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A Nonparametric Approach for Assessing Latent Trait Unidimensionality

Published online by Cambridge University Press:  01 January 2025

William Stout
William Stout*
Affiliation:
Department of Statistics and Mathematics, University of Illinois at Urbana-Champaign
*
Request for reprints should be sent to William Stout, Department of Statistics, University of Illinois, 101 lllini Hall, 725 South Wright Street, Champaign, IL 61821.
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Abstract

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.

Keywords

unidimensionalitylocal independencetest of unidimensionalitylatent trait theorylatent structure analysisitem response theorylarge sample theoryasymptotic distribution theorynonparametric test
Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 4 , December 1987 , pp. 589 - 617
Copyright
Copyright © 1987 The Psychometric Society

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Footnotes

The referees' comments were remarkably detailed and greatly enhanced the writeup and sensitized the author to certain pertinent issues. Discussions with Fritz Drasgow, Lloyd Humphreys, Dennis Jennings, Brian Junker, Robert Linn, Ratna Nandakumar, and Robin Shealy were also very useful.

This research was supported by the Office of Naval Research under grant N00014-84-K-0186; NR 150-533, and by the National Science Foundation under grant DMS 85-03321.

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