Bivariate multinomial models

Sun, Bingrui (2014) Bivariate multinomial models. Doctoral (PhD) thesis, Memorial University of Newfoundland.

[English] PDF (Migrated (PDF/A Conversion) from original format: (application/pdf)) - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (1MB) [English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. (Original Version)

Abstract

Analyzing multivariate categorical data is an important and practical research topic. Even though there exist many studies on the analysis of bivariate (possibly multivariate) categorical data, the modeling of correlations among the bivariate multinomial variables is, however, not adequately addressed. In this thesis, we develop three correlation models for bivariate multinomial data. The first model accommodates fully specified marginal probabilities and uses a bivariate normal type conditional probability relationship to model the correlations of the bivariate multinomial variables. Next, we propose a random effects based familial type model to accommodate the correlations, where conditional on the random effects the marginal probabilities are fully specified. The third model is developed by considering the marginal probabilities of one variable as fully specified, and using conditional multinomial logistic type probability model to accommodate correlations. The estimation of the parameters for all three models is discussed in details through both simulation studies and analysis of real data.

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