Longitudinal data analysis using generalized linear models

Abstract

In this work we examine various conditions under which the usual asymptotic results (i.e. the weak consistency, the asymptotic normality and the strong consistency) hold for the regressor parameter beta which arises in a linear model (Chapter 2), a generalized linea model (GLM) with a fully specified likelihood (Chapter 3) or as a root of the generalized estimating equation (GEE) associated with a sequence of longitudinal observations (Chapter 4). Our main references for each of these chapters are [12], [9], respectively [20]. We provide detailed proofs of the results found in the above-mentioned references, and we extend the results of [9] to, the case of stochastic regressors (Section 3.4). Finally, in Chapter 5, we identify a fundamental mistake appearing in the recent article [4], which examines the strong consistency of the regressor parameter beta in a GLM for which the likelihood of the density is not specified. In Section 5.2, we give a correction to the main theorem of [4], as well as some new results concerning the weak consistency and asymptotic normality of beta.