Corrections to Classical Procedures for Estimating Thurstone's Case V Model for Ranking Data

The classical method (Mosteller, 1951) for estimating Thurstone's Case V model for ranking data consists in a) transforming the observed ranking patterns to patterns of binary paired comparisons, b) obtaining the normal deviate corresponding to the men of each binary variable, and c) estimate the model parameters from these deviates by least squares. However, classical procedures do not take into account the dependencies among the deviates and as a result, asymptotic standard errors (SEs) and goodness of fit (GOF) test are incorrect. We provide formulae that provide correct asymptotic SEs and GOF in this situation. A small simulation study shows that adequate standard errors and goodness of fit tests can be obtained with rather small sample sizes even in very large models