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Detecting Differential Item Functioning Using the Logistic Regression Procedure in Small Samples.

Sunbok Lee1

  • 1Massachusetts Institute of Technology, Cambridge, MA, USA.

Applied Psychological Measurement
|June 9, 2018
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The likelihood ratio test (LRT) performs well for differential item functioning (DIF) even with small sample sizes. This logistic regression procedure is reliable for detecting DIF, offering accurate statistical power and type I error rates.

Keywords:
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Area of Science:

  • Psychometrics
  • Statistical modeling
  • Educational measurement

Background:

  • Logistic regression (LR) procedures for differential item functioning (DIF) often rely on asymptotic sampling distributions.
  • Common tests like the likelihood ratio test (LRT) and Wald test depend on asymptotic chi-square and normality assumptions, which may fail in small samples.
  • Penalized maximum likelihood (PML) estimation and bootstrap methods are alternatives for addressing finite sample biases and constructing empirical distributions.

Purpose of the Study:

  • To compare the performance of different logistic regression (LR) procedures for testing uniform and non-uniform differential item functioning (DIF).
  • To evaluate statistical power and type I error rates of the likelihood ratio test (LRT), Wald test, penalized likelihood ratio test (PLRT), and bootstrap likelihood ratio test (BLRT).
  • To assess the effectiveness of these methods, particularly in small sample scenarios where asymptotic assumptions may not hold.

Main Methods:

  • A simulation study was conducted to compare the performance of four logistic regression (LR) based procedures for DIF testing.
  • The procedures evaluated included the likelihood ratio test (LRT), Wald test, penalized likelihood ratio test (PLRT), and bootstrap likelihood ratio test (BLRT).
  • Performance was assessed based on statistical power and type I error rates for detecting both uniform and non-uniform DIF.

Main Results:

  • The simulation results indicated that the likelihood ratio test (LRT) using the asymptotic chi-square distribution performed well.
  • This performance was consistent even when applied to small sample sizes.
  • The study provides evidence for the robustness of the LRT in DIF testing across various sample sizes.

Conclusions:

  • The likelihood ratio test (LRT) is a reliable method for testing differential item functioning (DIF), even in small samples.
  • Its performance in terms of statistical power and type I error is robust, making it a suitable choice for DIF analysis.
  • The findings suggest that traditional asymptotic assumptions for LRT in DIF testing may be less critical than previously thought for practical applications.