,  1.21697798e+00, -5.71888358e-02,
               -1.64322203e+00,  3.91445938e-01],
      ...
              [-5.67329131e-01,  1.76047939e+00, -4.19268290e-02,
               -1.06332758e+00,  1.93750459e-01],
              [-6.83153024e-01,  1.53733630e+00,  1.53101468e-01,
               -1.31212866e+00, -2.10291445e-02],
              [-6.47892224e-01,  1.65960342e+00,  1.38563022e-01,
               -1.47301193e+00,  1.25520297e-01],
              [-7.50360871e-01,  1.61879207e+00,  1.05192745e-01,
               -1.52689699e+00, -3.30048890e-02],
              [-7.09096842e-01,  1.64557235e+00, -1.75834648e-02,
               -1.30466350e+00,  1.58316782e-01],
              [-5.59208577e-01,  1.62516518e+00,  1.80804959e-02,
               -1.18962282e+00,  1.68207396e-01],
              [ 6.07885247e-01,  1.16472139e+00, -7.04944822e-02,
               -1.58037438e+00,  3.17227910e-01],
              [ 4.10117260e-01,  1.14567646e+00, -8.16513108e-02,
               -1.53766223e+00,  3.61765198e-01],
              [-7.80895686e-01,  1.63641206e+00,  2.36945613e-01,
               -1.29920608e+00,  1.69343677e-01],
              [-6.93088124e-01,  1.66430630e+00, -1.18634230e-01,
               -1.34549323e+00,  1.97187704e-01]]])

    • reg::re
      (chain, draw, reg::re_dim_0)
      float64
      -0.0006393 0.05691 ... 0.1294

      array([[[-6.39291415e-04,  5.69065455e-02,  3.99908969e-02,
                1.82348413e-02,  1.31631061e-01],
              [ 1.28120449e-03,  3.30497882e-02,  2.93698104e-02,
                1.45237804e-02,  1.21486436e-01],
              [ 2.39296445e-03,  4.26391472e-02,  2.38064492e-02,
                3.49431789e-02,  1.14032922e-01],
              [-3.27418860e-02,  8.09299472e-03, -1.47198451e-03,
               -1.05629622e-02,  9.21964576e-03],
              [-2.58310697e-02,  8.07825602e-03,  2.03927817e-03,
               -6.58925928e-03,  3.56489532e-03],
              [-2.63088634e-02,  8.38069720e-03,  3.77476217e-03,
               -6.38004518e-03,  8.43074246e-03],
              [-8.31572354e-03,  2.51590881e-02,  1.15069710e-02,
                1.36306958e-02,  9.15035865e-02],
              [-1.01171914e-02,  6.02977063e-02,  1.51701413e-02,
                3.47088514e-03,  9.97570197e-02],
              [-3.47141768e-02,  8.96605077e-03,  2.68486382e-03,
               -7.94935000e-03,  1.10524752e-02],
              [-3.30703326e-02,  7.54553092e-03,  2.94691259e-03,
               -1.19062676e-02,  1.26026739e-02],
      ...
              [-9.59017326e-03,  5.43080561e-02,  3.08315556e-02,
                7.00145733e-03,  1.56649470e-01],
              [-2.66713198e-03,  5.66245635e-02,  2.03618290e-02,
                1.34330273e-02,  1.23957255e-01],
              [-3.73301245e-03,  4.63696369e-02,  2.10447981e-02,
                8.96751748e-04,  1.51647125e-01],
              [-1.91215644e-04,  4.21684746e-02,  2.72474328e-02,
                9.47772891e-03,  9.29054702e-02],
              [-1.64725820e-04,  5.37481132e-02,  1.44285837e-02,
                1.39670506e-02,  1.06450871e-01],
              [ 5.04108760e-03,  6.17045352e-02,  2.77935276e-02,
                6.11314097e-03,  1.28634671e-01],
              [-2.60362097e-02,  7.46018096e-03, -1.39314475e-03,
               -7.52927974e-03,  7.91874658e-03],
              [-2.46152526e-02,  7.79353992e-03,  5.84881036e-04,
               -8.28715394e-03,  6.08128225e-03],
              [ 4.88107597e-03,  5.48277216e-02,  2.15698885e-02,
                4.41893721e-02,  1.43849067e-01],
              [ 9.89443596e-03,  5.58267589e-02,  3.53572774e-02,
                8.72651627e-03,  1.29418289e-01]]])

    • reg::re_slope
      (chain, draw, reg::re_slope_dim_0)
      float64
      -0.009483 0.02663 ... 0.003689

      array([[[-9.48296107e-03,  2.66253040e-02, -3.21324735e-06,
               -2.28302044e-02,  8.06879970e-04],
              [-1.42383811e-02,  2.96028281e-02,  2.53139659e-03,
               -2.58533708e-02,  1.34812187e-03],
              [-8.32826980e-03,  2.08326075e-02, -1.72602971e-04,
               -1.85005041e-02,  1.81253138e-03],
              [ 7.22539788e-02,  1.76914407e-01,  6.10909755e-03,
               -2.44217029e-01,  5.30514147e-02],
              [ 7.98279729e-02,  1.59850958e-01, -1.17661600e-02,
               -1.94186407e-01,  5.48968220e-02],
              [ 5.59861038e-02,  1.15222979e-01, -8.66474657e-04,
               -1.73337189e-01,  3.25339450e-02],
              [-1.45353176e-02,  3.55450830e-02,  2.01863212e-03,
               -2.90018317e-02,  1.00298440e-03],
              [-1.16555946e-02,  2.59959559e-02, -1.57348673e-03,
               -2.30483710e-02,  2.62366541e-03],
              [ 5.50924073e-02,  1.34084663e-01, -3.91015881e-03,
               -2.05433097e-01,  5.45142370e-02],
              [ 9.34068932e-02,  1.60160646e-01, -7.52634887e-03,
               -2.16256584e-01,  5.15163257e-02],
      ...
              [-1.00470557e-02,  3.11770251e-02, -7.42498779e-04,
               -1.88308881e-02,  3.43120342e-03],
              [-1.28582382e-02,  2.89355908e-02,  2.88166059e-03,
               -2.46967550e-02, -3.95808463e-04],
              [-1.08170574e-02,  2.77083514e-02,  2.31341589e-03,
               -2.45930635e-02,  2.09565759e-03],
              [-1.58725050e-02,  3.42425709e-02,  2.22515918e-03,
               -3.22986993e-02, -6.98157762e-04],
              [-1.37025407e-02,  3.17989318e-02, -3.39781717e-04,
               -2.52112316e-02,  3.05930307e-03],
              [-1.21659791e-02,  3.53566206e-02,  3.93354008e-04,
               -2.58810879e-02,  3.65947115e-03],
              [ 6.17329691e-02,  1.18281715e-01, -7.15897237e-03,
               -1.60492795e-01,  3.22156540e-02],
              [ 4.57521239e-02,  1.27810108e-01, -9.10890921e-03,
               -1.71539507e-01,  4.03580336e-02],
              [-1.49586768e-02,  3.13467722e-02,  4.53888133e-03,
               -2.48873240e-02,  3.24391259e-03],
              [-1.29678820e-02,  3.11396587e-02, -2.21968122e-03,
               -2.51745728e-02,  3.68943974e-03]]])

    • reg::sigma
      (chain, draw)
      float64
      0.08813 0.07908 ... 0.1005 0.0895

      array([[0.08812664, 0.07907763, 0.0755379 , 0.02339471, 0.01680242,
              0.02060382, 0.06873765, 0.07635048, 0.02218036, 0.02072057,
              0.07962673, 0.08445686, 0.01711604, 0.08908331, 0.0201382 ,
              0.07209037, 0.07447384, 0.08840647, 0.07556492, 0.08080883,
              0.08559498, 0.02116452, 0.01330677, 0.08288938, 0.08794344,
              0.08420917, 0.07714999, 0.01874058, 0.07891215, 0.02037823,
              0.08293799, 0.06945986, 0.01974636, 0.08713446, 0.08490153,
              0.02449008, 0.1020045 , 0.07134418, 0.08158291, 0.07644258,
              0.08204946, 0.02476577, 0.07499212, 0.01932586, 0.07899135,
              0.02072002, 0.02503045, 0.07931183, 0.09033794, 0.0894206 ,
              0.0163356 , 0.07953534, 0.09206766, 0.02226975, 0.09774977,
              0.08575799, 0.01380905, 0.08325807, 0.0169077 , 0.07818293,
              0.06665016, 0.01679378, 0.01654502, 0.08895286, 0.01700048,
              0.0169586 , 0.02349913, 0.08589165, 0.07782466, 0.02469869,
              0.11013167, 0.01745278, 0.08397839, 0.07343027, 0.0811376 ,
              0.07860301, 0.02295119, 0.08100577, 0.07044576, 0.07130101,
              0.07797258, 0.06313554, 0.07353453, 0.07700542, 0.06871679,
              0.08005565, 0.01877467, 0.01845697, 0.07427652, 0.01762236,
              0.01656324, 0.07261255, 0.07719198, 0.08032375, 0.0168683 ,
              0.01874586, 0.06457243, 0.07404008, 0.07572535, 0.07737262,
              0.01856718, 0.07732297, 0.06786102, 0.02377801, 0.08666888,
              0.08961555, 0.08963719, 0.02069949, 0.07460028, 0.01582172,
              0.08921096, 0.07656225, 0.1031019 , 0.09058167, 0.08780429,
              0.07802934, 0.07445486, 0.09617323, 0.07833349, 0.09399497,
              0.02036568, 0.08566146, 0.07198647, 0.07832377, 0.0196142 ,
              0.08439749, 0.08548126, 0.07405734, 0.01977568, 0.0868947 ,
              0.08677704, 0.08905975, 0.0772863 , 0.07551651, 0.01842973,
              0.08826458, 0.07034037, 0.0194799 , 0.08407376, 0.0773202 ,
              0.09514917, 0.01904899, 0.02176851, 0.01765198, 0.02614435,
              0.06843965, 0.08357998, 0.0878671 , 0.07382223, 0.08692551,
              0.090971  , 0.07332485, 0.01749673, 0.02320403, 0.08143746,
              0.08340748, 0.06992193, 0.0946582 , 0.0847831 , 0.025308  ,
              0.07577311, 0.08966429, 0.07507821, 0.07775608, 0.06704168,
              0.07229406, 0.0943867 , 0.09172561, 0.08436587, 0.09114981,
              0.02123081, 0.06461204, 0.07941763, 0.09487616, 0.09848182,
              0.02009487, 0.06679215, 0.01849734, 0.08357229, 0.02016565,
              0.07521679, 0.02116056, 0.01860991, 0.07878449, 0.01945086,
              0.02225271, 0.08495931, 0.08552359, 0.09102177, 0.07057736,
              0.098503  , 0.07926615, 0.09991486, 0.07200605, 0.08610963,
              0.08687653, 0.01738216, 0.01684312, 0.10046536, 0.08950172]])

