Distance models for analysis of multivariate binary data

Abstract

In this dissertation we developed statistical tools for analyzing multivariate binary data. In many disciplines multivariate binary data, in which there are multiple binary dependent variables and one or more independent variables, are often collected. In this dissertation we further developed the IPC model for analyzing multivariate binary data. The IPC model is a probabilistic multidimensional unfolding model and closely related to the Ideal Point Discriminant Analysis (IPDA). In Chapter 4, we proposed a Multivariate Logistic Distance (MLD) model for analyzing multivariate binary data. The MLD model unifies two domains of statistical methods, i.e., Multidimensional Scaling (MDS) and Generalized Linear Model (GLM). The MLD model can be used to simultaneously assess the dimensional structure of the data and to study the effect of the predictor variables on the response variables. For the NESDA data, for example, a researcher can use the MLD model to determine the dimensional structure of the mental disorders, and to investigate effect of the personality traits and the background variables on prevalence of the mental disorders.