🤖 AI Summary
This study addresses a critical oversight in current practice wherein successful model fitting using the probit Bayesian Kernel Machine Regression (BKMR) implementation in the bkmr package is often mistakenly equated with Markov chain Monte Carlo (MCMC) convergence, without rigorous posterior diagnostic assessment. Through an extensive simulation study, the work systematically demonstrates that under standard settings, the probit BKMR model exhibits considerable fragility in achieving convergence: among 430 successfully fitted models, only 30 simultaneously satisfied stringent convergence criteria—namely, rank-normalized $\hat{R} \leq 1.01$, bulk effective sample size (bulk-ESS) $\geq 400$, and tail effective sample size (tail-ESS) $\geq 400$. Data were generated via bkmr::SimData() and models fitted using kmbayes(), with convergence evaluated through a multi-metric framework incorporating rank-normalized $\hat{R}$, bulk-ESS, and tail-ESS, underscoring the necessity of multidimensional diagnostics to ensure reliable inference.
📝 Abstract
Background. Bayesian kernel machine regression (BKMR) is widely used for exposure-mixture analyses with binary outcomes through a probit extension. Because a bkmr fit can complete without providing adequate effective posterior information, simulation studies should separate execution success from MCMC convergence diagnostics. Methods. We evaluated the public bkmr probit workflow using bkmr::SimData() for data generation, bkmr::kmbayes() for model fitting, and posterior for convergence diagnostics. The balanced generator used family = "binomial", hfun = 2, beta.true = 0.5, ind = 1:2, and M = 4. SimData() generated the covariate as X = 3*cos(z1) + 2*rnorm(n). Four chains were initialized with chain-specific randomized starting values generated reproducibly from the fixed initial-value base seed 20260621. These values affected only the initial state of the sampler and did not alter the BKMR model, default priors, or Metropolis-Hastings proposals. Results. Of 431 prespecified tasks, 430 returned fitted objects and one task had a numerical non-completion. Diagnostic adequacy was limited: rank-normalized R-hat <= 1.01 threshold was achieved in 55/431 tasks, bulk-ESS >= 400 in 85/431, tail-ESS >= 400 in 44/431, and both ESS criteria in 44/431. The primary diagnostic criterion, R-hat at or below the 1.01 threshold with both bulk-ESS and tail-ESS >= 400, was met in 30/431 prespecified tasks, corresponding to 30/430 completed fits. Conclusions. Completion of probit BKMR fits in bkmr should not be equated with convergence of the retained MCMC draws. Applied analyses should report the number of chains, warmup and retained iterations, rank-normalized R-hat, bulk-ESS, and tail-ESS rather than rely on a fixed iteration count or on fit completion alone.