
Accession Number : AD0695468
Title : ON EXTENDING THE BRADLEYTERRY 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 BradleyTerry 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 RaoKupper 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