Bayesian Estimation and Variable Selection for Group Differences in Markov Random Fields
Source:R/bgmCompare.R
bgmCompare.RdThe bgmCompare function estimates group differences in category
threshold parameters (main effects) and pairwise interactions (pairwise
effects) of a Markov Random Field (MRF) for binary and ordinal variables.
Groups can be defined either by supplying two separate datasets (x and
y) or by a group membership vector. Optionally, Bayesian variable
selection can be applied to identify differences across groups.
Usage
bgmCompare(
x,
y,
group_indicator,
difference_selection = TRUE,
variable_type = "ordinal",
baseline_category,
difference_scale = 1,
difference_prior = c("Bernoulli", "Beta-Bernoulli"),
difference_probability = 0.5,
beta_bernoulli_alpha = 1,
beta_bernoulli_beta = 1,
pairwise_scale = 2.5,
main_alpha = 0.5,
main_beta = 0.5,
iter = 1000,
warmup = 1000,
na_action = c("listwise", "impute"),
update_method = c("nuts", "adaptive-metropolis", "hamiltonian-mc"),
target_accept,
hmc_num_leapfrogs = 100,
nuts_max_depth = 10,
learn_mass_matrix = FALSE,
chains = 4,
cores = parallel::detectCores(),
display_progress = c("per-chain", "total", "none"),
seed = NULL,
main_difference_model,
reference_category,
main_difference_scale,
pairwise_difference_scale,
pairwise_difference_prior,
main_difference_prior,
pairwise_difference_probability,
main_difference_probability,
pairwise_beta_bernoulli_alpha,
pairwise_beta_bernoulli_beta,
main_beta_bernoulli_alpha,
main_beta_bernoulli_beta,
interaction_scale,
threshold_alpha,
threshold_beta,
burnin,
save
)Arguments
- x
A data frame or matrix of binary and ordinal responses for Group 1. Variables should be coded as nonnegative integers starting at 0. For ordinal variables, unused categories are collapsed; for Blume–Capel variables, all categories are retained.
- y
Optional data frame or matrix for Group 2 (two-group designs). Must have the same variables (columns) as
x.- group_indicator
Optional integer vector of group memberships for rows of
x(multi-group designs). Ignored ifyis supplied.- difference_selection
Logical. If
TRUE, spike-and-slab priors are applied to difference parameters. Default:TRUE.- variable_type
Character vector specifying type of each variable:
"ordinal"(default) or"blume-capel".- baseline_category
Integer or vector giving the baseline category for Blume–Capel variables.
- difference_scale
Double. Scale of the Cauchy prior for difference parameters. Default:
1.- difference_prior
Character. Prior for difference inclusion:
"Bernoulli"or"Beta-Bernoulli". Default:"Bernoulli".- difference_probability
Numeric. Prior inclusion probability for differences (Bernoulli prior). Default:
0.5.- beta_bernoulli_alpha, beta_bernoulli_beta
Doubles. Shape parameters of the Beta prior for inclusion probabilities in the Beta–Bernoulli model. Defaults:
1.- pairwise_scale
Double. Scale of the Cauchy prior for baseline pairwise interactions. Default:
2.5.- main_alpha, main_beta
Doubles. Shape parameters of the beta-prime prior for baseline threshold parameters. Defaults:
0.5.- iter
Integer. Number of post–warmup iterations per chain. Default:
1e3.- warmup
Integer. Number of warmup iterations before sampling. Default:
1e3.- na_action
Character. How to handle missing data:
"listwise"(drop rows) or"impute"(impute within Gibbs). Default:"listwise".- update_method
Character. Sampling algorithm:
"adaptive-metropolis","hamiltonian-mc", or"nuts". Default:"nuts".- target_accept
Numeric between 0 and 1. Target acceptance rate. Defaults: 0.44 (Metropolis), 0.65 (HMC), 0.80 (NUTS).
- hmc_num_leapfrogs
Integer. Leapfrog steps for HMC. Default:
100.- nuts_max_depth
Integer. Maximum tree depth for NUTS. Default:
10.- learn_mass_matrix
Logical. If
TRUE, adapt the mass matrix during warmup (HMC/NUTS only). Default:FALSE.- chains
Integer. Number of parallel chains. Default:
4.- cores
Integer. Number of CPU cores. Default:
parallel::detectCores().- display_progress
Character. Controls progress reporting:
"per-chain","total", or"none". Default:"per-chain".- seed
Optional integer. Random seed for reproducibility.
