Inference in semiparametric dynamic models for binary longitudinal data

This article deals with the analysis of a hierarchical sermparametric model for dynamic binary longitudinal responses. The main complicating components of the model are an unknown covariate function and serial correlation in the errors. Existing estimation methods for models with these features are of O(N-3), where N is the total number of observations in the sample. Therefore, nonparametric estimation is largely infeasible when the sample size is large, as in typical in the longitudinal setting. Here we propose a new O(N) Markov chain Monte Carlo based algorithm for estimation of the nonparametric function when the errors are correlated, thus contributing to the growing literature on semiparametric and nonparametric mixed-effects models for binary data. In addition, we address the problem of model choice to enable the formal comparison of our semiparametric model with competing parametric and semiparametric specifications. The performance of the methods is illustrated with detailed studies involving simulated and real data.