Analysis of correlated categorical data

Abstract

We look at some recent developments in the analysis of correlated observations. Attention is focussed on the case of discrete data with categorical responses, with particular emphasis on the GEE approaches of Liang and Zeger (hereafter LZ). Firstly we describe different independent marginal and dependent joint models that have been used in the past. We introduce a new model based on the Frank family of copulas. This provides the basis of our simulations throughout this thesis. The main aim of our studies is to compare four basic methods of analysis under different circumstances. The methods are: 1) the usual logistic regression model with the assumption of independence of responses between subjects and within subjects; 2) the GEE of LZ with independent "working" correlation; 3) the GEE of LZ with non-independent "working" correlation, and 4) exact likelihood. LZ methods are often used when the whole population is of interest. If a researcher is interested in information about an individual, then the extended GEE methods which may be used to fit the subject specific models provided by Prentice and Lipsitz, Laird and Harrington are desirable. Comparisons of the two extended GEE methods axe made with (3), the LZ method 2. Robust methods such as one-step jackknife and fully iterated jackknife are compared with (2), the LZ method 1. Finally we carry out an empirical examination of the simple method proposed by Rao and Scott, which can be applied to a variety of problems involved correlated binary responses.

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