This paper develops a new approach to the analysis of longitudinal paired comparison data, where comparisons of the same objects by the same judges are made on more than one occasion. As an alternative to other recent approaches to such data, which are based on Kalman filter- ing, our approach treats the problem as one of multivariate multinomial data, allowing dependence terms between comparisons over time to be incorporated. The resulting model can be fitted as a Poisson log-linear model and has parallels with the quadratic binary exponential distribution of Cox. An example from the British Household Panel Survey illustrates the approach. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics

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. A second application area is also discussed, namely using model trees to detect ill-fitting subsets in the data. The second article uses model trees to model the number of fatalities in Afghanistan war, based on the WikiLeaks Afghanistan war diary. Data pre-processing with a topic model generates predictors that are used as explanatory variables in a model tree for overdispersed count data. Here the combination of model trees and topic models allows to flexibly analyse database data, frequently encountered in data journalism, and provides a coherent description of fatalities in the Afghanistan war. The third paper uses a new framework built around model trees to approach the classic problem of segmentation, frequently encountered in marketing and management science. Here, the framework is used for segmentation of a sample of the US electorate for identifying likely and unlikely voters. It is shown that the framework's model trees enable accurate identification which in turn allows efficient targeted mobilisation of eligible voters. (author's abstract)

Dirichlet regression models can be used to analyze a set of variables lying in a bounded interval that sum up to a constant (e.g., proportions, rates, compositions, etc.) exhibiting skewness and heteroscedasticity, without having to transform the data. There are two parametrization for the presented model, one using the common Dirichlet distribution's alpha parameters, and a reparametrization of the alpha's to set up a mean-and-dispersion-like model. By applying appropriate link-functions, a GLM-like framework is set up that allows for the analysis of such data in a straightforward and familiar way, because interpretation is similar to multinomial logistic regression. This paper gives a brief theoretical foundation and describes the implementation as well as application (including worked examples) of Dirichlet regression methods implemented in the package DirichletReg (Maier, 2013) in the R language (R Core Team, 2013). (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics