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Psychometrika

, Volume 61, Issue 2, pp 313–330 | Cite as

Statistical inference based on latent ability estimates

  • Herbert Hoijtink
  • Anne Boomsma
Article

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.

Key words

item response theory true score theory latent ability estimates maximum likelihood weighted maximum likelihood Bayes modal latent regression 

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Copyright information

© The Psychometric Society 1996

Authors and Affiliations

  1. 1.Department of Statistics and Measurement TheoryUniversity of GroningenGroningenThe Netherlands

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