This article discusses the application of logit models for the analyses of 2-way categorical observations. The models described are generalized linear models using the logit link function. One of the models is the Rasch model (Rasch, 1960). The objective is to test hypotheses of marginal and conditional independence between explanatory quantities and multiple binary responses. By means of a numerical example, the relevance of such hypotheses for educational research is demonstrated. The aim is, in particular, to extend the applicability of the Rasch model to test hypotheses of conditional independence. (Contains 4 tables.)