Analysis of Ranked Preference Data | Kristine Frisenfeldt Thuesen
| | Abstract | This thesis is addressing theory on models for ranked preference data, based on paired comparisons. The three models,which will be in focus are Mallows- Bradley-Terry (MBT), Bradley-Terry-Luce (BTL) as presented in [4], and a variation of the MBT model, where it is assumed that the number of times each ranking occurs in the data, is Poisson distributed in stead of polynomial distributed.
The predominant body of the literature on the subject today is limited to a data analytical approach. Either applying the models in a concrete analysis of data, or presenting a theoretic description of how to use the models in the readers forthcoming practical application.
This thesis will in contrast to the existing literature on the subject provide the reader with a thorough description of the models all from the psychophysical idea to the mathematical formulation of the model and the model inference, in a theoretical and strict mathematical way.
The data analytical approach in the existing literature might be the reason why an introductory description of theoretical comparison of the models is missing. This comparison will be made in this thesis.
The attention will especially be on the restraining factors for the ability to describe ranking preference data, and the possibilities for writing them as Generalized Linear Models (GLM), to be able to derive Maximum Likelihood estimates through an Iterative Reweighted Least Squares (IRLS) algorithm.
For practical approaches a very relevant extension of the ranking models is the extension to handle panel segmentations.Therefore this work will in the last chapters turn the focus to Latent Class Models (LC), which can handle the presence of unobserved segmentation of the consumers. Like other mixture models the inference from the latent class models will happen iteratively by using an Expectation-Maximization (EM) algorithm.
Through the thesis illustrative and relevant tests are made on simple test data, to assist the theoretical descriptions. In a separate chapter some more realistic ranked preference data from the Danish audio- and videoproducer, Bang & Olufsen (B&O) is analyzed. | | Type | Master's thesis [Academic thesis] | | Year | 2007 | | Publisher | Informatics and Mathematical Modelling, Technical University of Denmark, DTU | | Address | Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby | | Series | IMM-Thesis-2007-50 | | Note | Supervised by Prof. Per Bruun Brockhoff, IMM, DTU. | | Electronic version(s) | [pdf] | | BibTeX data | [bibtex] | | IMM Group(s) | Mathematical Statistics |
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