Objectives of Inference for Stochastic Models

Abstract

AbstractThroughout this book, we have been using the pseudonym GLMMs to denote generalized linear mixed models. The common denominator among all these models is that they all contain a linear model (LM) part, which refers to the fixed effects component of the linear predictor Xβ. In a GLMM, the prefix “G” indicates that the distribution of observations may not be normal, the suffix of the first M means that the linear predictor includes mixed effects and thus contains random effects, which are expressed by the term “Zb.” The fixed linear component of the predictor Xβ is important because the fixed effects describe the treatment design, which, in turn, is determined by the objectives or the initial research questions that the study wishes to answer. Therefore, if the researcher proposes using a reasonable model to analyze an experiment, then he/she must be able to express each objective as a question about a model parameter or as a linear combination of model parameters.