    • reg::sigma_slope
      (chain, draw)
      float64
      0.01679 0.01949 ... 0.01916 0.01871

      array([[0.01678707, 0.01948622, 0.01384418, 0.13791717, 0.12723409,
              0.10537785, 0.02111721, 0.0179294 , 0.11241468, 0.13160521,
              0.02506246, 0.01922628, 0.1110206 , 0.01930831, 0.13062042,
              0.0255418 , 0.01873365, 0.01704097, 0.01671067, 0.01736435,
              0.0205847 , 0.12598167, 0.11028949, 0.01657961, 0.01711598,
              0.01752564, 0.01726455, 0.11885131, 0.0211007 , 0.14115803,
              0.01964799, 0.01721774, 0.114013  , 0.01880987, 0.01846854,
              0.13473736, 0.01846527, 0.01974748, 0.02124478, 0.0198981 ,
              0.01786235, 0.12471865, 0.01911645, 0.13442426, 0.01700577,
              0.1160886 , 0.12901802, 0.01838565, 0.01616363, 0.01742249,
              0.12291229, 0.01784437, 0.01914205, 0.12875276, 0.01877912,
              0.0199872 , 0.10522809, 0.02096274, 0.11097124, 0.01667925,
              0.01879494, 0.11301447, 0.13125443, 0.01571848, 0.10994511,
              0.10986192, 0.10981145, 0.01486289, 0.01942138, 0.13370181,
              0.02348771, 0.13273107, 0.01848246, 0.01798533, 0.01723019,
              0.01953688, 0.09843175, 0.01811437, 0.0175928 , 0.02007466,
              0.02041961, 0.01786695, 0.02125964, 0.02232135, 0.02006564,
              0.02106065, 0.11077113, 0.12620038, 0.01941734, 0.11215113,
              0.13888588, 0.01887674, 0.0221657 , 0.01873372, 0.14970389,
              0.12919836, 0.02210133, 0.01686706, 0.0184927 , 0.020084  ,
              0.11037525, 0.02234251, 0.01959722, 0.14014735, 0.01760072,
              0.01757888, 0.01782752, 0.09991548, 0.02088737, 0.14632451,
              0.01715731, 0.02046909, 0.0217503 , 0.02118222, 0.0207863 ,
              0.01804382, 0.02204811, 0.01730606, 0.01734991, 0.0179657 ,
              0.10638309, 0.0169583 , 0.01951481, 0.01977756, 0.10193567,
              0.01511767, 0.01967095, 0.02133872, 0.13265767, 0.02272153,
              0.02016999, 0.01755384, 0.02069716, 0.01689648, 0.13937076,
              0.01833213, 0.01744129, 0.12380757, 0.02076908, 0.01740741,
              0.01680971, 0.11184407, 0.12618048, 0.12703031, 0.12259919,
              0.01675265, 0.02276327, 0.01983692, 0.01680924, 0.0194772 ,
              0.0178748 , 0.01777017, 0.12343812, 0.1407427 , 0.01892341,
              0.01896449, 0.01839348, 0.01499466, 0.01899331, 0.14555314,
              0.01846372, 0.01953081, 0.01831951, 0.02009463, 0.01871228,
              0.02167221, 0.01628388, 0.0153294 , 0.02152293, 0.01832621,
              0.11637858, 0.01898326, 0.01624775, 0.01882265, 0.01695026,
              0.11680931, 0.01922854, 0.09362155, 0.01801394, 0.09840157,
              0.02066269, 0.10365499, 0.11870627, 0.01758076, 0.11973655,
              0.1427294 , 0.01704298, 0.01872739, 0.01710105, 0.01781323,
              0.0177094 , 0.0188219 , 0.01669577, 0.02115316, 0.01932393,
              0.02175571, 0.10155366, 0.11155864, 0.01915579, 0.01871029]])

    • reg_age::raw
      (chain, draw, reg_age::raw_dim_0)
      float64
      -1.553 -0.9517 ... 0.3894 -0.5979

      array([[[-1.55279399, -0.95166696,  0.11251144, ...,  1.62726053,
                0.56901074, -0.56591603],
              [-1.50964305, -0.76728804,  0.38929629, ...,  1.53244939,
                0.3648577 , -0.50211504],
              [-1.76103916, -0.62295048,  0.28010077, ...,  1.6321083 ,
                0.48462277, -0.59291534],
              ...,
              [-0.23089211, -0.10797002, -0.29867965, ...,  0.44180474,
                0.02544666, -0.07234521],
              [-1.53444134, -0.61287108,  0.31790144, ...,  1.55558851,
                0.46637086, -0.56375968],
              [-1.50658027, -0.60534228,  0.16037289, ...,  1.77359989,
                0.38943034, -0.59786027]]], shape=(1, 200, 20))

    • reg_age::re
      (chain, draw, reg_age::re_dim_0)
      float64
      -0.2884 -0.1768 ... 0.08255 -0.1267

      array([[[-0.28839881, -0.17675211,  0.02089663, ...,  0.3022294 ,
                0.10568177, -0.10510699],
              [-0.2781436 , -0.14136869,  0.07172574, ...,  0.28234555,
                0.06722307, -0.09251199],
              [-0.32734975, -0.11579679,  0.05206637, ...,  0.30338351,
                0.09008382, -0.11021372],
              ...,
              [-0.02630038, -0.01229861, -0.03402189, ...,  0.05032494,
                0.00289857, -0.00824067],
              [-0.31289205, -0.12497218,  0.06482413, ...,  0.31720422,
                0.09509893, -0.11495775],
              [-0.31935136, -0.12831502,  0.03399441, ...,  0.37595178,
                0.08254795, -0.12672905]]], shape=(1, 200, 20))

    • reg_age::sigma
      (chain, draw)
      float64
      0.1857 0.1842 ... 0.2039 0.212

      array([[0.18572896, 0.18424461, 0.18588442, 0.15166692, 0.11166266,
              0.13846454, 0.19445652, 0.19726597, 0.09255049, 0.10711261,
              0.19474365, 0.18723996, 0.14315922, 0.18162835, 0.11297059,
              0.20632849, 0.18646131, 0.1844824 , 0.19440042, 0.19611449,
              0.18137331, 0.10902452, 0.12198421, 0.20041312, 0.19148108,
              0.17377386, 0.19338416, 0.13349273, 0.17655195, 0.11849087,
              0.20322373, 0.19417046, 0.12116232, 0.18099219, 0.21238223,
              0.11508495, 0.21435116, 0.17341715, 0.18829213, 0.17256021,
              0.19995467, 0.17278353, 0.1982158 , 0.12437866, 0.18654067,
              0.11404751, 0.13034724, 0.2015335 , 0.17731383, 0.19251784,
              0.12058878, 0.18668714, 0.17749813, 0.14344325, 0.19119448,
              0.17247924, 0.12300344, 0.17876623, 0.12775523, 0.19761884,
              0.18185453, 0.13748259, 0.18552604, 0.19582242, 0.11989503,
              0.12436072, 0.107996  , 0.18324988, 0.19560155, 0.12463476,
              0.1993246 , 0.15575036, 0.18377711, 0.18913724, 0.20660784,
              0.18598281, 0.12562646, 0.20382591, 0.18056823, 0.19708883,
              0.18962054, 0.17920199, 0.18303547, 0.20021293, 0.1779447 ,
              0.19604046, 0.10773532, 0.1741893 , 0.1873189 , 0.13366941,
              0.12437562, 0.18943622, 0.20675838, 0.19903487, 0.15238312,
              0.13136506, 0.18255706, 0.18605194, 0.18307959, 0.19718353,
              0.15309012, 0.20024064, 0.19737187, 0.13308764, 0.18485699,
              0.20355934, 0.17784266, 0.14174749, 0.18068636, 0.1251904 ,
              0.2220755 , 0.19977004, 0.19208036, 0.17889573, 0.20928615,
              0.20757278, 0.18366371, 0.19105091, 0.18158994, 0.18260133,
              0.12989829, 0.18246067, 0.181889  , 0.19462142, 0.12075485,
              0.20280006, 0.20271746, 0.20891265, 0.12576961, 0.19322258,
              0.18241521, 0.18337952, 0.18174094, 0.19347858, 0.16252837,
              0.17749819, 0.20715386, 0.15352447, 0.18218062, 0.19411597,
              0.1949271 , 0.15405811, 0.12280773, 0.12010607, 0.13684874,
              0.19007932, 0.20365419, 0.1860434 , 0.17389444, 0.19666459,
              0.1886778 , 0.18239832, 0.11486716, 0.14109231, 0.18811775,
              0.18709883, 0.1870429 , 0.19445146, 0.20586245, 0.14558291,
              0.18693162, 0.19337029, 0.19190172, 0.20254352, 0.18710656,
              0.17939946, 0.19857424, 0.19293769, 0.18386123, 0.21147426,
              0.14695385, 0.20324738, 0.1808562 , 0.19217863, 0.18608233,
              0.17252739, 0.18337446, 0.1861462 , 0.19887572, 0.11748593,
              0.19888324, 0.12690071, 0.10490075, 0.17269821, 0.13269553,
              0.16632839, 0.19183534, 0.18258822, 0.19031838, 0.19395807,
              0.19484988, 0.16443378, 0.19684974, 0.18819924, 0.21289348,
              0.18532676, 0.1217108 , 0.11390764, 0.20391268, 0.21197102]])

