Inferences in longitudinal multinomial fixed and mixed models

Abstract

Analyzing categorical data collected over time is an important research topic. Even though there exists numerous studies on analysis of categorical data in cross sectional setup, the analysis of this type of data in the longitudinal setup is, however, not adequately addressed. In this thesis, we develop two correlation models for multinomial (> 2 categories) longitudinal data, namely, a conditional linear probability based model and a non-linear logistic probability based model; and provide likelihood inferences for category effects, fixed covariate effects and correlations or dynamic dependence parameters. The inferences are done for both complete history and contingency tables based data. For the history based data, the thesis also models the influences of individual random effects in addition to the fixed covariate effects. Furthermore, as in many practical situations the number of individuals involved in the study may be small, in the thesis, we have examined the finite sample performance of the likelihood estimates both in fixed and mixed model setups.