Extensions for paired comparisons models Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/dz010t60w

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  • The Thurstone-Mosteller and Bradley-Terry Models are commonly used to rank items from paired comparisons experiments in which one item in each pair "wins," and to assess the importance of time-independent explanatory variables on such rankings. The first part of this thesis clarifies the use of probit and logistic regression models for such designs, including the incorporation of time-dependent explanatory variables and the analysis of unbalanced designs. In addition, likelihood inference, using the EM Algorithm, is proposed for Thurstone's Case HI Model allowing the estimation of variance parameters to account for variable item performances. The second half of this thesis presents an extension of the model to permitting the "performances" or "worths" of each competitor to be serially correlated. As an example, the performance of a basketball team in its current game is allowed to be correlated with its performance from the previous game. The Thurstone-Mosteller Model is sometimes motivated through the use of an underlying, normally-distributed performance distribution for each item or competitor, with a competitor winning a trial if a draw from its performance distribution exceeds that from its competitor's. The observed outcome is solely the win or loss for each team, but regression models, using either time-dependent or time-independent explanatory variables, may be specified for the performance means. The extension in this thesis comes from supposing the error structure for the performance distribution for each team is normal with first-order autocorrelation. The EM Algorithm is used, treating the underlying draws from the performance distributions as "missing data." This provides approximate maximum likelihood estimates; the approximation is due to the use of Monte Carlo integration in the E-step of the algorithm. Unfortunately, the heavy computational requirement and the inability to calculate the maximized likelihood function or the information matrix, make the approach unattractive for practical use. Two approximations are presented, however, which can be carried out with standard routines and some minor programming. Keywords: auto-regressive model, Bradley-Terry Model, EM Algorithm, generalized linear model, logistic regression, MCEM Algorithm, probit regression, serial correlation, Thurstone-Mosteller Model.
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