Partitioned GMM logistic regression models for longitudinal data

Correlation is inherent in longitudinal studies due to the repeated measurements on subjects, as well as due to time-dependent covariates in the study. In the National Longitudinal Study of Adolescent to Adult Health (Add Health), data were repeatedly collected on children in grades 7-12 across four waves. Thus, observations obtained on the same adolescent were correlated, while predictors were correlated with current and future outcomes such as obesity status, among other health issues. Previous methods, such as the generalized method of moments (GMM) approach have been proposed to estimate regression coefficients for time-dependent covariates. However, these approaches combined all valid moment conditions to produce an averaged parameter estimate for each covariate and thus assumed that the effect of each covariate on the response was constant across time. This assumption is not necessarily optimal in applications such as Add Health or health-related data. Thus, we depart from this assumption and instead use the Partitioned GMM approach to estimate multiple coefficients for the data based on different time periods. These extra regression coefficients are obtained using a partitioning of the moment conditions pertaining to each respective relationship. This approach offers a deeper understanding and appreciation into the effect of each covariate on the response. We conduct simulation studies, as well as analyses of obesity in Add Health, rehospitalization in Medicare data, and depression scores in a clinical study. The Partitioned GMM methods exhibit benefits over previously proposed models with improved insight into the nonconstant relationships realized when analyzing longitudinal data.