Canonical correspondence analysis in social science research

The use of simple and multiple correspondence analysis is well-established in social science research for understanding relationships between two or more categorical variables. By contrast, canonical correspondence analysis, which is a correspondence analysis with linear restrictions on the solution, has become one of the most popular multivariate techniques in ecological research. Multivariate ecological data typically consist of frequencies of observed species across a set of sampling locations, as well as a set of observed environmental variables at the same locations. In this context the principal dimensions of the biological variables are sought in a space that is constrained to be related to the environmental variables. This restricted form of correspondence analysis has many uses in social science research as well, as is demonstrated in this paper. We first illustrate the result that canonical correspondence analysis of an indicator matrix, restricted to be related an external categorical variable, reduces to a simple correspondence analysis of a set of concatenated (or “stacked”) tables. Then we show how canonical correspondence analysis can be used to focus on, or partial out, a particular set of response categories in sample survey data. For example, the method can be used to partial out the influence of missing responses, which usually dominate the results of a multiple correspondence analysis.