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Entropy-Based Measures for Person Fit in Item Response Theory
William R Dardick1, Brandi A Weiss1
1The George Washington University, DC, USA.
Applied Psychological Measurement
|June 9, 2018
Summary
This study introduces new entropy-based measures (EM and EMR) for detecting person misfit in item response theory (IRT) models. These novel metrics effectively identify aberrant response patterns and are recommended for assessing data-model fit.
Area of Science:
- Psychometrics
- Statistical Modeling
- Educational Measurement
Background:
- Entropy has been utilized to assess data-model fit and classification quality in statistical models.
- Existing person-fit measures in Item Response Theory (IRT) lack sufficient sensitivity in certain scenarios.
Purpose of the Study:
- Introduce and evaluate three novel entropy variants (E, EM, EMR) for detecting person misfit in IRT.
- Compare the performance of these new measures against established IRT person-fit statistics (e.g., l, W).
Main Methods:
- Conceptual examples and Monte Carlo simulations were employed for analysis.
- Contaminated and uncontaminated subgroups were simulated to test the detection of aberrant response patterns.
- The new entropy measures were compared with existing person-fit statistics.
Main Results:
- The EM and EMR entropy measures demonstrated success in detecting aberrant response patterns.
- EM and EMR showed comparable performance in distinguishing between contaminated and uncontaminated subgroups.
- EMR showed potential advantages when dealing with subtests containing a small number of items.
Conclusions:
- EM and EMR are recommended as approximate person-fit measures for IRT models.
- These novel entropy-based measures can aid in identifying individuals with response patterns that deviate from the theoretical model.
- Further investigation into these entropy variants is warranted for their practical application.
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