Generalized Linear Mixed Effect Models with Crossed Random Effects for Experimental Designs having Non-repeated Items: Model Specification and Selection

Abstract

A non-repeated items (NRI) design is an experimental design in which items are not repeated across the levels of an experimental condition. When binary outcomes are collected, a generalized linear mixed-effect model (GLMM) with crossed random effects (person random effect and item random effect) is applied to the NRI design as an alternative method for an analysis of variance (ANOVA) framework. However, the existing model specification of GLMM with crossed random effects does not account for all possible dependences among the outcomes in the NRI design, and model misspecification to model the dependence results in adverse effects on the statistical inferences about the experimental conditions under GLMMs. In the dissertation, first, the GLMMs with crossed random effects for the NRI design are specified and illustrated using an empirical data; then, the parameter recovery of the newly specified GLMMs and the performance of the hypothesis testing, likelihood ratio test (LRT), and information criteria are evaluated via a simulation study to detect the experimental condition effect. The simulation study results show that the accuracy of the condition effect is acceptable when there are at least 50 persons and 30 items per level of the condition. In addition, acceptable Type I error and power differed depending on the GLMM random effect structures. Based on the simulation results, we recommended the use of the likelihood ratio test for an experimental condition effect over information criteria in selecting a GLMM among candidate models with different random effects.