    • reg_eth::raw
      (chain, draw, reg_eth::raw_dim_0)
      float64
      -0.06558 0.3518 ... 0.3253 0.3558

      array([[[-0.06557606,  0.35176611,  0.69164529, ...,  0.36918424,
                0.13602253,  0.38041309],
              [ 0.21686447,  0.26766122,  0.42858577, ...,  0.12563348,
                0.31719947,  0.35679945],
              [ 0.2371162 ,  0.32464709,  0.56879593, ...,  0.32264231,
                0.25985301,  0.39446855],
              ...,
              [-1.12456997, -0.48064167,  0.00847201, ..., -0.04056239,
               -0.0436988 ,  0.12843495],
              [-0.16186822, -0.03221945,  0.76725977, ...,  0.25162734,
                0.26525792,  0.3694816 ],
              [ 0.07167239,  0.27236958,  0.5810714 , ...,  0.47351773,
                0.3252993 ,  0.35575288]]], shape=(1, 200, 20))

    • reg_eth::re
      (chain, draw, reg_eth::re_dim_0)
      float64
      -0.005056 0.02712 ... 0.0283

      array([[[-5.05570076e-03,  2.71200214e-02,  5.33235996e-02, ...,
                2.84629028e-02,  1.04868941e-02,  2.93286101e-02],
              [ 1.78641300e-02,  2.20484929e-02,  3.53045927e-02, ...,
                1.03490109e-02,  2.61291879e-02,  2.93912213e-02],
              [ 2.05960841e-02,  2.81990806e-02,  4.94060246e-02, ...,
                2.80249438e-02,  2.25710200e-02,  3.42638223e-02],
              ...,
              [-4.59787122e-03, -1.96513206e-03,  3.46383273e-05, ...,
               -1.65841730e-04, -1.78665155e-04,  5.25113944e-04],
              [-1.33330769e-02, -2.65391431e-03,  6.31991486e-02, ...,
                2.07265313e-02,  2.18492813e-02,  3.04341807e-02],
              [ 5.70250195e-03,  2.16706595e-02,  4.62320364e-02, ...,
                3.76746971e-02,  2.58819297e-02,  2.83049215e-02]]],
            shape=(1, 200, 20))

    • reg_eth::sigma
      (chain, draw)
      float64
      0.0771 0.08237 ... 0.08237 0.07956

      array([[0.07709674, 0.08237463, 0.08686072, 0.00547145, 0.00635371,
              0.00405944, 0.08275401, 0.07329517, 0.00638683, 0.00466412,
              0.07731281, 0.08938496, 0.00330681, 0.08738747, 0.00557877,
              0.08316265, 0.08245352, 0.08153406, 0.07036526, 0.08084617,
              0.08199621, 0.00467039, 0.00519975, 0.05953052, 0.08517425,
              0.09112505, 0.08390311, 0.00475009, 0.08226451, 0.00378203,
              0.06413671, 0.07058202, 0.00460527, 0.08529048, 0.07299689,
              0.00459803, 0.07395231, 0.06234831, 0.08059304, 0.07879894,
              0.08485878, 0.0053545 , 0.07830826, 0.00441896, 0.08092145,
              0.00439027, 0.00371841, 0.08073094, 0.0897211 , 0.0802617 ,
              0.00515239, 0.06985881, 0.08336157, 0.00582536, 0.08349904,
              0.07987688, 0.0030181 , 0.08482626, 0.00420914, 0.08014973,
              0.06037709, 0.00422256, 0.00472256, 0.07734775, 0.00518427,
              0.00651962, 0.00360125, 0.06260436, 0.07379013, 0.00371166,
              0.09588365, 0.00504584, 0.08472892, 0.06655341, 0.08364437,
              0.07696572, 0.00439889, 0.07474464, 0.07418111, 0.10101355,
              0.0762445 , 0.07210437, 0.08360939, 0.08085945, 0.07159583,
              0.07235081, 0.0045245 , 0.0047967 , 0.07246407, 0.00329195,
              0.00376546, 0.07879115, 0.08549721, 0.07192711, 0.00385206,
              0.00350069, 0.08506288, 0.07448096, 0.07972234, 0.08919412,
              0.00356481, 0.08410558, 0.0811574 , 0.00375981, 0.0756702 ,
              0.07335126, 0.08699958, 0.00412435, 0.08692194, 0.00334778,
              0.07470118, 0.07253797, 0.06982692, 0.08058039, 0.06910133,
              0.08655258, 0.07980532, 0.08541629, 0.09034068, 0.07141017,
              0.00470035, 0.09147873, 0.08582384, 0.07807159, 0.00597833,
              0.07196778, 0.0783576 , 0.07601894, 0.00455621, 0.08197988,
              0.07739254, 0.07409279, 0.0825933 , 0.07442007, 0.00457245,
              0.07625391, 0.07379876, 0.00488436, 0.07971153, 0.07750871,
              0.07881982, 0.00411079, 0.00467121, 0.00418148, 0.00480615,
              0.08458554, 0.07683744, 0.08341797, 0.08570527, 0.08659586,
              0.07471932, 0.06744842, 0.00477125, 0.00381018, 0.07501259,
              0.08367525, 0.07680711, 0.08526387, 0.07468439, 0.00387416,
              0.0749549 , 0.0724935 , 0.08609462, 0.07038397, 0.07257241,
              0.07973648, 0.07792866, 0.08260436, 0.07866975, 0.07294754,
              0.00505722, 0.07210019, 0.08074281, 0.08048985, 0.06677919,
              0.00528126, 0.0695425 , 0.00524695, 0.07644873, 0.00421327,
              0.08599362, 0.00278077, 0.00409748, 0.09047768, 0.00417479,
              0.0040195 , 0.07818837, 0.07363322, 0.06231134, 0.06440526,
              0.06806826, 0.07095079, 0.08047564, 0.08284532, 0.06622057,
              0.07620845, 0.00457828, 0.00408856, 0.08236995, 0.07956344]])

    • reg_inc::raw
      (chain, draw, reg_inc::raw_dim_0)
      float64
      -0.6521 -0.1228 ... -0.06948

      array([[[-0.65208478, -0.12281618, -0.57365142, ...,  0.3318492 ,
               -0.14510883,  0.05852641],
              [-0.40596742, -0.04642797, -0.62872351, ...,  0.22566874,
               -0.0590781 , -0.08326787],
              [-0.37655621,  0.10237213, -0.53403538, ...,  0.16259379,
               -0.02203809,  0.06172421],
              ...,
              [-0.13494883, -0.55287678, -1.34670751, ...,  0.47666505,
               -0.13253949,  0.24639146],
              [-0.37600989, -0.03525324, -0.46824441, ..., -0.0017987 ,
                0.13768754,  0.08670265],
              [-0.31253478,  0.02502621, -0.44822663, ...,  0.2437752 ,
                0.02717867, -0.06948351]]], shape=(1, 200, 25))

    • reg_inc::re
      (chain, draw, reg_inc::re_dim_0)
      float64
      -0.08983 -0.01692 ... -0.00849

      array([[[-0.0898347 , -0.01691982, -0.0790293 , ...,  0.04571733,
               -0.01999097,  0.00806291],
              [-0.04548036, -0.00520131, -0.07043563, ...,  0.02528157,
               -0.00661849, -0.00932846],
              [-0.04065853,  0.0110536 , -0.0576623 , ...,  0.01755601,
               -0.00237956,  0.00666465],
              ...,
              [-0.00099131, -0.00406135, -0.00989272, ...,  0.00350151,
               -0.00097362,  0.00180996],
              [-0.04588687, -0.00430218, -0.05714283, ..., -0.00021951,
                0.01680288,  0.01058087],
              [-0.03818642,  0.00305778, -0.05476565, ...,  0.02978517,
                0.00332077, -0.0084897 ]]], shape=(1, 200, 25))

