The Bradley-Terry Regression Trunk approach for Modeling Preference Data with Small Trees.

This paper introduces the Bradley-Terry regression trunk model, a novel probabilistic approach for the analysis of preference data expressed through paired comparison rankings. In some cases, it may be reasonable to assume that the preferences expressed by individuals depend on their characteristics. Within the framework of tree-based partitioning, we specify a tree-based model estimating the joint effects of subject-specific covariates over and above their main effects. We, therefore, combine a tree-based model and the log-linear Bradley-Terry model using the outcome of the comparisons as response variable. The proposed model provides a solution to discover interaction effects when no a-priori hypotheses are available. It produces a small tree, called trunk, that represents a fair compromise between a simple interpretation of the interaction effects and an easy to read partition of judges based on their characteristics and the preferences they have expressed. We present an application on a real dataset following two different approaches, and a simulation study to test the model's performance. Simulations showed that the quality of the model performance increases when the number of rankings and objects increases. In addition, the performance is considerably amplified when the judges' characteristics have a high impact on their choices.

Individual classification of Alzheimer's disease with diffusion magnetic resonance imaging.

Diffusion magnetic resonance imaging (MRI) is a powerful non-invasive method to study white matter integrity, and is sensitive to detect differences in Alzheimer's disease (AD) patients. Diffusion MRI may be able to contribute towards reliable diagnosis of AD. We used diffusion MRI to classify AD patients (N=77), and controls (N=173). We use different methods to extract information from the diffusion MRI data. First, we use the voxel-wise diffusion tensor measures that have been skeletonised using tract based spatial statistics. Second, we clustered the voxel-wise diffusion measures with independent component analysis (ICA), and extracted the mixing weights. Third, we determined structural connectivity between Harvard Oxford atlas regions with probabilistic tractography, as well as graph measures based on these structural connectivity graphs. Classification performance for voxel-wise measures ranged between an AUC of 0.888, and 0.902. The ICA-clustered measures ranged between an AUC of 0.893, and 0.920. The AUC for the structural connectivity graph was 0.900, while graph measures based upon this graph ranged between an AUC of 0.531, and 0.840. All measures combined with a sparse group lasso resulted in an AUC of 0.896. Overall, fractional anisotropy clustered into ICA components was the best performing measure. These findings may be useful for future incorporation of diffusion MRI into protocols for AD classification, or as a starting point for early detection of AD using diffusion MRI.