- main_difference_model, reference_category, pairwise_difference_scale, main_difference_scale, pairwise_difference_prior, main_difference_prior, pairwise_difference_probability, main_difference_probability, pairwise_beta_bernoulli_alpha, pairwise_beta_bernoulli_beta, main_beta_bernoulli_alpha, main_beta_bernoulli_beta, interaction_scale, threshold_alpha, threshold_beta, burnin, save
`r lifecycle::badge("deprecated")` Deprecated arguments as of **bgms 0.1.6.0**. Use `difference_scale`, `difference_prior`, `difference_probability`, `beta_bernoulli_alpha`, `beta_bernoulli_beta`, `baseline_category`, `pairwise_scale`, and `warmup` instead.
Value
A list of class "bgmCompare" containing posterior summaries,
posterior mean matrices, and raw MCMC samples:
posterior_summary_main_baseline,posterior_summary_pairwise_baseline: summaries of baseline thresholds and pairwise interactions.posterior_summary_main_differences,posterior_summary_pairwise_differences: summaries of group differences in thresholds and pairwise interactions.posterior_summary_indicator: summaries of inclusion indicators (ifdifference_selection = TRUE).posterior_mean_main_baseline,posterior_mean_pairwise_baseline: posterior mean matrices (legacy style).raw_samples: list of raw draws per chain for main, pairwise, and indicator parameters.arguments: list of function call arguments and metadata.
The summary() method prints formatted summaries, and
coef() extracts posterior means.
NUTS diagnostics (tree depth, divergences, energy, E-BFMI) are included
in fit$nuts_diag if update_method = "nuts".
Details
This function extends the ordinal MRF framework Marsman et al. (2025) to multiple groups. The basic idea of modeling, analyzing, and testing group differences in MRFs was introduced in Marsman et al. (2024) , where two–group comparisons were conducted using adaptive Metropolis sampling. The present implementation generalizes that approach to more than two groups and supports additional samplers (HMC and NUTS) with staged warmup adaptation.
Key components of the model:
Pairwise Interactions
For variables \(i\) and \(j\), the group-specific interaction is represented as: $$\theta_{ij}^{(g)} = \phi_{ij} + \delta_{ij}^{(g)},$$ where \(\phi_{ij}\) is the baseline effect and \(\delta_{ij}^{(g)}\) are group differences constrained to sum to zero.
Ordinal Variables
Regular ordinal variables: category thresholds are decomposed into a baseline plus group differences for each category.
Blume–Capel variables: category thresholds are quadratic in the category index, with both the linear and quadratic terms split into a baseline plus group differences.
Variable Selection
When difference_selection = TRUE, spike-and-slab priors are
applied to difference parameters:
Bernoulli: fixed prior inclusion probability.
Beta–Bernoulli: inclusion probability given a Beta prior.
Sampling Algorithms and Warmup
Parameters are updated within a Gibbs framework, using the same
sampling algorithms and staged warmup scheme described in
bgm:
Adaptive Metropolis–Hastings: componentwise random–walk proposals with Robbins–Monro adaptation of proposal SDs.
Hamiltonian Monte Carlo (HMC): joint updates with fixed leapfrog trajectories; step size and optionally the mass matrix are adapted during warmup.
No–U–Turn Sampler (NUTS): an adaptive HMC variant with dynamic trajectory lengths; warmup uses the same staged adaptation schedule as HMC.
For details on the staged adaptation schedule (fast–slow–fast phases),
see bgm. In addition, when
difference_selection = TRUE, updates of inclusion indicators are
delayed until late warmup. In HMC/NUTS, this appends two extra phases
(Stage-3b and Stage-3c), so that the total number of warmup iterations
exceeds the user-specified warmup.
After warmup, adaptation is disabled: step size and mass matrix are fixed at their learned values, and proposal SDs remain constant.
References
Marsman M, van den Bergh D, Haslbeck JMB (2025).
“Bayesian analysis of the ordinal Markov random field.”
Psychometrika, 90, 146–-182.
Marsman M, Waldorp LJ, Sekulovski N, Haslbeck JMB (2024).
“Bayes factor tests for group differences in ordinal and binary graphical models.”
Retrieved from https://osf.io/preprints/osf/f4pk9.
OSF preprint.
See also
vignette("comparison", package = "bgms") for a worked example.
