Analysis of two-way ordinal contingency tables for social research

In the social research the variables often consist of ordered categories. When the row and column variables of a contingency table both are on ordinal scale, several techniques (Beh, 1997) have been proposed, most of which are based on the partition of Pearson’s chi-squared statistic. Recently doubly ordered cumulative correspondence analysis (D’ambra, Beh, Camminatiello, 2014) has been proposed by partitioning Hirotsu’s chi-squared statistic (Hirotsu, 1994). The association in these tables can be also described by using various types of odds ratios, among which, global odds ratios (Agresti, Coull, 2002). In this contribution we propose a modification of the above doubly ordered cumulative correspondence analysis based on the logarithms of the elements of the doubly cumulative table obtained by collapsing row and column classifications into dichotomies. By means of this generalization we can compute and represent the global odds ratios in the two-dimensional plot.