Tests of ignoring and eliminating in nonsymmetric correspondence analysis

Nonsymmetric correspondence analysis (NSCA) aims to examine predictive relationships between rows and columns of a contingency table. The predictor categories of such tables are often accompanied by some auxiliary information. Constrained NSCA (CNSCA) incorporates such information as linear constraints on the predictor categories. However, imposing constraints also means that part of the predictive relationship is left unaccounted for by the constraints. A method of NSCA is proposed for analyzing the residual part along with the part accounted for by the constraints. The CATANOVA test may be invoked to test the significance of each part. The two tests parallel the distinction between tests of ignoring and eliminating, and help gain some insight into what is known as Simpson’s paradox in the analysis of contingency tables. Two examples are given to illustrate the distinction.