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.