Multivariate paired comparisons: The extension of a univariate model and associated estimation and test procedures

This study is concerned with the development of an extension of the Bradley-Terry model for paired comparisons to situations in which responses to paired comparisons are obtained on each of several characteristics. At the outset a probability model for multivariate paired comparisons is proposed that may be represented in several distinct ways. An iterative procedure for obtaining maximum-likelihood estimates of the parameters introduced into the model is given and its behaviour examined in some detail. It is observed that the procedure generally performed well, the key to this conclusion being the relative stability of the initial estimates of the preference parameters. On the basis of some initial applications of the test of the appropriateness of the multivariate paired comparisons procedure, one might surmise that the model yields a reasonable representation of actual experimentation. However, further applications of the model to actual data are required before a realistic evaluation of its utility can be made.