Estimating Variance Components and Variance Partition Coefficients on the Inverse Link Scale for Cross-Classified Random Effects Models

• Activity Number: 354
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Brian R. Gray*+
• Companies: U.S. Geological Survey
• Keywords: hierarchical models ; Laplace estimation ; logit-normal models ; multilevel models ; variance partition coefficient ; variance components

Abstract

Studies of the estimation of variance components (VCs) and relative VCs (variance partition coefficients, VPCs) on inverse link scales from generalized linear mixed model (GLMM) estimates have been limited to outcomes from nested designs. Also, the influence of GLMM analytical method on VC and VPC estimation has received limited attention. I propose an approach for calculating VCs and VPCs on inverse link scales from outcomes from two-way cross-classified random effects designs, and evaluate this method using Monte Carlo simulations of grouped binomial data. GLMMs were fitted using first-order marginal and penalized quasi-likelihood (PQL1), the REML analogue of PQL1 (RPQL1), Laplace estimation and Markov chain Monte Carlo. Bias and precision in VC and VPC estimates improved as group (cluster) size for both random main effects increased and, for a given main effect, when the number of groups associated with the alternate main effect increased. The influence of estimation method on bias and precision of VC and VPC estimates was typically slight when numbers of groups for both main effects were 10 and 20 but when numbers of groups equaled 5 were best under RPQL1.