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Applied Psychological Measurement
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Article

Likelihood-Ratio DIF Testing: Effects of Nonnormality

Carol M. Woods, Ph.D.*

* To whom correspondence should be addressed. E-mail: cwoods{at}artsci.wustl.edu.


  Abstract
Differential item functioning (DIF) occurs when an item has different measurement properties for members of one group versus another. Likelihood-ratio (LR) tests for DIF based on item response theory (IRT) involve statistically comparing IRT models that vary with respect to their constraints. A simulation study evaluated how violation of the normality assumption about the random latent variable for one or both groups affected IRT-LR-DIF results. Item response data with or without DIF were generated from the two-parameter logistic model and fitted under the assumption that the latent distribution was normal for both groups. Although the IRT-LR-DIF method performed well when latent distributions were normal for both groups, results were distorted when the distribution was skewed for one or both groups. Specifically, Type I error was inflated, differences between reference- and focal-group item parameter estimates were inaccurate, and group differences in the mean and variance of the latent distribution were overestimated.

First published on January 30, 2008, doi:10.1177/0146621607310402

Applied Psychological Measurement 2008;32:511.

A more recent version of this article appeared on October 1, 2008

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