Hostname: page-component-6766d58669-h8lrw Total loading time: 0 Render date: 2026-05-21T22:32:13.170Z Has data issue: false hasContentIssue false
  • English
  • Français

Statistical Inference Based on Latent Ability Estimates

Published online by Cambridge University Press:  01 January 2025

Herbert Hoijtink  and
Anne Boomsma
Herbert Hoijtink*
Affiliation:
Department of Statistics and Measurement Theory, University of Groningen, The Netherlands
Anne Boomsma
Affiliation:
Department of Statistics and Measurement Theory, University of Groningen, The Netherlands
*
Requests for reprints should be sent to Herbert Hoijtink, Department of Statistics and Measurement Theory, University of Groningen, Grote Kruisstraat 2/1, 9712 TS Groningen, THE NETHERLANDS. E-mail: h.j.a.hoytink@ppsw.rug.nl
Get access Rights & Permissions [Opens in a new window]

Abstract

The quality of approximations to first and second order moments (e.g., statistics like means, variances, regression coefficients) based on latent ability estimates is being discussed. The ability estimates are obtained using either the Rasch, or the two-parameter logistic model. Straightforward use of such statistics to make inferences with respect to true latent ability is not recommended, unless we account for the fact that the basic quantities are estimates. In this paper true score theory is used to account for the latter; the counterpart of observed/true score being estimated/true latent ability. It is shown that statistics based on the true score theory are virtually unbiased if the number of items presented to each examinee is larger than fifteen. Three types of estimators are compared: maximum likelihood, weighted maximum likelihood, and Bayes modal. Furthermore, the (dis)advantages of the true score method and direct modeling of latent ability is discussed.

Keywords

item response theorytrue score theorylatent ability estimatesmaximum likelihoodweighted maximum likelihoodBayes modallatent regression

Information

Type
Original Paper
Information
Psychometrika , Volume 61 , Issue 2 , June 1996 , pp. 313 - 330
Copyright
Copyright © 1996 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Andersen, E. B. (1980). Comparing latent distributions. Psychometrika, 45, 121–134.CrossRefGoogle Scholar
Chang, H. H., Stout, W. (1993). The asymptotic posterior normality of the latent trait in an IRT model. Psychometrika, 58, 37–52.CrossRefGoogle Scholar
Hacquebord, H. I. (1989). Tekstbegrip van Turkse en Nederlandse leerlingen in het voortgezet onderwijs [Text comprehension of Turkish and Dutch high school students]. Unpublished doctoral dissertation, University of Groningen.Google Scholar
Hambleton, R. K., Swaminathan, H. (1985). Item response theory, Boston: Kluwer-Nijhoff.CrossRefGoogle Scholar
Hoijtink, H., Boomsma, A. (1991). Statistical inference with latent ability estimates, Groningen: Rijksuniversiteit, Vakgroep Statistiek en Meettheorie.Google Scholar
Lehmann, E. L. (1983). Theory of point estimation, New York: Wiley.CrossRefGoogle Scholar
Lord, F. M. (1983). Unbiased estimators of ability parameters, of their variance, and of their parallel-forms reliability. Psychometrika, 48, 233–245.CrossRefGoogle Scholar
Mislevy, R. J. (1991). Randomization based inferences about latent variables from complex samples. Psychometrika, 56, 177–196.CrossRefGoogle Scholar
Tatsuoka, M. M. (1988). Multivariate analysis, New York: MacMillan.Google Scholar
Verhelst, N. D., Eggen, T. J. H. M. (1989). Psychometrische en statistische aspecten van peilingsonderzoek [Psychometric and statistical aspects of survey research (PPON Report Nr. 4)], Arnhem: CITO.Google Scholar
Warm, T. A. (1989). Weighted likelihood estimation of ability in item response models. Psychometrika, 54, 427–450.CrossRefGoogle Scholar
Zwinderman, A. H. (1991). A generalized Rasch model for manifest predictors. Psychometrika, 56, 589–600.CrossRefGoogle Scholar