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Belitz, Christiane (2007): Model Selection in Generalised Structured Additive Regression Models. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics
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Abstract

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.