Advances On The Analysis Of Ordinal Data Expressed As Rankings And Paired Comparisons: Distance-based Approaches, New Probabilistic Models, And Tree-based Applications

This thesis represents an original contribution to knowledge on ordinal data, which constitutes the leitmotif of the entire research product. Specifically, a short review of preference data presents the leading distance and correlations measures with a focus on two weighted measures (i.e., distance and correlation). A simulation study investigates the effect of introducing positional weights when preferences are analyzed through distance-based approaches. The weighted correlation coefficient is then used as cost function within an evolutionary algorithm for finding the consensus ranking. Then, we will focus on analyzing ordinal data through probabilistic approaches, presenting a new tree-based model, the Bradley-Terry Regression Trunk model (BTRT). Again, a simulation study is conducted to evaluate the performance of the pruning procedure implemented in the new algorithm. This model is applied on two different datasets: the first is composed of self-reported data by students from the University of Cagliari; the second derives from well-known databases and contains financial information about tax revenues by central governments worldwide and their socio-economic characteristics. The BTRT model is applied to the first dataset to partition students based on their preference rankings about the attributes they expect from an ideal professor. For the second dataset, the goal is to apply the BTRT model for partitioning countries based on the size of their tax revenues and how their socio-economic characteristics influence these revenues. The BTRT model furnishes an easy-to-read partition in the form of a small regression tree, called trunk, able to capture the interactions between covariates that cause the most significant decrease in model deviance. Hence, it finds the best interactions between covariates by simultaneously considering their main effects. Finally, the last chapter shows an advance for the BTRT model by following the Mallows specification of the Bradley-Terry model. The Mallows specification works on rankings instead of paired comparisons. It assumes independence across the ranked objects so that the probability of observing a specific ranking is proportional to the product of the estimated worth parameters for each object. The BTRT model with the Mallows specification is applied to the financial dataset to discover the causal effect between government expenditure and tax revenues.