Accession Number : AD0695468

Title :   ON EXTENDING THE BRADLEY-TERRY MODEL TO ACCOMMODATE TIES IN PAIRED COMPARISON EXPERIMENTS.

Descriptive Note : Technical rept.,

Corporate Author : FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS

Personal Author(s) : Davidson,Roger R.

Report Date : AUG 1969

Pagination or Media Count : 27

Abstract : The study is concerned with the extension of the Bradley-Terry model for paired comparisons to situations which allow an expression of no preference. A new model is developed and its performance compared with a model proposed by Rao and Kupper. The maximum likelihood estimates of the parameters are found using an iterative procedure which, under a weak assumption, converges monotonically to the solution of the likelihood equations. It is noted that for a balanced paired comparison experiment the ranking obtained from the maximum likelihood estimates agrees with that obtained from a scoring system which allots two points for a win, one for a tie and zero for a loss. The likelihood ratio test of the hypothesis of equal preferences is shown to have the same asymptotic efficiency as that for the Rao-Kupper model. Two examples are presented, one of which introduces a set of data for an unbalanced paired comparison experiment. Initial applications of the test of goodness of fit suggest that the proposed model yields a reasonable representation of actual experimentation. (Author)

Descriptors :   (*COMBINATORIAL ANALYSIS, MATHEMATICAL MODELS), (*STATISTICAL DATA, *CORRELATION TECHNIQUES), QUALITY CONTROL, STATISTICAL TESTS, DECISION THEORY, SAMPLING

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE