Estimating the smoothing parameter in generalized spline-based regression: I - Cross-validatory criteria for binary data using small sample sizes

Estimation of a smooth predictor function in logistic regression requires the determination of a smoothing parameter. Several cross-validatory criteria for finding such a smoothing parameter have been proposed generalizing techniques that are asymptotically well performing for Gaussian data. Here it is argued that a smoothing parameter is a model parameter and can be estimated cross-validating model fit criteria for generalized regression models taking explicitly into account the non-Gaussian distribution of the observed variables. Several criteria based on model choice for binary data are introduced and their performance is investigated in a simulation study where smooth predictor functions are estimated by smoothing splines. The empirical results indicate that cross-validated model fit criteria perform well.