A Small-Sample Randomization-Based Approach to Semi-Parametric Estimation and Misspeci cation in Generalized Linear Mixed Models

Abstract

In a generalized linear mixed model (GLMM), the random effects are typically uncorrelated and assumed to follow a normal distribution. However, fi ndings from recent studies on how the misspeci cation of the random effects distribution affects the estimated model parameters are inconclusive. In the thesis, we extend the randomization approach for deriving linear models to the GLMM framework. Based on this approach, we develop an algorithm for estimating the model parameters of the randomization-based GLMM (RBGLMM) for the completely randomized design (CRD) which does not require normally distributed random effects. Instead, the discrete uniform distribution on the symmetric group of permutations is used for the random effects. Our simulation results suggest that the randomization-based algorithm may be an alternative when the assumption of normality is violated. In the second part of the thesis, we consider an RB-GLMM for the randomized complete block design (RCBD) with random block effects. We investigate the effect of misspecifi cation of the correlation structure and of the random effects distribution via simulation studies. In the simulation, we use the variance covariance matrices derived from the randomization approach. The misspecifi ed model with uncorrelated random effects is fi tted to data generated from the model with correlated random effects. We also t the model with normally distributed random effects to data simulated from models with different random effects distributions. The simulation results show that misspeci cation of both the correlation structure and of the random effects distribution has hardly any effect on the estimates of the fi xed effects parameters. However, the estimated variance components are frequently severely biased and standard errors of these estimates are substantially higher.