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Article Published: Entropy-Based Measures for Person Fit in Item Response Theory

Drs. William Dardick and Brandi Weiss published an article titled Entropy-based measures for person fit in item response theory in Applied Psychological Measurement (DOI:10.1177/0146621617698945).

This article introduces three new variants of entropy to detect person misfit (Ei, EMi, and EMRi), and provides preliminary evidence that these measures are worthy of further investigation. Previously, entropy has been used as a measure of approximate data–model fit to quantify how well individuals are classified into latent classes, and to quantify the quality of classification and separation between groups in logistic regression models. In the current study, entropy is explored through conceptual examples and Monte Carlo simulation comparing entropy with established measures of person fit in item response theory (IRT) such as lz, lz*, U, and W. Simulation results indicated that EMi and EMRiwere successfully able to detect aberrant response patterns when comparing contaminated and uncontaminated subgroups of persons. In addition, EMi and EMRi performed similarly in showing separation between the contaminated and uncontaminated subgroups. However, EMRi may be advantageous over other measures when subtests include a small number of items. EMi and EMRiare recommended for use as approximate person-fit measures for IRT models. These measures of approximate person fit may be useful in making relative judgments about potential persons whose response patterns do not fit the theoretical model.

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