Generalized Method of Moments Logistic Regression Model

When analyzing longitudinal binary data, it is essential to account for both the correlation inherent from the repeated measures of the responses and the correlation realized due to the feedback created between the responses at a particular time and the covariates at other times. Ignoring any of these correlations leads to invalid conclusions. Such is the case when the covariates are time-dependent and a standard logistic regression model is used. There are two sets of correlations: responses with responses and responses with covariates. We need a model that addresses both these types of correlation. The correlation between responses at time t impacts the covariates in time t + s; and when the covariates in time t impact the responses in time t + s. These correlations measuring the association between feedback from Yt on to the future Xt + s and vice-versa are important in obtaining the estimates of the regression coefficients. This chapter provides a means of modeling repeated responses with time-dependent and time-independent covariates. The coefficients are obtained using generalized method of moments. We fit these data with SAS Macro (Cai & Wilson, 2015). Our methods are based on the following: