The role of symmetric and asymmetric association in correspondence anal?ysis

Eric Beh and Rosaria Lombardo 

Typically, for the analysis of a two-way contingency table, the association between the variables is assumed to be structured such that they are both predictor variables. This is because such a structure allows for Pearson's chi-squared statistic to be used to assess the statistical significance of the association. However, there are times when (for practical reasons) it is more reasonable to treat one variable as being a predictor variable and the second variable as the response variable. Such an asymmetric association structured can be formally assessed using the Goodman-Kruskal tau index and visually assessed using non-symmetrical correspondence analysis (NSCA). Many of the features of NSCA remain the same as the traditional “symmetric" approach that uses the Pearson chi-squared statistic at its foundations with the interpretation of a correspondence plot, or biplot, being slightly different – due solely to the asymmetric structure of the variables. This ongoing project examines the features of NSCA, in particular for nominal and ordinal variables as well as variations of correspondence analysis that expand the technique for the analysis of the association between multiple categorical variables.?