Examples
# \dontrun{
# Run bgmCompare on subset of the Boredom dataset
x = Boredom[Boredom$language == "fr", 2:6]
y = Boredom[Boredom$language != "fr", 2:6]
fit <- bgmCompare(x, y)
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 50/2200 (2.3%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 46/2200 (2.1%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 44/2200 (2.0%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 53/2200 (2.4%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 193/8800 (2.2%)
#> Elapsed: 24s | ETA: 17m 50s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 100/2200 (4.5%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 93/2200 (4.2%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 98/2200 (4.5%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 108/2200 (4.9%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 399/8800 (4.5%)
#> Elapsed: 57s | ETA: 20m
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 150/2200 (6.8%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 149/2200 (6.8%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 151/2200 (6.9%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 156/2200 (7.1%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 606/8800 (6.9%)
#> Elapsed: 1m 26s | ETA: 19m 22s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 200/2200 (9.1%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 199/2200 (9.0%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 201/2200 (9.1%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 213/2200 (9.7%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 813/8800 (9.2%)
#> Elapsed: 1m 56s | ETA: 18m 59s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 250/2200 (11.4%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 253/2200 (11.5%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 253/2200 (11.5%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 262/2200 (11.9%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1018/8800 (11.6%)
#> Elapsed: 2m 24s | ETA: 18m 20s
#> Chain 1 (Warmup): ⦗━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 300/2200 (13.6%)
#> Chain 2 (Warmup): ⦗━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 297/2200 (13.5%)
#> Chain 3 (Warmup): ⦗━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 296/2200 (13.5%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 305/2200 (13.9%)
#> Total (Warmup): ⦗━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1198/8800 (13.6%)
#> Elapsed: 2m 47s | ETA: 17m 39s
#> Chain 1 (Warmup): ⦗━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 350/2200 (15.9%)
#> Chain 2 (Warmup): ⦗━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 351/2200 (16.0%)
#> Chain 3 (Warmup): ⦗━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 350/2200 (15.9%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 364/2200 (16.5%)
#> Total (Warmup): ⦗━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1415/8800 (16.1%)
#> Elapsed: 3m 16s | ETA: 17m 2s
#> Chain 1 (Warmup): ⦗━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 400/2200 (18.2%)
#> Chain 2 (Warmup): ⦗━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 408/2200 (18.5%)
#> Chain 3 (Warmup): ⦗━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 405/2200 (18.4%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 415/2200 (18.9%)
#> Total (Warmup): ⦗━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1628/8800 (18.5%)
#> Elapsed: 3m 43s | ETA: 16m 22s
#> Chain 1 (Warmup): ⦗━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 450/2200 (20.5%)
#> Chain 2 (Warmup): ⦗━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 458/2200 (20.8%)
#> Chain 3 (Warmup): ⦗━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 452/2200 (20.5%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 468/2200 (21.3%)
#> Total (Warmup): ⦗━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1828/8800 (20.8%)
#> Elapsed: 4m 9s | ETA: 15m 49s
#> Chain 1 (Warmup): ⦗━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 500/2200 (22.7%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 501/2200 (22.8%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 494/2200 (22.5%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 519/2200 (23.6%)
#> Total (Warmup): ⦗━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2014/8800 (22.9%)
#> Elapsed: 4m 34s | ETA: 15m 23s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 550/2200 (25.0%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 546/2200 (24.8%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 535/2200 (24.3%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 566/2200 (25.7%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2197/8800 (25.0%)
#> Elapsed: 4m 58s | ETA: 14m 55s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 600/2200 (27.3%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 597/2200 (27.1%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 596/2200 (27.1%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 623/2200 (28.3%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2416/8800 (27.5%)
#> Elapsed: 5m 26s | ETA: 14m 21s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 650/2200 (29.5%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 644/2200 (29.3%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 647/2200 (29.4%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 668/2200 (30.4%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2609/8800 (29.6%)
#> Elapsed: 5m 49s | ETA: 13m 48s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 700/2200 (31.8%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 692/2200 (31.5%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 700/2200 (31.8%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 718/2200 (32.6%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2810/8800 (31.9%)
#> Elapsed: 6m 15s | ETA: 13m 19s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 750/2200 (34.1%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 740/2200 (33.6%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 746/2200 (33.9%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 759/2200 (34.5%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2995/8800 (34.0%)
