On the identification of the unrestricted Thurstonian model for ranking data

• The identification issues of the unrestricted Thurstonian model for ranking data is the focus of the current paper. Within the Thurstonian framework, each object among those to be ranked is associated with a latent continuous variable, often interpreted as the utility of the object. The unrestricted Thurstonian model, due to the discrete and comparative nature of ranking data, faces more serious identification problems than the indeterminacy of the latent scale origin and unit. Most researchers resort to the study of the unrestricted model referring to the differences of the object utilities but then the inference on object utilities becomes tricky. Maydeu-Olivares and Böckenholt (2005) suggest a strategy to overcome the identification problem of the unrestricted model referring to object utilities but this requires many extra identification constraints, additional to the ones needed for defining the scale origin and unit. In the current paper, we study the general applicability of the suggested identification approach. Our simulation study indicates that the estimates obtained can be seriously biased with relatively large mean squared errors (MSE) when the extra constraints deviate from the true values of the parameters. Besides, the bias and MSE do not seem to decrease with increase in the sample size, and the effect of the constraints is not uniform on all estimated parameters.

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unrestricted Thurstonian model; identification; ranking data

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