To identify and consider the interactions between predictor variables in regression models, the logistic regression method can be used, in which new predictor variables are constructed as logical combinations of the initial binary variables and entered into the model so that the interaction between independent variables is considered in the form of this logical combination. So far, logistic regression has been introduced and used to analyze data with independent responses, but although correlated observations occur in scientific studies for various reasons, logistic regression has not been performed to analyze longitudinal correlated observations. Due to the importance of examining interaction effects in longitudinal studies, this article presents the theoretical foundations of extending logistic regression to analyze longitudinal data and proposes a logistic regression model to identify the interactions affecting the binary longitudinal response variable. A computer program for the logistic regression model was written using the Akaike Information Criterion (AIC) as the model score function, and the model parameters were estimated. To evaluate the performance of the proposed model, a simulation study was conducted in different scenarios, the results of which indicate the acceptable performance of the proposed model in finding the effective interaction effects on the bimodal longitudinal response. As an applied example, an analysis of the association between polymorphisms and other risk factors with low blood HDL levels over time in the Tehran Lipid and Glucose Study was performed with the proposed model.