Decomposition of the Main Effects and Interaction term by using Orthogonal Polynomials in Multiple Non Symmetrical Correspondence Analysis

The Multiple Non-symmetric correspondence analysis (MNSCA) is a useful technique for analyzing a two-way contingency table. In more complex case, the predictors variables are more than one. In this paper, the Multiple Non- Symmetric Correspondence Analysis- MNSCA, along with the decomposition of the Gray-Williams Tau Index, in main effects and interaction term, is used to analyze a contingency table with two predictor categorical variables and a ordinal response variable. The Multiple-TAU index is a measure of association that contains both main effects and interaction terms. The main effects represent the change in the response variables due to the change in the level/categories of the predictor variables, considering the effects of their addition. While, the interaction effect represents the combined effect of predictor categorical variables on the ordinal response variable. Moreover, for ordinal scale-variables, we propose a further decomposition in order to check the existence of the power components by using Emerson's orthogonal polynomials.