Logit models for the analysis of contingency tables derived from survey data

Ewings, Paul David (1985) Logit models for the analysis of contingency tables derived from survey data. University of Southampton, Doctoral Thesis.

Abstract

This thesis is concerned with the analysis of cross-classified categorical data from complex sample surveys. A modified logit model is developed that includes a random component representing a cluster effect. The model is reformulated to avoid a potential limitation, and generalised least squares methods of estimation and testing are applied. Alternative forms for the structure of the cluster effect are considered, and it is shown that a simplified version discussed by Anderson and Aitkin (1985) may often be too restrictive.

Empirical results compare the developed methods for logil models with other methods for corresponding log-linear models, namely the generalised Wald statistic and a modified Pearson statistic suggested by Rao and Scott (1981, 1984). Our simulations suggest that these latter statistics, and in particular the Wald statistic, may sometimes lead to an excessive number of rejections of the null hypothesis. In general the modified logit model test statistics behave well.

Simulations arc also used to identify the important factors that contribute to the overall effect of clustering on the standard test procedures. Analyses on real data suggest that the standard methods may sometimes be very misleading and could lead to incorrect inferences. It is suggested however that in large contingency tables the effects of clustering will usually diminish, providing the number of degrees of freedom in each individual lest is not too large.

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