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Regression is one of the most important statistical tools in data analysis and study of the relationship between predictive variables and the response variable. in most issues, regression models and decision tress only can show the main effects of predictor variables on the response and considering interactions between variables does not exceed of two way and ultimately three-way, due to complexity of such interactions. To consider such interactions in the regression models, instead of individual variables in the model, we can construct a combination of them and use this combination as a new independent variable into the model Logic regression is a generalized regression and classification method that in this model, predictive variables are Boolean combinations that are made of the original binary variables. Annealing algorithm is used to find such combinations and their coefficients. randomization test or “null model test” is an overall test for signal in the data.also, cross-validation test can be used to determine the size of the logic tree model with the best predictive capability. As an example, we applied Logic Regression to predict diabetes in TLGS study.

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Logic regression is a generalized regression and classification method that is able to make Boolean combinations
as new predictive variables from the original binary variables. Logic regression was introduced for case control or
cohort study with independent observations. Although in various studies, correlated observations occur due to different
reasons, logic regression have not been studied in theory and application to analyze of correlated observations
and longitudinal data.
Due to the importance of identifying and considering the interactions between variables in longitudinal studies,
in this paper we propose Transition Logic Regression as an extension of Logic Regression to binary longitudinal
data. AIC of the models are used as score function of Annealing algorithm. In order to assess the performance of
the method, simulation study is done in various conditions of sample size, first order dependency and interaction
effect. According to results of simulation study, by increasing the sample size, percentage of identification of true
interactions and MSE of estimations get better. As an application, we assess interaction effect of some SNPs on
HDL level over time in TLGS study using our proposed model.