Correlation and Association Models for Studying Measurements on Ordinal Relations

Abstract

This paper describes and illustrates correlation models (correspondence analysis and canonical correlation analysis) and association models for studying the order and spacing of categories of ordinal relational variables. Both correlation models and association models study departures from independence in two-way contingency tables. One result of fitting these models is the possibility of assignment of scores to the categories of the row andlor the column variables to reflect the relative spacing oJ these categories. If the model fitting is done using statistical procedures, then restricted versions of these models allow one to test hypotheses about the spacing, linearity, or equality of the categories. Correlation and association models are especially useful for studying discrete ordinal variables, which arise quite frequently in the social and behavioral sciences. We illustrate correlation and association models using two empirical examples in which respondents used ordered