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. / Graduation date: 1996
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/34588 |
| Date | 03 May 1996 |
| Creators | Kolsky, James D. |
| Contributors | Schafer, Daniel W. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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