Quasi-complete separation in random effects of binary response mixed models. Issue 14 (21st September 2016)

• Record Type: Journal Article
• Authors: Sauter, Rafael; Held, Leonhard
• Is Part Of: Journal of statistical computation and simulation. Volume 86:Issue 14(2016)
• Page Start: 2781
• Page End: 2796
• Publication Date: 2016-09-21
• Subjects: Integrated nested Laplace approximations -- Bayesian generalized mixed models -- cluster-specific quasi-complete separation; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2015.1129539
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: Clustered observations such as longitudinal data are often analysed with generalized linear mixed models (GLMM). Approximate Bayesian inference for GLMMs with normally distributed random effects can be done using integrated nested Laplace approximations (INLA), which is in general known to yield accurate results. However, INLA is known to be less accurate for GLMMs with binary response. For longitudinal binary response data it is common that patients do not change their health state during the study period. In this case the grouping covariate perfectly predicts a subset of the response, which implies a monotone likelihood with diverging maximum likelihood (ML) estimates for cluster-specific parameters. This is known as quasi-complete separation. In this paper we demonstrate, based on longitudinal data from a randomized clinical trial and two simulations, that the accuracy of INLA decreases with increasing degree of cluster-specific quasi-complete separation. Comparing parameter estimates by INLA, Markov chain Monte Carlo sampling and ML shows that INLA increasingly deviates from the other methods in such a scenario.