#> Elapsed: 6m 39s | ETA: 12m 53s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 800/2200 (36.4%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 789/2200 (35.9%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 798/2200 (36.3%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 815/2200 (37.0%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 3202/8800 (36.4%)
#> Elapsed: 7m 5s | ETA: 12m 23s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━⦘ 850/2200 (38.6%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━⦘ 838/2200 (38.1%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━⦘ 851/2200 (38.7%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 861/2200 (39.1%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━⦘ 3400/8800 (38.6%)
#> Elapsed: 7m 32s | ETA: 11m 57s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━⦘ 900/2200 (40.9%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 876/2200 (39.8%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━⦘ 898/2200 (40.8%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 909/2200 (41.3%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━⦘ 3583/8800 (40.7%)
#> Elapsed: 7m 56s | ETA: 11m 33s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━⦘ 950/2200 (43.2%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 932/2200 (42.4%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━⦘ 946/2200 (43.0%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━⦘ 960/2200 (43.6%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━⦘ 3788/8800 (43.0%)
#> Elapsed: 8m 22s | ETA: 11m 4s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━⦘ 1000/2200 (45.5%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━⦘ 991/2200 (45.0%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━⦘ 1007/2200 (45.8%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━⦘ 1014/2200 (46.1%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━⦘ 4012/8800 (45.6%)
#> Elapsed: 8m 48s | ETA: 10m 30s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━⦘ 1050/2200 (47.7%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1036/2200 (47.1%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━⦘ 1063/2200 (48.3%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━⦘ 1064/2200 (48.4%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━⦘ 4213/8800 (47.9%)
#> Elapsed: 9m 13s | ETA: 10m 2s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1100/2200 (50.0%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1086/2200 (49.4%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━⦘ 1126/2200 (51.2%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━⦘ 1110/2200 (50.5%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━⦘ 4422/8800 (50.2%)
#> Elapsed: 9m 38s | ETA: 9m 32s
#> Chain 1 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1150/2200 (52.3%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1134/2200 (51.5%)
#> Chain 3 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━⦘ 1178/2200 (53.5%)
#> Chain 4 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━⦘ 1182/2200 (53.7%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━⦘ 4644/8800 (52.8%)
#> Elapsed: 9m 54s | ETA: 8m 51s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1200/2200 (54.5%)
#> Chain 2 (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1186/2200 (53.9%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━⦘ 1229/2200 (55.9%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━⦘ 1237/2200 (56.2%)
#> Total (Warmup): ⦗━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━⦘ 4852/8800 (55.1%)
#> Elapsed: 10m 7s | ETA: 8m 13s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1250/2200 (56.8%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1239/2200 (56.3%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━⦘ 1271/2200 (57.8%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1293/2200 (58.8%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 5053/8800 (57.4%)
#> Elapsed: 10m 20s | ETA: 7m 39s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1300/2200 (59.1%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1295/2200 (58.9%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1318/2200 (59.9%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━⦘ 1344/2200 (61.1%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 5257/8800 (59.7%)
#> Elapsed: 10m 35s | ETA: 7m 7s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1350/2200 (61.4%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1348/2200 (61.3%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1363/2200 (62.0%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━⦘ 1394/2200 (63.4%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 5455/8800 (62.0%)
#> Elapsed: 10m 48s | ETA: 6m 37s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━⦘ 1400/2200 (63.6%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━⦘ 1391/2200 (63.2%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1408/2200 (64.0%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━⦘ 1442/2200 (65.5%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 5641/8800 (64.1%)
#> Elapsed: 11m 1s | ETA: 6m 10s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━⦘ 1450/2200 (65.9%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━⦘ 1438/2200 (65.4%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1458/2200 (66.3%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━⦘ 1501/2200 (68.2%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 5847/8800 (66.4%)
#> Elapsed: 11m 16s | ETA: 5m 41s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━⦘ 1500/2200 (68.2%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1478/2200 (67.2%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━⦘ 1503/2200 (68.3%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━⦘ 1544/2200 (70.2%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━⦘ 6025/8800 (68.5%)
