Mixed model based inference in structured additive regression

Due to the increasing availability of spatial or spatio-temporal regression data, models that allow to incorporate the special structure of such data sets in an appropriate way are highly desired in practice. A flexible modeling approach should not only be able to account for spatial and temporal correlations, but also to model further covariate effects in a semi- or nonparametric fashion. In addition, regression models for different types of responses are available and extensions require special attention in each of these cases. Within this thesis, numerous possibilities to model non-standard covariate effects such as nonlinear effects of continuous covariates, temporal effects, spatial effects, interaction effects or unobserved heterogeneity are reviewed and embedded in the general framework of structured additive regression. Beginning with exponential family regression, extensions to several types of multicategorical responses and the analysis of continuous survival times are described. A new inferential procedure based on mixed model methodology is introduced, allowing for a unified treatment of the different regression problems. Estimation of the regression coefficients is based on penalized likelihood, whereas smoothing parameters are estimated using restricted maximum likelihood or marginal likelihood. In several applications and simulation studies, the new approach turns out to be a promising alternative to competing methodology, especially estimation based on Markov Chain Monte Carlo simulation techniques.

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