A nonparametric approach for assessing latent trait unidimensionality
 William Stout
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Assuming a nonparametric family of item response theory models, a theorybased 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.
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 Title
 A nonparametric approach for assessing latent trait unidimensionality
 Journal

Psychometrika
Volume 52, Issue 4 , pp 589617
 Cover Date
 19871201
 DOI
 10.1007/BF02294821
 Print ISSN
 00333123
 Online ISSN
 18600980
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

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

 William Stout ^{(1)}
 Author Affiliations

 1. Department of Statistics and Mathematics, University of Illinois at UrbanaChampaign, USA