Thurstone scaling in order statistics

Thurstone scaling is widely used for presenting the priorities among the compared items. The mean values of the quantiles corresponding to frequencies of each stimilus’ preference over the other stimuli define the items’ locations on the psychological continuum of the Thurstone scale. This paper considers an extension of the scale levels to the aggregates of the independent covariates. In a sense, it is similar to a multiple regression extension of the mean value of the dependent variable to its conditional mean expressed by the linear aggregate of the independent variables. A maximum likelihood objective constructed by the probabilities of the order statistics applied to the ranked or paired comparison data is suggested. Probit, logit and multinomial links are tried to obtain the Thurstonian scale exposition by the covariates, and to estimate probabilities of the items’ choice. This approach is very convenient and can substantially enrich both theoretical interpretation and practical application of Thurstone modelling, particularly in marketing and advertising research.