Functional clustering methods for binary longitudinal data with temporal heterogeneity

In the analysis of binary longitudinal data, it is of interest to model a dynamic relationship between a response and covariates as a function of time, while also investigating similar patterns of time-dependent interactions. We present a novel generalized varying-coefficient model that accounts for within-subject variability and simultaneously clusters varying-coefficient functions, without restricting the number of clusters nor overfitting the data. In the analysis of a heterogeneous series of binary data, the model extracts population-level fixed effects, cluster-level varying effects, and subject-level random effects. Various simulation studies show the validity and utility of the proposed method to correctly specify cluster-specific varying-coefficients when the number of clusters is unknown. The proposed method is applied to a heterogeneous series of binary data in the German Socioeconomic Panel (GSOEP) study, where we identify three major clusters demonstrating the different varying effects of socioeconomic predictors as a function of age on the working status.