    • reg_inc::sigma
      (chain, draw)
      float64
      0.1378 0.112 0.108 ... 0.122 0.1222

      array([[0.13776536, 0.11202958, 0.10797468, 0.00803001, 0.00903653,
              0.00644652, 0.09905872, 0.11608911, 0.00802887, 0.00825808,
              0.11902066, 0.14690154, 0.00661046, 0.12011525, 0.00604266,
              0.12182085, 0.10146491, 0.09924205, 0.11173464, 0.12625285,
              0.12973399, 0.00793128, 0.00744526, 0.10424276, 0.13095665,
              0.12650674, 0.08861404, 0.00549075, 0.07700484, 0.00679101,
              0.10216074, 0.15986743, 0.00667287, 0.13894608, 0.13107867,
              0.00647029, 0.15186338, 0.12131079, 0.14202289, 0.10717613,
              0.10521685, 0.00574273, 0.17115434, 0.00781984, 0.09130646,
              0.00682845, 0.00624403, 0.13446358, 0.11569264, 0.12233402,
              0.00645504, 0.14549836, 0.12295125, 0.00679748, 0.1502296 ,
              0.12393667, 0.00579712, 0.12013254, 0.00594375, 0.12336458,
              0.11528815, 0.00634268, 0.00695876, 0.1251459 , 0.00759169,
              0.0072289 , 0.00625627, 0.1180844 , 0.11808089, 0.00738579,
              0.1289063 , 0.0063247 , 0.16907538, 0.09738921, 0.10715443,
              0.1391832 , 0.0050117 , 0.13134499, 0.13014004, 0.1232166 ,
              0.1130177 , 0.09538252, 0.1361461 , 0.10657841, 0.11889346,
              0.11255158, 0.00718686, 0.00683891, 0.13406198, 0.00633646,
              0.00529881, 0.13442426, 0.12627378, 0.12192419, 0.0063209 ,
              0.00752127, 0.09547103, 0.11120898, 0.12089653, 0.15068259,
              0.0054157 , 0.1083216 , 0.12594688, 0.00512246, 0.13302646,
              0.10576229, 0.12285418, 0.00557283, 0.13420986, 0.0074744 ,
              0.13041882, 0.10931205, 0.12222698, 0.11556653, 0.08846739,
              0.12299293, 0.11076756, 0.11667752, 0.14224014, 0.1360012 ,
              0.00558017, 0.12643593, 0.10420837, 0.10478189, 0.00680175,
              0.12128714, 0.12544837, 0.14574474, 0.00566734, 0.08919624,
              0.10005797, 0.12084327, 0.11090881, 0.11264374, 0.00527984,
              0.15025795, 0.12703254, 0.00569638, 0.13085894, 0.09715138,
              0.11774428, 0.00538932, 0.00598182, 0.00805816, 0.00657605,
              0.125431  , 0.13073912, 0.20244714, 0.14817981, 0.15505939,
              0.09028214, 0.15452944, 0.00595069, 0.00649863, 0.12372455,
              0.12009888, 0.10873249, 0.12917085, 0.10844203, 0.00613594,
              0.10735633, 0.14815258, 0.11487389, 0.11893683, 0.14448648,
              0.12610676, 0.12039346, 0.15961186, 0.09858897, 0.10907364,
              0.00633597, 0.10150806, 0.12513645, 0.13378766, 0.12046162,
              0.0061879 , 0.0857046 , 0.00785835, 0.11441042, 0.00769427,
              0.12833525, 0.00664952, 0.00719343, 0.13701422, 0.00603267,
              0.00796356, 0.14615756, 0.11881775, 0.12100943, 0.12089781,
              0.11019473, 0.12136003, 0.12698029, 0.13963786, 0.10970651,
              0.10983841, 0.00879238, 0.00734586, 0.12203633, 0.12218295]])

    • stt::raw
      (chain, draw, stt::raw_dim_0)
      float64
      -0.2326 -0.1037 ... 0.08738 -0.503

      array([[[-0.2326193 , -0.10374608,  0.12566835, ..., -0.45597669,
                0.01541912, -0.49536951],
              [-0.26003477, -0.05346609,  0.36874509, ..., -0.29119659,
               -0.00869196, -0.34349502],
              [-0.18078961,  0.03276903,  0.43562148, ..., -0.32140138,
                0.26356455, -0.44204638],
              ...,
              [-0.10038573, -0.23655138,  0.30439222, ..., -0.38681692,
               -0.13412805, -0.34546912],
              [-0.2625085 , -0.18200197,  0.43812312, ..., -0.53215713,
               -0.04881309, -0.49447057],
              [-0.2405059 , -0.30879257,  0.38174874, ..., -0.3654414 ,
                0.08737767, -0.50296796]]], shape=(1, 200, 51))

    • stt::raw_slope
      (chain, draw, stt::raw_slope_dim_0)
      float64
      -0.1531 -0.04979 ... 0.1203 -0.332

      array([[[-0.15305676, -0.04979318,  0.18462109, ...,  0.43021933,
                0.17789764, -0.30087485],
              [-0.07530648, -0.1735875 ,  0.11729415, ...,  0.37131688,
                0.20669852, -0.28750807],
              [-0.02226464,  0.05882708,  0.06247124, ...,  0.54649537,
                0.06432376, -0.27890557],
              ...,
              [-0.09377448, -0.07340353,  0.02369662, ...,  0.49747862,
                0.18519336, -0.47106951],
              [-0.33823585, -0.11290258,  0.34330088, ...,  0.40570933,
                0.15221728, -0.3122667 ],
              [-0.24322257, -0.30102709,  0.17891865, ...,  0.42166083,
                0.1203121 , -0.33197615]]], shape=(1, 200, 51))

    • stt::re
      (chain, draw, stt::re_dim_0)
      float64
      -0.03846 -0.01715 ... -0.08571

      array([[[-3.84644462e-02, -1.71547913e-02,  2.07797174e-02, ...,
               -7.53974014e-02,  2.54960777e-03, -8.19111469e-02],
              [-5.96376528e-02, -1.22621766e-02,  8.45698129e-02, ...,
               -6.67844589e-02, -1.99345596e-03, -7.87788374e-02],
              [-3.53207643e-02,  6.40206645e-03,  8.51071210e-02, ...,
               -6.27920055e-02,  5.14924559e-02, -8.63623504e-02],
              ...,
              [-4.63629077e-06, -1.09250688e-05,  1.40582819e-05, ...,
               -1.78650472e-05, -6.19467172e-06, -1.59554087e-05],
              [-4.21502566e-02, -2.92235482e-02,  7.03482052e-02, ...,
               -8.54469827e-02, -7.83778082e-03, -7.93957570e-02],
              [-4.09822226e-02, -5.26182765e-02,  6.50500142e-02, ...,
               -6.22712423e-02,  1.48891606e-02, -8.57057775e-02]]],
            shape=(1, 200, 51))

    • stt::re_slope
      (chain, draw, stt::re_slope_dim_0)
      float64
      -0.102 -0.03318 ... 0.07969 -0.2199

      array([[[-0.10198664, -0.0331788 ,  0.12301897, ...,  0.28666896,
                0.11853891, -0.20048258],
              [-0.05815219, -0.13404548,  0.09057536, ...,  0.28673348,
                0.15961404, -0.22201573],
              [-0.01567381,  0.04141294,  0.04397835, ...,  0.38472049,
                0.04528249, -0.19634327],
              ...,
              [-0.05444704, -0.04261932,  0.01375866, ...,  0.28884442,
                0.10752637, -0.27351084],
              [-0.26216627, -0.08751068,  0.26609217, ...,  0.3144649 ,
                0.11798346, -0.2420376 ],
              [-0.16110572, -0.19939427,  0.1185121 , ...,  0.27929962,
                0.07969231, -0.2198943 ]]], shape=(1, 200, 51))

    • stt::sigma
      (chain, draw)
      float64
      0.1654 0.2293 ... 0.1606 0.1704

      array([[1.65353632e-01, 2.29344917e-01, 1.95369433e-01, 4.32376090e-05,
              3.36999237e-05, 6.01792175e-05, 1.69841682e-01, 2.09656950e-01,
              6.45988762e-05, 4.46467976e-05, 1.79408779e-01, 2.06901174e-01,
              5.45211736e-05, 1.92135361e-01, 5.43841897e-05, 1.81860758e-01,
              1.97334477e-01, 2.19261043e-01, 2.01750872e-01, 2.15773335e-01,
              1.69241822e-01, 5.49030805e-05, 3.82891599e-05, 1.84622647e-01,
              2.17356080e-01, 1.85642756e-01, 1.47412387e-01, 4.30727238e-05,
              1.62139181e-01, 4.90949426e-05, 1.72779148e-01, 2.06752843e-01,
              5.49716968e-05, 1.81229533e-01, 1.94312271e-01, 6.39786715e-05,
              2.31985741e-01, 1.86804478e-01, 1.79230556e-01, 1.54967855e-01,
              1.97554270e-01, 7.15735639e-05, 1.92019028e-01, 6.61130236e-05,
              1.77903871e-01, 5.11129646e-05, 4.28591231e-05, 1.73712007e-01,
              2.02213471e-01, 1.77485732e-01, 4.09839769e-05, 1.73992527e-01,
              1.96749008e-01, 5.17356377e-05, 2.45276431e-01, 2.02106792e-01,
              3.72650691e-05, 1.68593922e-01, 4.83739141e-05, 1.92135852e-01,
              2.06786230e-01, 5.78631338e-05, 5.05585564e-05, 2.44119801e-01,
              4.87378453e-05, 4.79641355e-05, 3.97929880e-05, 2.21144923e-01,
              1.97051808e-01, 6.54585592e-05, 2.00298898e-01, 4.20268947e-05,
              2.06862025e-01, 1.53831375e-01, 1.89741626e-01, 2.27537498e-01,
              6.17164608e-05, 2.05239893e-01, 1.88434740e-01, 2.03838900e-01,
      ...
              4.05851322e-05, 1.97132186e-01, 2.11190230e-01, 1.69720059e-01,
              4.08967678e-05, 2.09628726e-01, 2.01228013e-01, 2.12356837e-01,
              4.99797855e-05, 1.97747988e-01, 1.74665657e-01, 1.85755289e-01,
              1.72559272e-01, 1.90427797e-01, 6.97545384e-05, 2.35546535e-01,
              1.83698734e-01, 5.57212612e-05, 1.95203079e-01, 1.81632048e-01,
              2.21631453e-01, 4.66521846e-05, 6.23025528e-05, 7.87032471e-05,
              7.79467574e-05, 2.15276362e-01, 2.23970198e-01, 2.06396735e-01,
              2.13866941e-01, 1.73348741e-01, 2.20568507e-01, 1.82174838e-01,
              4.29630201e-05, 6.02735334e-05, 2.04427204e-01, 1.83241171e-01,
              1.74130887e-01, 2.10563145e-01, 1.92231418e-01, 5.82337056e-05,
              1.81393535e-01, 1.75636612e-01, 2.21570066e-01, 1.68283982e-01,
              2.00499532e-01, 2.08348667e-01, 1.97296005e-01, 2.06282054e-01,
              2.01376458e-01, 1.98159144e-01, 5.10831082e-05, 1.86646955e-01,
              1.78483196e-01, 1.96019520e-01, 2.42682530e-01, 3.97924532e-05,
              1.59899029e-01, 5.30895441e-05, 2.10727746e-01, 5.22901722e-05,
              2.12204661e-01, 4.19871083e-05, 5.95608174e-05, 2.15533672e-01,
              3.75081304e-05, 3.93989663e-05, 2.11492785e-01, 1.84587776e-01,
              2.08098118e-01, 1.98953855e-01, 1.95871227e-01, 1.67166781e-01,
              2.06307050e-01, 2.08255152e-01, 1.96665830e-01, 1.85776154e-01,
              4.40582081e-05, 4.61847610e-05, 1.60567205e-01, 1.70400074e-01]])

