Model Selection in Generalised Structured Additive Regression Models

In recent years data sets have become increasingly more complex
requiring more flexible instruments for their analysis. Such a
flexible instrument is regression analysis based on a structured
additive predictor which allows an appropriate modelling for
different types of information, e.g.~by using smooth functions for
spatial information, nonlinear functions for continuous covariates
or by using effects for the modelling of cluster--specific
heterogeneity. In this thesis, we review many important effects.
Moreover, we place an emphasis on interaction terms and introduce a
possibility for the simple modelling of a complex interaction
between two continuous covariates. \\ Mainly, this thesis is
concerned with the topic of variable and smoothing parameter
selection within structured additive regression models. For this
purpose, we introduce an efficient algorithm that simultaneously
selects relevant covariates and the degree of smoothness for their
effects. This algorithm is even capable of handling complex
situations with many covariates and observations. Thereby, the
validation of different models is based on goodness of fit
criteria, like e.g.~AIC, BIC or GCV. The methodological development
was strongly motivated by case studies from different areas. As
examples, we analyse two different data sets regarding determinants
of undernutrition in India and of rate making for insurance
companies. Furthermore, we examine the performance or our selection
approach in several extensive simulation studies.