  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.
