, Volume 52, Issue 4, pp 589–617

A nonparametric approach for assessing latent trait unidimensionality

  • William Stout

DOI: 10.1007/BF02294821

Cite this article as:
Stout, W. Psychometrika (1987) 52: 589. doi:10.1007/BF02294821


Assuming a nonparametric family of item response theory models, a theory-based procedure for testing the hypothesis of unidimensionality of the latent space is proposed. The asymptotic distribution of the test statistic is derived assuming unidimensionality, thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait. Based upon a new notion of dimensionality, the test is shown to have asymptotic power 1. A 6300 trial Monte Carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice.

Key words

unidimensionality local independence test of unidimensionality latent trait theory latent structure analysis item response theory large sample theory asymptotic distribution theory nonparametric test 

Copyright information

© The Psychometric Society 1987

Authors and Affiliations

  • William Stout
    • 1
  1. 1.Department of Statistics and MathematicsUniversity of Illinois at Urbana-ChampaignUSA

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