Abstract
We propose a regression model for count data when the classical generalized linear model approach is too rigid due to a high outcome of zero counts and a nonlinear influence of continuous covariates. Zero-Inflation is applied to take into account the presence of excess zeros with separate link functions for the zero and the nonzero component. Nonlinearity in covariates is captured by spline functions based on B-splines. Our algorithm relies on maximum-likelihood estimation and allows for adaptive box-constrained knots, thus improving the goodness of the spline fit and allowing for detection of sensitivity changepoints. A simulation study substantiates the numerical stability of the algorithm to infer such models. The AIC criterion is shown to serve well for model selection, in particular if nonlinearities are weak such that BIC tends to overly simplistic models. We fit the introduced models to real data of children's dental sanity, linking caries counts with the so-called Body-Mass-Index (BMI) and other socioeconomic factors. This reveals a puzzling nonmonotonic influence of BMI on caries counts which is yet to be explained by clinical experts.