ANALYSIS OF CROSS-CLASSIFICATIONS OF COUNTS USING MODELS FOR MARGINAL DISTRIBUTIONS - AN APPLICATION TO TRENDS IN ATTITUDES ON LEGALIZED ABORTION

Models parameterized in terms of linear models for marginal logits and linear models for marginal log-ends ratios provide a useful framework for the analysis of cross-classifications of counts when there is interest in comparing marginal distribution,s, or studying changes in marginal distributions. Examples of such cross-classifications include tabulations of responses to a collection of items from a questionnaire, and contingency tables cross-classifying the repeated measurements of a categorical response variable from longitudinal studies. The example used for illustrative purposes in this chapter is based on four items common to the National Opinion Research Center's (NORC) 1965 SRS870, 1975 General Social Survey (GSS), and 1985 GSS. Each of the items asked respondents to indicate whether or not they approved of the availability of legalized abortions for women in a specific situation. The utility of the marginal models approach to analyzing repented categorical measurements is demonstrated through comparisons with two analyses based on conventional log-linear models. An algorithm that can be used to fit marginal models by the method of maximum likelihood is described in the appendix to this chapter.