Multicategorical regression models are an established tool in statistical data analysis. The present thesis extends common parametric regression models for nominal and ordinal responses to more flexible nonparametric approaches. In order to obtain a flexible form of the functional effects of metrically scaled covariates, expansions in basis functions are used. The resulting predictor allows parameter estimation within the framework of multivariate generalized linear models. Estimates are obtained by maximizing a penalized likelihood with discrete penalty terms restricting the variation of estimated smooth effects.

As a result of theoretical considerations, P-Splines seem to be the ideal alternative for applying penalized basis function approaches. Based on this result, nonparametric extensions of the multinomial logit model for nominal and the cumulative logit model for ordinal responses are derived. An important feature of the proposed multinomial logit model is the distinction between global and category-specific variables. Variables of both types may enter the model in a linear form or as unspecified smooth functions. For cumulative logit models the penalization concept adopted from P-Splines is used to restrict category-specific parameters in adjacent categories. Penalization across response categories ensures availability of estimates when common estimation procedures fail to converge, so that tests for proportional odds may be performed even for critical settings. Additionally, penalties across response categories are taken into account as fixed methodical parts when fitting semiparametric partial proportional odds models.