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

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