On Thurstone’s Model for Paired Comparisons and Ranking Data

Summary

We investigate by means of a simulation study whether standard structural equation modeling techniques are suitable for estimating an unrestricted Thurstonian model to: (a) multiple judgment paired comparisons data, and (b) ranking data. We point out that Thurstone’s (1927) original model is not a proper model for multiple judgment paired comparisons data as it assigns zero probability to all intransitive paired comparisons patterns. To fit multiple judgment paired comparisons data one must employ Takane’s (1987) extension of Thurstone’s original model, or alternatively, a Thurstonian correlation structure model, which we introduce. We found that for some models as few as 100 observations suffice to obtain accurate parameter estimates, standard errors and goodness of fit tests when 7 stimuli are modeled (21 binary variables). For other models, however, sample sizes of 1000 observations are needed. All in all, the procedure investigated appears to be an attractive choice to estimate these models.