Skew random effects in multilevel binomial models:an alternative to nonparametric approach

摘要

Compared to modelling observable data, it is more difficult to choose a suitable distributionto describe latent variables since no prior knowledge or observable information can be used and onlynormal or nonparametric distributions are mainly applied to random effects for generalized linearmixed models (GLMMs) in the literature. To enhance the modelling toolkit, this article investigatesa class of parametric skew elliptical random effects in multilevel binomial regression models using aBayesian approach; the class includes skew normal, skew Students' t-distributions and others. Skewnessmechanism is considered through multiplying skewness parameter A by standardized folded ellipticalrandom variables, and the posterior sampling is realized by working on a binary skewness indicator(BSI) instead of continuous A for parameter identifiability. Simulation study shows that the originalcontinuous skewness parameter A and the posterior mean of BSI may have dichotomous signs todescribe the directional (right/left) skewness; thus we address the importance of assuming specificrandom effects distribution and interpreting the skewness carefully. The methodology is exemplifiedthrough reanalyzing a teratogenic activity study of two niacin analogs published in the biologicalliterature, and sampling-based model comparison shows that the parametric skew normal randomeffects model works largely better than nonparametric Dirichlet process mixture models for this data set.