We show that when the thresholds and the polychoric correlation are estimated in two stages, neither Pearson's X^2 nor the likelihood ratio G^2 goodness of fit test statistics are asymptotically chi-square. We propose a new test statistic, Mn, that is asymptotically chi-square in this situation....

Thurstone's (1927) is not a proper model for multiple judgment paired comparison data as it assigns zero probabilities to all intransitive patterns. To obtain a proper model, Takane (1987) extended Thurstone's model by adding a vector of pair specific random errors. We investigate an...