Entropy-Based Measures for Person Fit in Item Response Theory

This article introduces three new variants of entropy to detect person misfit ( E i , EM i , and EMR i ), 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 l z , l z *, U, and W. Simulation results indicated that EM i and EMR i were successfully able to detect aberrant response patterns when comparing contaminated and uncontaminated subgroups of persons. In addition, EM i and EMR i performed similarly in showing separation between the contaminated and uncontaminated subgroups. However, EMR i may be advantageous over other measures when subtests include a small number of items. EM i and EMR i are 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.