This paper is concerned with the application of generalized linear interactive modelling(GLIM) to the binary categorical data. To analyze the categorical data given by a contingency table, finding a good-fitting loglinear model is commonly adopted. In the case of a contingency table with a response variable, we can fit a logit model to find a good-fitting loglinear model. For a given $2^4$ contingency table with a binary response variable, we show the process of fitting a loglinear model by fitting a logit model using GLIM and SAS and then we estimate parameters to interpret the nature of associations implied by the model.