Abstract: We consider nonparametric smoothing and variable selection in generalized varying coefficient models. Generalized varying coefficient models are commonly used for analyzing the time-dependent effects of covariates on responses that are not necessary continuous, for example counts or categories. We present the P-spline estimator in this context and show its estimation consistency for a diverging number of knots (or B-spline basis functions), by using an approximation of the link function. The combination of P-splines with nonnegative garrote (which is a variable selection method) leads to good estimation and variable selection. The method is illustrated with a simulation study and a data example.
Key words and phrases: generalized varying coefficient models, longitudinal data, nonparametric smoothing, P-splines, variable selection.