Link Specification and Spatial Dependence for Generalized Linear Mixed Models

Date of Completion

January 2011






The link function plays an essential role in the generalized linear model and generalized linear mixed model (GLMM). In a GLMM framework, I introduce a class of link functions that are implied from a new way to incorporate random effects. The new class covers all existing link functions as special cases and offers a new avenue to construct, links for various discrete and continuous response variables. Using a copula approach combined with either a Gaussian random field (GRF) or a Gaussian Markov random field (GMRF). I extend the new class of link functions to accommodate spatial dependence under the GLMM frarnework, proposing a new class of random fields with desired margins. The new class of random fields, named transformed Gaussian random fields (TGRFs) and transformed Gaussian Markov random fields (TGMRFs), provide a more general and flexible modeling framework than do GRFs and GMRFs respectively. The proposed methods are applied to analyze the spatial count data and the spatial binary data of snail in the Luquillo Experimental Forest in Puerto Rico. The performance of different TGMRFs is illustrated via a simulation study. In the simulation study, it is shown that the the conditional predictive ordinate criterion is effective in selecting the correct model. The simulation study also presented that the introduced TGMRFs models are more flexible to accommodate asymmetric and heavy tails data sets. ^