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A nonparametric approach for assessing latent trait unidimensionality

A nonparametric approach for assessing latent trait unidimensionality 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Psychometrika Springer Journals

A nonparametric approach for assessing latent trait unidimensionality

Psychometrika , Volume 52 (4): 29 – Dec 1, 1987

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References (46)

Publisher
Springer Journals
Copyright
1987 The Psychometric Society
ISSN
0033-3123
eISSN
1860-0980
DOI
10.1007/BF02294821
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

PsychometrikaSpringer Journals

Published: Dec 1, 1987

Keywords: Psychometrics; Assessment, Testing and Evaluation; Statistics for Social Sciences, Humanities, Law; Statistical Theory and Methods

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