On Extending the Bradley-Terry Model to Incorporate Within-Pair Order Effects

The Bradley-Terry model for paired comparisons is generalized to account for the effect of the order of presentation of the objects within a pair. A multiplicative order effect is suggested as an alternative to the additive order effect proposed by Beaver and Gokhale (1975). The multiplicative order effect is then incorporated into the tie models given by Rao-Kupper and Davidson (1967, 1970). The associated estimation and testing procedures are presented with emphasis on likelihood methods as well as on the weighted least squares methods recently applied to paired comparison situations by Imrey, Johnson, and Koch (1976) and by Beaver (1977). Two numerical examples are provided, one with ties and one without.