    • stt::sigma_slope
      (chain, draw)
      float64
      0.6663 0.7722 ... 0.7751 0.6624

      array([[0.66633214, 0.77220697, 0.70397758, 0.60635612, 0.59233532,
              0.52785634, 0.85747307, 0.68924084, 0.57889899, 0.58239562,
              0.81301288, 0.70476185, 0.52961058, 0.64307396, 0.57781942,
              0.87173574, 0.91644489, 0.60958201, 0.6992408 , 0.77210302,
              0.70716553, 0.64155804, 0.60132367, 0.66803359, 0.91715052,
              0.74832261, 0.65525188, 0.53734819, 0.8134836 , 0.5593252 ,
              0.63765362, 0.67344892, 0.64911491, 0.86619375, 0.8097715 ,
              0.5050237 , 0.70385989, 0.72020191, 0.73008266, 0.82902158,
              0.87595468, 0.61126671, 0.77204889, 0.6501014 , 0.74597563,
              0.60659137, 0.66718087, 0.82699497, 0.77662882, 0.73065756,
              0.67796652, 0.78725113, 0.68192572, 0.56324771, 0.80712366,
              0.68593103, 0.54871759, 0.78230503, 0.52902218, 0.68695542,
              0.73427814, 0.60520413, 0.69539328, 0.73529718, 0.51155453,
              0.67719693, 0.50151303, 0.5962946 , 0.76504235, 0.62701689,
              0.8652226 , 0.64234512, 0.75570303, 0.75038695, 0.79385392,
              0.72868904, 0.7095378 , 0.81944887, 0.61357932, 0.76582673,
              0.80839374, 0.73525606, 0.68383598, 0.84288832, 0.7932353 ,
              0.83852495, 0.52211796, 0.65439052, 0.69491126, 0.57673021,
              0.59953391, 0.84523326, 0.82860276, 0.68832769, 0.60063756,
              0.57144816, 0.90946993, 0.71510736, 0.60978583, 0.65165201,
              0.61224229, 0.84303756, 0.7201567 , 0.51220129, 0.66062805,
              0.62236398, 0.7039758 , 0.59692721, 0.83333783, 0.57114125,
              0.80919331, 0.78721295, 0.62044772, 0.81978968, 0.90783846,
              0.67161654, 0.64222355, 0.62995711, 0.77601003, 0.69851525,
              0.583683  , 0.68104456, 0.76943991, 0.80787064, 0.57317904,
              0.79169764, 0.682082  , 0.85566927, 0.59333491, 0.87907365,
              0.61798425, 0.80978744, 0.77421386, 0.82988846, 0.58609324,
              0.62712337, 0.72053449, 0.55689154, 0.74465873, 0.8643046 ,
              0.66056559, 0.60906513, 0.52379227, 0.53968442, 0.59847975,
              0.72785214, 0.75170609, 0.68285413, 0.6040874 , 0.83270793,
              0.66563436, 0.73157923, 0.53607681, 0.51416574, 0.76232614,
              0.72201548, 0.9754777 , 0.90541952, 0.96605758, 0.60346511,
              0.70062617, 0.70111714, 0.77706879, 0.91359333, 0.75775151,
              0.72337623, 0.81535278, 0.8057199 , 0.79337584, 0.74746196,
              0.56411287, 0.78016926, 0.64005587, 0.71272633, 0.73139956,
              0.49475955, 0.85305457, 0.62699271, 0.78407842, 0.49410314,
              0.65354281, 0.59899354, 0.50874905, 0.72524055, 0.62902075,
              0.63188419, 0.75364602, 0.68389069, 0.76166295, 0.56775406,
              0.8181508 , 0.90371105, 0.72561049, 0.63903944, 0.57081783,
              0.65395689, 0.61079775, 0.58061675, 0.775099  , 0.66237982]])

    • stt_age::raw
      (chain, draw, stt_age::raw_dim_0)
      float64
      -0.05746 -0.4186 ... -0.02523

      array([[[-0.05746382, -0.41860074, -0.09889784, ...,  0.05361416,
               -0.21131617,  0.01988118],
              [-0.14555176, -0.57963759, -0.14127501, ..., -0.06349775,
               -0.01509056, -0.0168948 ],
              [-0.16074846, -0.50462558, -0.15375648, ...,  0.01747221,
                0.01244521, -0.140755  ],
              ...,
              [-0.03147338, -0.60930827, -0.15493189, ..., -0.04868196,
                0.06871106,  0.05706097],
              [ 0.22670901, -0.42873713, -0.06623979, ..., -0.08428823,
               -0.22245688, -0.05510388],
              [ 0.29159535, -0.5113509 , -0.11975254, ..., -0.02375087,
               -0.28284671, -0.02522818]]], shape=(1, 200, 204))

    • stt_age::re
      (chain, draw, stt_age::re_dim_0)
      float64
      -0.03798 -0.2766 ... -0.01821

      array([[[-0.03797722, -0.2766487 , -0.06536051, ...,  0.03543302,
               -0.13965657,  0.01313926],
              [-0.09415029, -0.3749391 , -0.09138387, ..., -0.04107358,
               -0.00976134, -0.01092842],
              [-0.09272693, -0.29109071, -0.08869365, ...,  0.01007876,
                0.00717895, -0.08119381],
              ...,
              [-0.0202584 , -0.39219198, -0.09972463, ..., -0.031335  ,
                0.04422708,  0.0367283 ],
              [ 0.17105878, -0.32349508, -0.04997992, ..., -0.06359801,
               -0.16785042, -0.04157754],
              [ 0.2104835 , -0.36911058, -0.08644148, ..., -0.01714419,
               -0.20416843, -0.01821056]]], shape=(1, 200, 204))

    • stt_age::sigma
      (chain, draw)
      float64
      0.6609 0.6469 ... 0.7545 0.7218

      array([[0.66088919, 0.6468509 , 0.57684494, 0.64095216, 0.64879044,
              0.54406907, 0.68579058, 0.75461003, 0.64863338, 0.65077223,
              0.65375303, 0.78390161, 0.57393003, 0.75430953, 0.59480319,
              0.74381547, 0.69034397, 0.64157337, 0.67762666, 0.68510727,
              0.72913121, 0.62362195, 0.62352984, 0.65968939, 0.67812033,
              0.69654748, 0.72595398, 0.53752416, 0.71286589, 0.58300392,
              0.68483988, 0.74574242, 0.62896989, 0.68501318, 0.69639077,
              0.68930927, 0.75099126, 0.74960913, 0.83771303, 0.69398833,
              0.690486  , 0.65288181, 0.73870196, 0.62867394, 0.71065053,
              0.59676599, 0.64056241, 0.73523886, 0.77462475, 0.60724987,
              0.57575961, 0.74008839, 0.64553493, 0.69115147, 0.67757179,
              0.70455984, 0.54153527, 0.74644066, 0.52912446, 0.72533453,
              0.83873877, 0.61858944, 0.61656184, 0.65618602, 0.6562887 ,
              0.71366943, 0.57731975, 0.73877532, 0.73221722, 0.66936346,
              0.78848666, 0.59347536, 0.71903255, 0.72948007, 0.64234444,
              0.65412325, 0.58832356, 0.7874654 , 0.68625873, 0.74450137,
              0.68488457, 0.78177028, 0.73993255, 0.75281316, 0.7561772 ,
              0.72803663, 0.56230628, 0.64556136, 0.73942222, 0.57611533,
              0.53073737, 0.73579452, 0.79741313, 0.75953625, 0.62210253,
              0.51023018, 0.80289795, 0.72259879, 0.70497134, 0.69541771,
              0.57941638, 0.76206032, 0.80877991, 0.60514594, 0.71629662,
              0.78878036, 0.6325054 , 0.64344264, 0.6931834 , 0.6049189 ,
              0.65773932, 0.73564377, 0.74369433, 0.73605618, 0.71533481,
              0.81389273, 0.74804619, 0.73251198, 0.67247597, 0.78815153,
              0.62957159, 0.77918839, 0.68275462, 0.67315462, 0.67282055,
              0.82026568, 0.79461176, 0.80850957, 0.5855859 , 0.70231072,
              0.78480773, 0.71623311, 0.80006304, 0.79776426, 0.69922491,
              0.8304343 , 0.80709208, 0.66784191, 0.76368357, 0.74175972,
              0.73369282, 0.601717  , 0.60887853, 0.70186927, 0.60841751,
              0.7611368 , 0.78088857, 0.70672839, 0.74502976, 0.78565187,
              0.6704099 , 0.66662437, 0.65823002, 0.61986836, 0.65751196,
              0.74191122, 0.68170733, 0.74954783, 0.77127849, 0.55603886,
              0.65750212, 0.82502794, 0.71079862, 0.68993747, 0.7853928 ,
              0.70787921, 0.80985327, 0.73250825, 0.83652006, 0.62359217,
              0.67203978, 0.78519976, 0.68251132, 0.76776433, 0.71979217,
              0.66644173, 0.68115825, 0.59472634, 0.77033029, 0.58720364,
              0.70606016, 0.71761296, 0.66642064, 0.76785048, 0.6372144 ,
              0.65875274, 0.78216849, 0.7664636 , 0.77431719, 0.6552967 ,
              0.73197203, 0.69274839, 0.75826875, 0.82121916, 0.70106291,
              0.7116144 , 0.62545445, 0.64366758, 0.75453014, 0.72183423]])

