On the identification of the unrestricted Thurstonian model for ranking data
2011 (English)Report (Other academic)
The identification issues of the unrestricted Thurstonian model for ranking data is the focus of the current paper. The Thurstonian framework has been proved very influential in modeling ranking data. Within this framework, the objects to be ranked are associated with a latent continuous variable, often interpreted as utility. The unrestricted Thurstonian model has a central role in the related theory development but due to the discrete and comparative nature of ranking data it 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 object utilities but then the inference on object utilities becomes tricky. Maydeu-Olivares & 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 suggested identification approach to investigate its general applicability. Our findings indicate that the estimates obtained based on this approach can be seriously biased when the extra constraints deviate from the true values of the parameters. Besides, the effect of the constraints is not uniform on all estimated parameters.
Place, publisher, year, edition, pages
Uppsala: Department of Statistics, Uppsala University , 2011. , 32 p.
Working paper / Department of Statistics, Uppsala University, 3
unrestricted Thurstonian model; identification
IdentifiersURN: urn:nbn:se:uu:diva-162086OAI: oai:DiVA.org:uu-162086DiVA: diva2:458835