GMM logistic regression models for longitudinal data with time-dependent covariates and extended classifications

When analyzing longitudinal data, it is essential to account both for the correlation inherent from the repeated measures of the responses as well as the correlation realized on account of the feedback created between the responses at a particular time and the predictors at other times. As such one can analyze these data using generalized estimating equation with the independent working correlation. However, because it is essential to include all the appropriate moment conditions as you solve for the regression coefficients, we explore an alternative approach using a generalized method of moments for estimating the coefficients in such data. We develop an approach that makes use of all the valid moment conditions necessary with each time-dependent and time-independent covariate. This approach does not assume that feedback is always present over time, or if present occur at the same degree. Further, we make use of continuously updating generalized method of moments in obtaining estimates. We fit the generalized method of moments logistic regression model with time-dependent covariates using SAS PROC IML and also in R. We used p-values adjusted for multiple correlated tests to determine the appropriate moment conditions for determining the regression coefficients. We examined two datasets for illustrative purposes. We looked at re-hospitalization taken from a Medicare database. We also revisited data regarding the relationship between the body mass index and future morbidity among children in the Philippines. We conducted a simulated study to compare the performances of extended classifications.