    • stt_eth::raw
      (chain, draw, stt_eth::raw_dim_0)
      float64
      -0.1001 -0.1798 ... 0.2956 0.07025

      array([[[-0.10005218, -0.17976914, -0.09287639, ..., -0.05772422,
                0.34639025,  0.25592839],
              [ 0.02024038, -0.09778767, -0.18914986, ..., -0.17003467,
                0.20798386, -0.02620975],
              [ 0.04456695, -0.04690262, -0.13941927, ..., -0.28058359,
                0.205815  , -0.1397181 ],
              ...,
              [-0.27126481,  0.00456292,  0.01104813, ..., -0.22856139,
                0.71634974,  0.01959798],
              [-0.07488154, -0.11718699,  0.06765698, ..., -0.03671952,
                0.11918367, -0.12202842],
              [-0.13126015,  0.01828983, -0.2122843 , ..., -0.21794583,
                0.29564486,  0.07024694]]], shape=(1, 200, 204))

    • stt_eth::re
      (chain, draw, stt_eth::re_dim_0)
      float64
      -0.001947 -0.003498 ... 0.001351

      array([[[-1.94691162e-03, -3.49812104e-03, -1.80727827e-03, ...,
               -1.12325345e-03,  6.74039521e-03,  4.98010109e-03],
              [ 5.02719553e-04, -2.42879697e-03, -4.69800112e-03, ...,
               -4.22322848e-03,  5.16578979e-03, -6.50983445e-04],
              [ 1.08915677e-03, -1.14623737e-03, -3.40722097e-03, ...,
               -6.85708872e-03,  5.02984410e-03, -3.41452414e-03],
              ...,
              [-1.42956261e-01,  2.40465617e-03,  5.82235271e-03, ...,
               -1.20451606e-01,  3.77515543e-01,  1.03281139e-02],
              [-2.24412540e-03, -3.51197780e-03,  2.02761257e-03, ...,
               -1.10044744e-03,  3.57181641e-03, -3.65707057e-03],
              [-2.52461184e-03,  3.51780281e-04, -4.08300215e-03, ...,
               -4.19189412e-03,  5.68632999e-03,  1.35110504e-03]]],
            shape=(1, 200, 204))

    • stt_eth::sigma
      (chain, draw)
      float64
      0.01946 0.02484 ... 0.02997 0.01923

      array([[0.01945896, 0.02483746, 0.02443867, 0.5081427 , 0.48158239,
              0.58955898, 0.02061836, 0.02257244, 0.47381683, 0.48018585,
              0.02031043, 0.02032222, 0.52749427, 0.01579054, 0.5957981 ,
              0.02508179, 0.02493017, 0.02127927, 0.02592088, 0.02148471,
              0.02272374, 0.51070937, 0.49253987, 0.02323248, 0.01804935,
              0.02388824, 0.02243681, 0.54917049, 0.02415858, 0.496113  ,
              0.02112523, 0.02122053, 0.44209505, 0.01868659, 0.02569226,
              0.52005852, 0.02835513, 0.02161131, 0.02438186, 0.02190894,
              0.02591265, 0.50966278, 0.02655017, 0.53063842, 0.01911115,
              0.49138838, 0.44013578, 0.02215257, 0.01922091, 0.02187251,
              0.51253786, 0.02230749, 0.02064636, 0.49175135, 0.02556845,
              0.01691961, 0.44992659, 0.02161005, 0.47374599, 0.0212611 ,
              0.0261251 , 0.4831849 , 0.55374163, 0.01714929, 0.44572667,
              0.49655905, 0.49304105, 0.02158141, 0.02478006, 0.55827913,
              0.02592138, 0.51720152, 0.02065952, 0.02296178, 0.0236107 ,
              0.02187134, 0.52499898, 0.02134094, 0.02838881, 0.02131641,
              0.01908861, 0.02519159, 0.02057112, 0.02335156, 0.02978279,
              0.03184294, 0.48766141, 0.60432352, 0.01476569, 0.50902056,
              0.52921284, 0.02009418, 0.01609008, 0.0198034 , 0.58496773,
              0.49341693, 0.01829804, 0.02374506, 0.02159072, 0.02062053,
              0.48582798, 0.02330398, 0.02410494, 0.54614403, 0.02215492,
              0.02950031, 0.02077091, 0.5517788 , 0.02466423, 0.50197147,
              0.0213943 , 0.02137185, 0.02429254, 0.02178737, 0.01783922,
              0.025829  , 0.02508762, 0.01842548, 0.01831611, 0.01870634,
              0.54894683, 0.01693626, 0.01929417, 0.01416051, 0.53404662,
              0.02368445, 0.01817348, 0.02373431, 0.47348462, 0.02076365,
              0.02750835, 0.02299491, 0.0228315 , 0.02241999, 0.47440854,
              0.01877382, 0.02937811, 0.49339146, 0.02586065, 0.02820184,
              0.02827471, 0.4921189 , 0.50154345, 0.5119933 , 0.48429946,
              0.02702251, 0.02033731, 0.01896364, 0.02543428, 0.02977471,
              0.01964849, 0.01931752, 0.5976074 , 0.49240288, 0.02517403,
              0.01907748, 0.02358239, 0.02770135, 0.02301773, 0.50196567,
              0.02052709, 0.02399788, 0.02196803, 0.02149095, 0.01839405,
              0.02551696, 0.02063519, 0.01882759, 0.02204709, 0.01931078,
              0.51825022, 0.01686463, 0.02483233, 0.03464053, 0.01805251,
              0.51676646, 0.01905626, 0.56475592, 0.0362369 , 0.48957112,
              0.03213554, 0.4679772 , 0.49879234, 0.02489215, 0.52525215,
              0.57025574, 0.02413967, 0.0179153 , 0.0215035 , 0.0252261 ,
              0.01587295, 0.0264971 , 0.02408873, 0.01999069, 0.01976173,
              0.02135235, 0.48110899, 0.52699892, 0.02996901, 0.01923365]])

    • stt_inc::raw
      (chain, draw, stt_inc::raw_dim_0)
      float64
      0.03465 -0.1598 ... 0.001327

      array([[[ 0.03464617, -0.15978203,  0.13442634, ...,  0.35301733,
               -0.13602671, -0.03495404],
              [ 0.11603703,  0.09640014,  0.25209577, ...,  0.18539628,
                0.04107794,  0.01436572],
              [ 0.06872347,  0.04797068,  0.17743086, ...,  0.24598679,
               -0.09313738,  0.07876704],
              ...,
              [ 0.07304528,  0.07903831, -0.29352915, ...,  0.12814368,
               -0.19351594, -0.02628112],
              [ 0.1185919 , -0.0325193 ,  0.05155271, ...,  0.02813712,
               -0.07400831, -0.08344153],
              [-0.02044238, -0.05925928, -0.00354094, ...,  0.26790106,
               -0.2156815 ,  0.0013274 ]]], shape=(1, 200, 255))

    • stt_inc::re
      (chain, draw, stt_inc::re_dim_0)
      float64
      0.0002668 -0.00123 ... 6.339e-06

      array([[[ 2.66783404e-04, -1.23035789e-03,  1.03511335e-03, ...,
                2.71831359e-03, -1.04743653e-03, -2.69154041e-04],
              [ 1.22355831e-03,  1.01649611e-03,  2.65823650e-03, ...,
                1.95492038e-03,  4.33148384e-04,  1.51480014e-04],
              [ 5.06944786e-04,  3.53860016e-04,  1.30883453e-03, ...,
                1.81454342e-03, -6.87036134e-04,  5.81032085e-04],
              ...,
              [ 7.64885813e-04,  8.27641199e-04, -3.07365910e-03, ...,
                1.34184280e-03, -2.02638151e-03, -2.75199964e-04],
              [ 7.99352929e-04, -2.19192025e-04,  3.47484167e-04, ...,
                1.89654507e-04, -4.98843157e-04, -5.62426521e-04],
              [-9.76267567e-05, -2.83004806e-04, -1.69104773e-05, ...,
                1.27941631e-03, -1.03003108e-03,  6.33927296e-06]]],
            shape=(1, 200, 255))

    • stt_inc::sigma
      (chain, draw)
      float64
      0.0077 0.01054 ... 0.00674 0.004776

      array([[0.00770023, 0.01054455, 0.00737659, 0.01105143, 0.01011072,
              0.0093797 , 0.00705931, 0.00883941, 0.01107214, 0.00975191,
              0.00601781, 0.00876624, 0.01040391, 0.00739756, 0.01251331,
              0.00704643, 0.00719423, 0.00869158, 0.00600975, 0.00782241,
              0.0076801 , 0.0093537 , 0.01167105, 0.00634029, 0.00642879,
              0.00579343, 0.00632271, 0.01206897, 0.0077821 , 0.01004862,
              0.00771503, 0.00693709, 0.00788793, 0.00813077, 0.00592187,
              0.00952728, 0.00760323, 0.0082627 , 0.00737139, 0.00650112,
              0.00804778, 0.00958624, 0.00518136, 0.0123129 , 0.00724945,
              0.00977901, 0.01327799, 0.00937786, 0.00662331, 0.00536107,
              0.01128424, 0.0071339 , 0.00707531, 0.01092463, 0.00632968,
              0.00792125, 0.01241559, 0.00731873, 0.01143452, 0.00639365,
              0.0063324 , 0.01160715, 0.01142151, 0.0069286 , 0.01106219,
              0.01266509, 0.00836598, 0.00533848, 0.00689564, 0.01147891,
              0.00931676, 0.01040181, 0.00784176, 0.00711925, 0.00775364,
              0.00641089, 0.01036168, 0.00701011, 0.00697697, 0.00699814,
              0.00611581, 0.0092191 , 0.00565811, 0.00667058, 0.00715582,
              0.00700726, 0.0113495 , 0.01102826, 0.00525508, 0.00901736,
              0.01009816, 0.00588079, 0.0061342 , 0.00903896, 0.0090573 ,
              0.01142557, 0.00730781, 0.00643929, 0.00519396, 0.00874826,
              0.00967661, 0.009585  , 0.00739067, 0.00911692, 0.00676987,
              0.00605617, 0.00528148, 0.01144048, 0.00682648, 0.01077439,
              0.00654596, 0.00717994, 0.00617506, 0.00745827, 0.00977398,
              0.00602506, 0.00815212, 0.00783637, 0.00765857, 0.00725297,
              0.01279389, 0.00779896, 0.00804058, 0.00700996, 0.01266478,
              0.00866223, 0.00532958, 0.01122821, 0.01382674, 0.00609004,
              0.00489212, 0.00583384, 0.00722292, 0.01063674, 0.00961126,
              0.00703355, 0.00681905, 0.01100822, 0.00833211, 0.00883681,
              0.00677102, 0.0136158 , 0.01177372, 0.01252419, 0.01114353,
              0.00901016, 0.00685762, 0.00652524, 0.00684125, 0.00597088,
              0.00678474, 0.00669495, 0.01496968, 0.00945175, 0.0073691 ,
              0.00773614, 0.00784135, 0.01051116, 0.00847697, 0.01003816,
              0.00714116, 0.00552876, 0.00673851, 0.00636227, 0.00769184,
              0.00457859, 0.00669741, 0.00871873, 0.00902841, 0.00771591,
              0.01072187, 0.00818989, 0.00628352, 0.00802559, 0.00673829,
              0.01030509, 0.0067336 , 0.01323707, 0.00563873, 0.0110515 ,
              0.00787134, 0.01151332, 0.01239139, 0.00788911, 0.00784836,
              0.01241314, 0.00558263, 0.00725136, 0.00582358, 0.0066221 ,
              0.0053142 , 0.00812159, 0.00722458, 0.00769187, 0.00614829,
              0.00704446, 0.01088031, 0.01047139, 0.00674037, 0.0047757 ]])

  • Indexes: (38)
    • chain
      PandasIndex

      PandasIndex(Index([0], dtype='int64', name='chain'))

      </input></input>
    • draw
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             190, 191, 192, 193, 194, 195, 196, 197, 198, 199],
            dtype='int64', name='draw', length=200))

      </input></input>
    • age::raw_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='age::raw_dim_0'))

      </input></input>
    • age::raw_slope_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='age::raw_slope_dim_0'))

      </input></input>
    • age::re_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='age::re_dim_0'))

      </input></input>
    • age::re_slope_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='age::re_slope_dim_0'))

      </input></input>
    • eth::raw_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='eth::raw_dim_0'))

      </input></input>
    • eth::raw_slope_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='eth::raw_slope_dim_0'))

      </input></input>
    • eth::re_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='eth::re_dim_0'))

      </input></input>
    • eth::re_slope_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3], dtype='int64', name='eth::re_slope_dim_0'))

      </input></input>
    • eth_age::raw_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], dtype='int64', name='eth_age::raw_dim_0'))

      </input></input>
    • eth_age::re_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], dtype='int64', name='eth_age::re_dim_0'))

      </input></input>
    • eth_inc::raw_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], dtype='int64', name='eth_inc::raw_dim_0'))

      </input></input>
    • eth_inc::re_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], dtype='int64', name='eth_inc::re_dim_0'))

      </input></input>
    • inc::raw_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4], dtype='int64', name='inc::raw_dim_0'))

      </input></input>
    • inc::re_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4], dtype='int64', name='inc::re_dim_0'))

      </input></input>
    • inc_age::raw_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], dtype='int64', name='inc_age::raw_dim_0'))

      </input></input>
    • inc_age::re_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], dtype='int64', name='inc_age::re_dim_0'))

      </input></input>
    • reg::raw_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4], dtype='int64', name='reg::raw_dim_0'))

      </input></input>
    • reg::raw_slope_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4], dtype='int64', name='reg::raw_slope_dim_0'))

      </input></input>
    • reg::re_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4], dtype='int64', name='reg::re_dim_0'))

      </input></input>
    • reg::re_slope_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4], dtype='int64', name='reg::re_slope_dim_0'))

      </input></input>
    • reg_age::raw_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], dtype='int64', name='reg_age::raw_dim_0'))

      </input></input>
    • reg_age::re_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], dtype='int64', name='reg_age::re_dim_0'))

      </input></input>
    • reg_eth::raw_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], dtype='int64', name='reg_eth::raw_dim_0'))

      </input></input>
    • reg_eth::re_dim_0
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], dtype='int64', name='reg_eth::re_dim_0'))

      </input></input>
    • reg_inc::raw_dim_0
      PandasIndex

      PandasIndex(Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24],
            dtype='int64', name='reg_inc::raw_dim_0'))

      </input></input>
    • reg_inc::re_dim_0
      PandasIndex

      PandasIndex(Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24],
            dtype='int64', name='reg_inc::re_dim_0'))

      </input></input>
    • stt::raw_dim_0
      PandasIndex

      PandasIndex(Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50],
            dtype='int64', name='stt::raw_dim_0'))

      </input></input>
    • stt::raw_slope_dim_0
      PandasIndex

      PandasIndex(Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50],
            dtype='int64', name='stt::raw_slope_dim_0'))

      </input></input>
    • stt::re_dim_0
      PandasIndex

      PandasIndex(Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50],
            dtype='int64', name='stt::re_dim_0'))

      </input></input>
    • stt::re_slope_dim_0
      PandasIndex

      PandasIndex(Index([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
             18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
             36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50],
            dtype='int64', name='stt::re_slope_dim_0'))

      </input></input>
    • stt_age::raw_dim_0
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             194, 195, 196, 197, 198, 199, 200, 201, 202, 203],
            dtype='int64', name='stt_age::raw_dim_0', length=204))

      </input></input>
    • stt_age::re_dim_0
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             194, 195, 196, 197, 198, 199, 200, 201, 202, 203],
            dtype='int64', name='stt_age::re_dim_0', length=204))

      </input></input>
    • stt_eth::raw_dim_0
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             194, 195, 196, 197, 198, 199, 200, 201, 202, 203],
            dtype='int64', name='stt_eth::raw_dim_0', length=204))

      </input></input>
    • stt_eth::re_dim_0
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             194, 195, 196, 197, 198, 199, 200, 201, 202, 203],
            dtype='int64', name='stt_eth::re_dim_0', length=204))

      </input></input>
    • stt_inc::raw_dim_0
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             245, 246, 247, 248, 249, 250, 251, 252, 253, 254],
            dtype='int64', name='stt_inc::raw_dim_0', length=255))

      </input></input>
    • stt_inc::re_dim_0
      PandasIndex

      PandasIndex(Index([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,
             ...
             245, 246, 247, 248, 249, 250, 251, 252, 253, 254],
            dtype='int64', name='stt_inc::re_dim_0', length=255))

      </input></input>
  • Attributes: (2)

    created_at :

    2025-12-05T12:59:15.097280+00:00

    arviz_version :

    0.22.0

  
  
• observed_data

  <xarray.Dataset> Size: 50kB
  Dimensions:  (obs_id: 3127)
  Coordinates:
    * obs_id   (obs_id) int64 25kB 0 1 2 3 4 5 6 ... 4070 4071 4073 4074 4077 4078
  Data variables:
      y_obs    (obs_id) int64 25kB 4 6 15 23 17 12 19 38 10 ... 1 2 1 6 1 1 3 1 1
  Attributes:
      created_at:                 2025-12-05T12:59:15.167498+00:00
      arviz_version:              0.22.0
      inference_library:          pymc
      inference_library_version:  5.26.1

  xarray.Dataset

  • Dimensions:
    • obs_id: 3127
  • Coordinates: (1)
    • obs_id
      (obs_id)
      int64
      0 1 2 3 4 ... 4073 4074 4077 4078

      array([   0,    1,    2, ..., 4074, 4077, 4078], shape=(3127,))

  • Data variables: (1)
    • y_obs
      (obs_id)
      int64
      4 6 15 23 17 12 19 ... 6 1 1 3 1 1

      array([ 4,  6, 15, ...,  3,  1,  1], shape=(3127,))

  • Indexes: (1)
    • obs_id
      PandasIndex

      PandasIndex(Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,
             ...
             4063, 4066, 4068, 4069, 4070, 4071, 4073, 4074, 4077, 4078],
            dtype='int64', name='obs_id', length=3127))

      </input></input>
  • Attributes: (4)

    created_at :

    2025-12-05T12:59:15.167498+00:00

    arviz_version :

    0.22.0

    inference_library :

    pymc

    inference_library_version :

    5.26.1

  
  
