Thurstonian models have proven useful in a wide range of applications because they can describe the multidimensional nature of choice objects and the effects of similarity and comparability in choice situations. This paper presents a unified framework for applying the Thurstonian approach to partial ranking data that includes paired comparison data and first choices. As a result, several new Thurstonian ranking models are introduced by imposing different constraints on the covariance matrix of the random utilities and their mean scale values. Furthermore, the estimation of probabilities for a multivariate normal distribution by numerical integration procedures and the Clark algorithm are discussed. To illustrate the approach, data from two partial ranking experiments are analysed.
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Ulf Böckenholt (1992) studied this question.