Thurstonian Covariance and Correlation Structures for Multiple Judgment Paired Comparison Data

(WP 04/03 Clave pdf) 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 unrestricted Thurstone-Takane model when (a) the variances of the paired specific errors are assumed to be equal, and (b) when they are assumed to be unequal. We also consider a new model, an unrestricted Thurstonian mean and correlation structure model.