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Some Exact Tests for Manifest Properties of Latent Trait Models

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  • Jan G. de Gooijer

    (University of Amsterdam, the Netherlands)

  • Ao Yuan

    (Howard University, Washington DC, USA)

Abstract

Item response theory is one of the modern test theories with applications in educational and psychological testing. Recent developments made it possible to characterize some desired properties in terms of a collection of manifest ones, so that hypothesis tests on these traits can, in principle, be performed. But the existing test methodology is based on asymptotic approximation, which is impractical in most applications since the required sample sizes are often unrealistically huge. To overcome this problem, a class of tests is proposed for making exact statistical inference about four manifest properties: covariances given the sum are non-positive (CSN), manifest monotonicity (MM), conditional association (CA), and vanishing conditional dependence (VCD). One major advantage is that these exact tests do not require large sample sizes. As a result, tests for CSN and MM can be routinely performed in empirical studies. For testing CA and VCD, the exact methods are still impractical in most applications, due to the unusually large number of parameters to be tested. However, exact methods are still derived for them as an exploration toward practicality. Some numerical examples with applications of the exact tests for CSN and MM are provided.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 10-044/4.

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Date of creation: 26 Apr 2010
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Handle: RePEc:dgr:uvatin:20100044

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Web page: http://www.tinbergen.nl

Related research

Keywords: Conditional distribution; Exact test; Monte Carlo; Markov chain Monte Carlo;

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  1. Paul Rosenbaum, 1987. "Comparing item characteristic curves," Psychometrika, Springer, Springer, vol. 52(2), pages 217-233, June.
  2. Jules Ellis & Brian Junker, 1997. "Tail-measurability in monotone latent variable models," Psychometrika, Springer, Springer, vol. 62(4), pages 495-523, December.
  3. William Stout, 1987. "A nonparametric approach for assessing latent trait unidimensionality," Psychometrika, Springer, Springer, vol. 52(4), pages 589-617, December.
  4. Brian Junker, 1991. "Essential independence and likelihood-based ability estimation for polytomous items," Psychometrika, Springer, Springer, vol. 56(2), pages 255-278, June.
  5. Noel Cressie & Paul Holland, 1983. "Characterizing the manifest probabilities of latent trait models," Psychometrika, Springer, Springer, vol. 48(1), pages 129-141, March.
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Cited by:
  1. Jules Ellis, 2014. "An Inequality for Correlations in Unidimensional Monotone Latent Variable Models for Binary Variables," Psychometrika, Springer, Springer, vol. 79(2), pages 303-316, April.

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