Independent and Identically Distributed Monte Carlo Algorithms for Semiparametric Linear Mixed Models

Abstract

Hybrid versions of independent and identically distributed weighted Chinese restaurant (WCR) algorithms are developed for inference in semiparametric linear mixed models under minimal assumptions for the random-effects distributions. The WCR method of working with the posterior partition structure leads to Rao–Blackwell estimates for higher-order moments of random effects, such as skewness and kurtosis, and can be used to estimate densities for random effects. A key feature of our approach is the manner in which we incorporate external estimates into our algorithms. The use of such information leads to simplified computational procedures, reduces the amount of user input required for specifying models, and results in numerical stability and accuracy. The resulting procedures are automated and can be readily used in standard statistical software. Our methods are tested by simulation and illustrated by application to a longitudinal study involving chronic renal disease.

KEY WORDS:

• Dirichlet process
• Moment
• Random effect
• Rao-blackwellization, restricted
• Maximum likelihood
• Sequential importance
• Sampling
• Weighted chinese restaurant