Conjoint Representation of the Main Effects and Interaction Term in Multiple Non Symmetrical Correspondence Analysis

The main effects represent the change in the response variables due to the change on the level/categories of the predictor variables, considering the adding effects of them. By contrast the interaction effect represents the combined effect of predictor variables on the response variable. In particular, there is an interaction between two predictor variables when the effect of one predictor variable varies as the levels/categories of the other predictor vary. If the interaction is not significant, it is possible to examine the main effects. Instead, if the interaction is statistically significant and of strong entity, then, it is not useful to consider the main effects. As the matter of fact, asserting that two predictor variables interact is the same as affirming that the two variables do not have separate effects. Moreover, in this paper we suggest a procedure of the simultaneous representation of the main effect and interaction term obtained by means the decomposition of tau Gray Williams. To identify a category which is statistically significant, the confidence ellipses for a Multiple Non-Symmetric Correspondence Analysis will be shown.