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On the identification of the unrestricted Thurstonian model for ranking data
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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.

Keyword [en]
unrestricted Thurstonian model; identification; ranking data
National Category
Social Sciences
Research subject
Statistics
Identifiers
URN: urn:nbn:se:uu:diva-187598OAI: oai:DiVA.org:uu-187598DiVA: diva2:575279
Available from: 2012-12-09 Created: 2012-12-09 Last updated: 2013-02-11
In thesis
1. Composite Likelihood Estimation for Latent Variable Models with Ordinal and Continuous, or Ranking Variables
Open this publication in new window or tab >>Composite Likelihood Estimation for Latent Variable Models with Ordinal and Continuous, or Ranking Variables
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The estimation of latent variable models with ordinal and continuous, or ranking variables is the research focus of this thesis. The existing estimation methods are discussed and a composite likelihood approach is developed. The main advantages of the new method are its low computational complexity which remains unchanged regardless of the model size, and that it yields an asymptotically unbiased, consistent, and normally distributed estimator.

The thesis consists of four papers. The first one investigates the two main formulations of the unrestricted Thurstonian model for ranking data along with the corresponding identification constraints. It is found that the extra identifications constraints required in one of them lead to unreliable estimates unless the constraints coincide with the true values of the fixed parameters.

In the second paper, a pairwise likelihood (PL) estimation is developed for factor analysis models with ordinal variables. The performance of PL is studied in terms of bias and mean squared error (MSE) and compared with that of the conventional estimation methods via a simulation study and through some real data examples. It is found that the PL estimates and standard errors have very small bias and MSE both decreasing with the sample size, and that the method is competitive to the conventional ones.

The results of the first two papers lead to the next one where PL estimation is adjusted to the unrestricted Thurstonian ranking model. As before, the performance of the proposed approach is studied through a simulation study with respect to relative bias and relative MSE and in comparison with the conventional estimation methods. The conclusions are similar to those of the second paper.

The last paper extends the PL estimation to the whole structural equation modeling framework where data may include both ordinal and continuous variables as well as covariates. The approach is demonstrated through an example run in R software. The code used has been incorporated in the R package lavaan (version 0.5-11).

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2013. 31 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Social Sciences, ISSN 1652-9030 ; 86
Keyword
latent variable models, factor analysis, structural equation models, Thurstonian model, item response theory, composite likelihood estimation, pairwise likelihood estimation, maximum likelihood, weighted least squares, ordinal variables, ranking variables, lavaan
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-188342 (URN)978-91-554-8571-9 (ISBN)
Public defence
2013-02-15, Hörsal 2, Ekonomikum, Kyrkogårdsgatan 10, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2013-01-23 Created: 2012-12-15 Last updated: 2013-02-11Bibliographically approved

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