• constant_data

  <xarray.Dataset> Size: 100kB
  Dimensions:   (obs_id: 3127)
  Coordinates:
    * obs_id    (obs_id) int64 25kB 0 1 2 3 4 5 ... 4070 4071 4073 4074 4077 4078
  Data variables:
      z_inc     (obs_id) float64 25kB -0.707 -0.707 -0.707 ... 0.3535 0.707 0.707
      z_incstt  (obs_id) float64 25kB -0.6491 -0.6491 -0.6491 ... -0.1106 -0.1106
      z_trnprv  (obs_id) float64 25kB -0.4547 -0.4547 -0.4547 ... 0.1959 0.1959
  Attributes:
      created_at:                 2025-12-05T12:59:15.168989+00:00
      arviz_version:              0.22.0
      inference_library:          pymc
      inference_library_version:  5.26.1

  xarray.Dataset

  • Dimensions:
    • obs_id: 3127
  • Coordinates: (1)
    • obs_id
      (obs_id)
      int64
      0 1 2 3 4 ... 4073 4074 4077 4078

      array([   0,    1,    2, ..., 4074, 4077, 4078], shape=(3127,))

  • Data variables: (3)
    • z_inc
      (obs_id)
      float64
      -0.707 -0.707 ... 0.707 0.707

      array([-0.70702012, -0.70702012, -0.70702012, ...,  0.35351006,
              0.70702012,  0.70702012], shape=(3127,))

    • z_incstt
      (obs_id)
      float64
      -0.6491 -0.6491 ... -0.1106 -0.1106

      array([-0.64907875, -0.64907875, -0.64907875, ..., -0.11058141,
             -0.11058141, -0.11058141], shape=(3127,))

    • z_trnprv
      (obs_id)
      float64
      -0.4547 -0.4547 ... 0.1959 0.1959

      array([-0.45468479, -0.45468479, -0.45468479, ...,  0.19587437,
              0.19587437,  0.19587437], shape=(3127,))

  • Indexes: (1)
    • obs_id
      PandasIndex

      PandasIndex(Index([   0,    1,    2,    3,    4,    5,    6,    7,    8,    9,
             ...
             4063, 4066, 4068, 4069, 4070, 4071, 4073, 4074, 4077, 4078],
            dtype='int64', name='obs_id', length=3127))

      </input></input>
  • Attributes: (4)

    created_at :

    2025-12-05T12:59:15.168989+00:00

    arviz_version :

    0.22.0

    inference_library :

    pymc

    inference_library_version :

    5.26.1

  
  
• pathfinder

  <xarray.Dataset> Size: 85kB
  Dimensions:                     (status: 12, path: 7, param: 941)
  Coordinates:
    * status                      (status) <U26 1kB 'CONVERGED' ... 'SUCCESS'
    * path                        (path) int64 56B 0 1 2 3 4 5 6
    * param                       (param) <U22 83kB 'b_0' ... 'inc_age::raw[19]'
  Data variables: (12/35)
      compile_time                float64 8B 2.876
      compute_time                float64 8B 83.67
      total_time                  float64 8B 86.55
      importance_sampling_method  <U4 16B 'psis'
      pareto_k                    float64 8B 9.31
      lbfgs_status_counts         (status) float64 96B 7.0 nan 3.0 ... 0.0 nan nan
      ...                          ...
      config/gtol                 float64 8B 1e-08
      config/maxls                int64 8B 1000
      config/jitter               float64 8B 2.0
      config/epsilon              float64 8B 1e-08
      config/num_elbo_draws       int64 8B 10
      config/num_retries          int64 8B 0
  Attributes:
      warnings:  ['INIT_FAILED: LBFGS failed to initialize. Consider reparamete...

  xarray.Dataset

  • Dimensions:
    • status: 12
    • path: 7
    • param: 941
  • Coordinates: (3)
    • status
      (status)
      <U26
      'CONVERGED' ... 'SUCCESS'

      array(['CONVERGED', 'ELBO_ARGMAX_AT_ZERO', 'INIT_FAILED',
             'INIT_FAILED_LOW_UPDATE_PCT', 'INVALID_LOGP', 'INVALID_LOGQ',
             'LBFGS_FAILED', 'LOW_UPDATE_PCT', 'MAX_ITER_REACHED', 'NON_FINITE',
             'PATH_FAILED', 'SUCCESS'], dtype='<U26')

    • path
      (path)
      int64
      0 1 2 3 4 5 6

      array([0, 1, 2, 3, 4, 5, 6])

    • param
      (param)
      <U22
      'b_0' ... 'inc_age::raw[19]'

      array(['b_0', 'b_z_inc', 'b_z_incstt', ..., 'inc_age::raw[17]',
             'inc_age::raw[18]', 'inc_age::raw[19]'], shape=(941,), dtype='<U22')

  • Data variables: (35)
    • compile_time
      ()
      float64
      2.876

      array(2.87595606)

    • compute_time
      ()
      float64
      83.67

      array(83.66940689)

    • total_time
      ()
      float64
      86.55

      array(86.54536295)

    • importance_sampling_method
      ()
      <U4
      'psis'

      array('psis', dtype='<U4')

    • pareto_k
      ()
      float64
      9.31

      array(9.30953372)

    • lbfgs_status_counts
      (status)
      float64
      7.0 nan 3.0 0.0 ... 0.0 0.0 nan nan

      array([ 7., nan,  3.,  0., nan, nan,  0.,  0.,  0.,  0., nan, nan])

    • path_status_counts
      (status)
      float64
      nan 0.0 nan nan ... nan nan 0.0 7.0

      array([nan,  0., nan, nan,  0.,  0.,  3., nan, nan, nan,  0.,  7.])

    • all_paths_failed
      ()
      bool
      False

      array(False)

    • num_successful_paths
      ()
      int64
      200

      array(200)

    • lbfgs_niter_mean
      ()
      float64
      284.3

      array(284.28571429)

    • lbfgs_niter_std
      ()
      float64
      43.24

      array(43.23924899)

    • elbo_argmax_mean
      ()
      float64
      78.86

      array(78.85714286)

    • elbo_argmax_std
      ()
      float64
      21.91

      array(21.90517598)

    • logP_mean
      ()
      float64
      -6.465e+03

      array(-6464.95491398)

    • logP_std
      ()
      float64
      166.0

      array(165.99286793)

    • logP_max
      ()
      float64
      -6.102e+03

      array(-6101.86538904)

    • logQ_mean
      ()
      float64
      927.0

      array(926.98235136)

    • logQ_std
      ()
      float64
      179.6

      array(179.63824298)

    • logQ_max
      ()
      float64
      1.396e+03

      array(1396.13479663)

    • paths/lbfgs_niter
      (path)
      int64
      245 268 263 246 379 304 285

      array([245, 268, 263, 246, 379, 304, 285])

    • paths/elbo_argmax
      (path)
      int64
      71 73 64 132 74 69 69

      array([ 71,  73,  64, 132,  74,  69,  69])

    • paths/logP_mean
      (path)
      float64
      -6.437e+03 ... -6.607e+03

      array([-6436.65494732, -6332.13067241, -6579.89180069, -6140.28420415,
             -6603.30649658, -6555.16992574, -6607.24635098])

    • paths/logP_max
      (path)
      float64
      -6.388e+03 ... -6.563e+03

      array([-6387.93013078, -6285.66214219, -6530.05277597, -6101.86538904,
             -6544.96607603, -6508.46793344, -6563.45515961])

    • paths/logQ_mean
      (path)
      float64
      835.6 949.9 905.6 ... 914.4 815.1

      array([ 835.58705407,  949.87675421,  905.57321372, 1332.18403393,
              736.14040748,  914.39493492,  815.12006123])

    • paths/logQ_max
      (path)
      float64
      892.0 1.019e+03 ... 982.8 880.9

      array([ 892.01504553, 1018.6086131 ,  983.54434847, 1396.13479663,
              802.17346513,  982.77047487,  880.92984565])

    • config/num_draws
      ()
      int64
      1000

      array(1000)

    • config/maxcor
      ()
      int32
      21

      array(21, dtype=int32)

    • config/maxiter
      ()
      int64
      1000

      array(1000)

    • config/ftol
      ()
      float64
      1e-05

      array(1.e-05)

    • config/gtol
      ()
      float64
      1e-08

      array(1.e-08)

    • config/maxls
      ()
      int64
      1000

      array(1000)

    • config/jitter
      ()
      float64
      2.0

      array(2.)

    • config/epsilon
      ()
      float64
      1e-08

      array(1.e-08)

    • config/num_elbo_draws
      ()
      int64
      10

      array(10)

    • config/num_retries
      ()
      int64
      0

      array(0)

  • Indexes: (3)
    • status
      PandasIndex

      PandasIndex(Index(['CONVERGED', 'ELBO_ARGMAX_AT_ZERO', 'INIT_FAILED',
             'INIT_FAILED_LOW_UPDATE_PCT', 'INVALID_LOGP', 'INVALID_LOGQ',
             'LBFGS_FAILED', 'LOW_UPDATE_PCT', 'MAX_ITER_REACHED', 'NON_FINITE',
             'PATH_FAILED', 'SUCCESS'],
            dtype='object', name='status'))

      </input></input>
    • path
      PandasIndex

      PandasIndex(Index([0, 1, 2, 3, 4, 5, 6], dtype='int64', name='path'))

      </input></input>
    • param
      PandasIndex

      PandasIndex(Index(['b_0', 'b_z_inc', 'b_z_incstt', 'b_z_trnprv', 'b_z_inc_z_incstt',
             'b_z_inc_z_trnprv', 'reg::sigma_log__', 'reg::raw[0]', 'reg::raw[1]',
             'reg::raw[2]',
             ...
             'inc_age::raw[10]', 'inc_age::raw[11]', 'inc_age::raw[12]',
             'inc_age::raw[13]', 'inc_age::raw[14]', 'inc_age::raw[15]',
             'inc_age::raw[16]', 'inc_age::raw[17]', 'inc_age::raw[18]',
             'inc_age::raw[19]'],
            dtype='object', name='param', length=941))

      </input></input>
  • Attributes: (1)

    warnings :

    ['INIT_FAILED: LBFGS failed to initialize. Consider reparameterizing the model or reducing jitter if this occurence is high relative to the number of paths.']

  
  

In [ ]: