Models of Multiple Response Independence

We consider the problem of how to measure a “correlation” (or interdependence) between two survey-questionnaire questions. In the real-life questionnaires it is usual to offer several options-answers for most of the questions. Some (or many) questions give the possibility to choose more than one answer. There are very few statistical methods that enable inferences for the questions with multiple answers. We consider two statistics of the chi-square type that serve to confirm a dependence of two questions. As a theoretical basis a notion of “independence” between two multiple questions should be introduced. We propose two definitions (or actually types of definitions): “random” and “generalized Poisson” independences. A simulation study was performed, which is based on those notions. The study confirms applicability of the chi-square statistics, which are similar to the classical ones.