Marginal Loglinear Models for Three Multiple-Response Categorical Variables

A lot of survey questions include a phrase like, “Choose all that apply”, which lets the respondents choose any number of options from predefined lists of items. Responses to thesequestions result in multiple-response categorical variables (MRCVs). This thesis focuses on analyzing and modeling three MRCVs. There are 232 possible models representing different combinations of associations. Parameters are estimated using generalized estimating equations generated by a pseudo-likelihood and variances of the estimators are corrected using sandwich methods. Due to the large number of possible models, model comparisons based on nested models would be inappropriate. As an alternative, model averaging is proposed as a model comparison tool as well as to account for model selection uncertainty. Further the calculations required for computing the variance of the estimators can exceed 32-bit machine capacity even for a moderately large number of items. This issue is addressed by reducing dimensions of the matrices.