Model choice and variable selection in mixed & semiparametric models

by Benjamin Säfken
Doctoral thesis
Date of Examination:2015-03-27
Date of issue:2015-04-10
Advisor:Prof. Dr. Thomas Kneib
Referee:Prof. Dr. Thomas Kneib
Referee:Prof. Dr. Tatyana Krivobokova
Persistent Address: http://dx.doi.org/10.53846/goediss-5020

 

 

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Abstract

English

Semiparametric and mixed models allow different kinds of data structures and data types to be considered in regression models. Spatial and temporal structures of discrete or spatial data can be treated as flexibly as, for instance, functional data. This growing flexibility increasingly requires a statistician to make choices between competing models. In model selection the degrees of freedom play an important role as a measure of model complexity. In this thesis three approaches for the estimation of the degrees of freedom in mixed and semiparametric models are developed, each for different distributions of the (conditional) responses. The interpretation of semiparametric models as mixed models justifies using the same model selection techniques for both model classes. By using Steinian methods, the degrees of freedom can be determined for a group of distributions belonging to the exponential family. The developed methods for determining the degrees of freedom are illustrated by an example of tree growth data. For a larger class of distributions the degrees of freedom can be determined by cross-validation and bootstrap methods. Additionally, an approximate Steinian method can be adapted for further distributions. Based on the implicit function theorem the degrees of freedom of a variance or smoothing parameter can de derived analytically if the response is normally distributed. Failure to take these degrees of freedom into account can lead to biased model selection. In addition to the methodological derivation, the geometrical properties of the degrees of freedom of the variance and smoothing parameters are analysed. Furthermore, numerical problems in the computation of the degrees of freedom are considered.
Keywords: semiparametric regression; mixed model; model selection
 
Statistik