TY - BOOK

T1 - Recursive Partitioning of Models of a Generalized Linear Model Type

AU - Rusch, Thomas

PY - 2012

Y1 - 2012

N2 - This thesis is concerned with recursive partitioning of models of a generalized linear model type (GLM-type), i.e., maximum likelihood models with a linear predictor for the linked mean, a topic that has received constant interest over the last twenty years. The resulting tree (a ``model tree'') can be seen as an extension of classic trees, to allow for a GLM-type model in the partitions. In this work, the focus lies on applied and computational aspects of model trees with GLM-type node models to work out different areas where application of the combination of parametric models and trees will be beneficial and to build a computational scaffold for future application of model trees. In the first part, model trees are defined and some algorithms for fitting model trees with GLM-type node model are reviewed and compared in terms of their properties of tree induction and node model fitting. Additionally, the design of a particularly versatile algorithm, the MOB algorithm (Zeileis et al. 2008) in R is described and an in-depth discussion of how the functionality offered can be extended to various GLM-type models is provided. This is highlighted by an example of using partitioned negative binomial models for investigating the effect of health care incentives. Part 2 consists of three research articles where model trees are applied to different problems that frequently occur in the social sciences. The first uses trees with GLM-type node models and applies it to a data set of voters, who show a non-monotone relationship between the frequency of attending past elections and the turnout in 2004. Three different type of model tree algorithms are used to investigate this phenomenon and for two the resulting trees can explain the counter-intuitive finding. Here model tress are used to learn a nonlinear relationship between a target model and a big number of candidate variables to provide more insight into a data set.

AB - This thesis is concerned with recursive partitioning of models of a generalized linear model type (GLM-type), i.e., maximum likelihood models with a linear predictor for the linked mean, a topic that has received constant interest over the last twenty years. The resulting tree (a ``model tree'') can be seen as an extension of classic trees, to allow for a GLM-type model in the partitions. In this work, the focus lies on applied and computational aspects of model trees with GLM-type node models to work out different areas where application of the combination of parametric models and trees will be beneficial and to build a computational scaffold for future application of model trees. In the first part, model trees are defined and some algorithms for fitting model trees with GLM-type node model are reviewed and compared in terms of their properties of tree induction and node model fitting. Additionally, the design of a particularly versatile algorithm, the MOB algorithm (Zeileis et al. 2008) in R is described and an in-depth discussion of how the functionality offered can be extended to various GLM-type models is provided. This is highlighted by an example of using partitioned negative binomial models for investigating the effect of health care incentives. Part 2 consists of three research articles where model trees are applied to different problems that frequently occur in the social sciences. The first uses trees with GLM-type node models and applies it to a data set of voters, who show a non-monotone relationship between the frequency of attending past elections and the turnout in 2004. Three different type of model tree algorithms are used to investigate this phenomenon and for two the resulting trees can explain the counter-intuitive finding. Here model tress are used to learn a nonlinear relationship between a target model and a big number of candidate variables to provide more insight into a data set.

U2 - 10.57938/f43bea09-fe60-44fb-a995-ba63733c8c69

DO - 10.57938/f43bea09-fe60-44fb-a995-ba63733c8c69

M3 - Doctoral thesis

ER -