As a multitude of real data problems involve preference ranking data, in the last decades analysis of rankings has become increasingly important and interesting in several fields as behavioral...Show moreAs a multitude of real data problems involve preference ranking data, in the last decades analysis of rankings has become increasingly important and interesting in several fields as behavioral sciences, machine learning and decision making. Ranking data arise when we ask to subjects to express their preference order on a set of items. Over the past two centuries methods and models to analyse ranking data, generally based on the assumption of a homogeneous population, have been proposed. Furthermore preference rankings are a particular kind of data that are difficult to visualize given their discrete structure, especially when the number of items to be ranked increases. We present a combination of cluster analysis of preference ranking data with the unfolding model. The unfolding model is used to derive a low-dimensional joint representation of both individuals and items to allow for the visualization of preference rankings even when the number of items considered is greater than 4, while the K-median cluster component analysis is used to obtain a group representation of preferences into homogeneous clusters by considering preference rankings in their natural discrete space. The use of this combined approach represents a coherent framework for the analysis of preference ranking data since it allows us to cover the space of all permutations in different ways. Two simulation studies and a real data analysis are presented to illustrate the proposed approach.Show less
For the applied statistician, data augmentation is a powerful tool for solving optimization problems. In this thesis, I address a problem in some data augmented Gibbs samplers. I show that although...Show moreFor the applied statistician, data augmentation is a powerful tool for solving optimization problems. In this thesis, I address a problem in some data augmented Gibbs samplers. I show that although introducing latent variables renders a sampling problem tractable, this comes at the price of raising the autocorrelation of the Markov chain, as the number of parameters increases, in this case the number of items in a test. By means of an example, I show that data augmentation is a powerful yet inefficient tool in cases of increased number of items, since the autocorrelation (and hence the rate of the convergence) of the addressed augmented Gibbs sampler is proved to be dependent on the number of item parameters. We wish to show that although most data-augmented samplers are well behaved, in this example the algorithm becomes really slow and faces the possibility of grinding to a haltShow less
In this thesis already existing methods for the construction of a computerized adaptive test(CAT) are extended, with as a goal to create an adaptive test which measures progress. For this project,...Show moreIn this thesis already existing methods for the construction of a computerized adaptive test(CAT) are extended, with as a goal to create an adaptive test which measures progress. For this project, data is available from seven different medical progress tests by university students in the Netherlands. A CAT, usually has an item response theory(IRT) model applied to the data which can be used to construct an item bank to select items from. However, many items in the medical progress data do not follow an IRT model. Therefore, a new method is proposed to measure progress in a CAT, which is based on a latent class model with 2 or 3 latent classes. The estimated probabilities to answer correctly when belonging to any of these classes are used to calculate Kullback Leibler(KL)-information for all the items. The KLinformation values can then be used to select items and to construct an adaptive test. Simulations show that item-selection based on KL-information outperforms random selection of items in progress testing. Finally, a scoring method based on latent class probabilities in the CAT is proposed.Show less