#> Elapsed: 11m 29s | ETA: 5m 17s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━⦘ 1550/2200 (70.5%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1531/2200 (69.6%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━⦘ 1559/2200 (70.9%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━⦘ 1603/2200 (72.9%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━⦘ 6243/8800 (70.9%)
#> Elapsed: 11m 43s | ETA: 4m 47s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━⦘ 1600/2200 (72.7%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1582/2200 (71.9%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━⦘ 1613/2200 (73.3%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━⦘ 1663/2200 (75.6%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━⦘ 6458/8800 (73.4%)
#> Elapsed: 11m 58s | ETA: 4m 20s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1650/2200 (75.0%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1640/2200 (74.5%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1678/2200 (76.3%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━⦘ 1707/2200 (77.6%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━⦘ 6675/8800 (75.9%)
#> Elapsed: 12m 12s | ETA: 3m 53s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1700/2200 (77.3%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1689/2200 (76.8%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━⦘ 1724/2200 (78.4%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1760/2200 (80.0%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━⦘ 6873/8800 (78.1%)
#> Elapsed: 12m 26s | ETA: 3m 29s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1750/2200 (79.5%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1741/2200 (79.1%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━⦘ 1769/2200 (80.4%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━⦘ 1821/2200 (82.8%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━⦘ 7081/8800 (80.5%)
#> Elapsed: 12m 39s | ETA: 3m 4s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1800/2200 (81.8%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1805/2200 (82.0%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1815/2200 (82.5%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━⦘ 1876/2200 (85.3%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━⦘ 7296/8800 (82.9%)
#> Elapsed: 12m 55s | ETA: 2m 39s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1850/2200 (84.1%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1846/2200 (83.9%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1863/2200 (84.7%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━⦘ 1931/2200 (87.8%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━⦘ 7490/8800 (85.1%)
#> Elapsed: 13m 7s | ETA: 2m 17s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1900/2200 (86.4%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1902/2200 (86.5%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1909/2200 (86.8%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━⦘ 1983/2200 (90.1%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 7694/8800 (87.4%)
#> Elapsed: 13m 22s | ETA: 1m 55s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━⦘ 1950/2200 (88.6%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1959/2200 (89.0%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 1971/2200 (89.6%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━⦘ 2043/2200 (92.9%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━⦘ 7923/8800 (90.0%)
#> Elapsed: 13m 38s | ETA: 1m 30s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━⦘ 2000/2200 (90.9%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2008/2200 (91.3%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2019/2200 (91.8%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━⦘ 2110/2200 (95.9%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 8137/8800 (92.5%)
#> Elapsed: 13m 52s | ETA: 1m 7s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━⦘ 2050/2200 (93.2%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2068/2200 (94.0%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2069/2200 (94.0%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺⦘ 2164/2200 (98.4%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 8351/8800 (94.9%)
#> Elapsed: 14m 7s | ETA: 46s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━⦘ 2100/2200 (95.5%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2119/2200 (96.3%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2119/2200 (96.3%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2200/2200 (100.0%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 8538/8800 (97.0%)
#> Elapsed: 14m 20s | ETA: 26s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺⦘ 2150/2200 (97.7%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2200/2200 (100.0%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2175/2200 (98.9%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2200/2200 (100.0%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 8725/8800 (99.1%)
#> Elapsed: 14m 33s | ETA: 8s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2200/2200 (100.0%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2200/2200 (100.0%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2200/2200 (100.0%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2200/2200 (100.0%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 8800/8800 (100.0%)
#> Elapsed: 14m 40s | ETA: 0s
#> Chain 1 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2200/2200 (100.0%)
#> Chain 2 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2200/2200 (100.0%)
#> Chain 3 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2200/2200 (100.0%)
#> Chain 4 (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 2200/2200 (100.0%)
#> Total (Sampling): ⦗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⦘ 8800/8800 (100.0%)
#> Elapsed: 14m 40s | ETA: 0s
#> NUTS Diagnostics Summary:
#> Total divergences: 0
#> Max tree depth hits: 8
#> Min E-BFMI across chains: 1.42
#> Note: 0.20% of transitions hit the maximum tree depth (8 of 4000).
#> Check efficiency metrics such as effective sample size (ESS) to ensure
#> sufficient exploration of the posterior.
# Posterior inclusion probabilities
summary(fit)$indicator
#> parameter mean sd mcse
#> 1 loose_ends (main) 0.01100 0.10430244 0.0027516823
#> 2 loose_ends-entertain (pairwise) 0.01750 0.13112494 0.0020967541
#> 3 loose_ends-repetitive (pairwise) 0.53625 0.49868421 0.0210601866
#> 4 loose_ends-stimulation (pairwise) 0.02575 0.15838856 0.0026949360
#> 5 loose_ends-motivated (pairwise) 0.02125 0.14421663 0.0027090088
#> 6 entertain (main) 0.00125 0.03533324 0.0005579686
#> 7 entertain-repetitive (pairwise) 0.13225 0.33876236 0.0091317860
#> 8 entertain-stimulation (pairwise) 0.06400 0.24475294 0.0044758298
#> 9 entertain-motivated (pairwise) 0.13050 0.33685271 0.0117371341
#> 10 repetitive (main) 0.01950 0.13827418 0.0065840091
#> 11 repetitive-stimulation (pairwise) 0.02700 0.16208331 0.0027417442
#> 12 repetitive-motivated (pairwise) 0.37000 0.48280431 0.0183140241
#> 13 stimulation (main) 0.00575 0.07561043 0.0021244267
#> 14 stimulation-motivated (pairwise) 0.01625 0.12643551 0.0020288388
#> 15 motivated (main) 0.00775 0.08769229 0.0017943499
#> n0->0 n0->1 n1->0 n1->1 n_eff Rhat
#> 1 3932 23 23 21 1436.7870 1.0120695
#> 2 3861 68 68 2 3910.8899 1.0089960
#> 3 1610 245 244 1900 560.6951 1.0348671
#> 4 3803 93 93 10 3454.2259 1.0634690
#> 5 3845 69 69 16 2834.0656 1.0077603
#> 6 3989 5 5 0 4010.0276 1.0189908
#> 7 3235 235 235 294 1376.1914 1.0062394
#> 8 3538 205 205 51 2990.2583 1.0037734
#> 9 3322 155 155 367 823.6752 0.9998781
#> 10 3907 15 15 62 441.0637 1.0563815
#> 11 3793 98 98 10 3494.8033 1.0003655
#> 12 2243 276 276 1204 694.9838 1.0111136
#> 13 3965 11 11 12 1266.7180 1.0525916
#> 14 3871 63 63 2 3883.6764 1.0113551
#> 15 3945 23 23 8 2388.4081 1.0488451
# Bayesian model averaged main effects for the groups
coef(fit)$main_effects_groups
#> group1 group2
#> loose_ends(c1) -0.9362769 -0.9359818
#> loose_ends(c2) -2.5179339 -2.5127982
#> loose_ends(c3) -3.7981250 -3.7928272
#> loose_ends(c4) -5.0797900 -5.0740541
#> loose_ends(c5) -7.6007935 -7.5988858
#> loose_ends(c6) -10.0972700 -10.0976351
#> entertain(c1) -0.8659544 -0.8664465
#> entertain(c2) -2.2416320 -2.2418983
#> entertain(c3) -3.8111927 -3.8107372
#> entertain(c4) -5.1627019 -5.1628435
#> entertain(c5) -7.0313885 -7.0314042
#> entertain(c6) -9.5519726 -9.5517896
#> repetitive(c1) -0.1363755 -0.1411118
#> repetitive(c2) -0.6565860 -0.6653765
#> repetitive(c3) -1.0861156 -1.0890458
#> repetitive(c4) -1.8651075 -1.8610839
#> repetitive(c5) -3.2568743 -3.2458412
#> repetitive(c6) -5.0369638 -5.0278509
#> stimulation(c1) -0.5445581 -0.5472669
#> stimulation(c2) -1.7879766 -1.7884573
#> stimulation(c3) -2.5344790 -2.5359269
#> stimulation(c4) -3.6196551 -3.6223656
#> stimulation(c5) -5.1016273 -5.1030127
#> stimulation(c6) -7.0723928 -7.0758961
#> motivated(c1) -0.5536415 -0.5557471
#> motivated(c2) -1.8020700 -1.8031799
#> motivated(c3) -3.2899142 -3.2885118
#> motivated(c4) -4.7861815 -4.7829924
#> motivated(c5) -6.7726503 -6.7744059
#> motivated(c6) -9.1423627 -9.1404826
# Bayesian model averaged pairwise effects for the groups
coef(fit)$pairwise_effects_groups
#> group1 group2
#> loose_ends-entertain 0.16887734 0.16899403
#> loose_ends-repetitive 0.04636777 0.06887841
#> loose_ends-stimulation 0.12668721 0.12722641
#> loose_ends-motivated 0.14086346 0.14046466
#> entertain-repetitive 0.06462204 0.06916138
#> entertain-stimulation 0.10838206 0.11010747
#> entertain-motivated 0.08399076 0.08852485
#> repetitive-stimulation 0.05638198 0.05686680
#> repetitive-motivated 0.12989007 0.14453391
#> stimulation-motivated 0.10760726 0.10770698
# }