Log linear representation for paired and multiple comparisons models

SUMAIARY This paper develops log linear model representations for the Bradley-Terry paired comparisons and Luce multiple comparisons models. Various multivariate extensions of the Bradley-Terry model are then considered. A model is presented, similar to one of Davidson & Bradley (1969), but which is based on the log odds ratio as a measure of association rather than the 0 coefficient of correlation. It is shown that, by the adaptive use of log linear model theory, complex data sets involving paired and multiple comparisons as well as rankings may be easily analyzed. In all cases estimates of cell expectations may be computed using an iterative proportional scaling algorithm that is computationally easy to carry out.