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Asymptotically Correct Person Fit z-Statistics For the Rasch Testlet Model
Zhongtian Lin1, Tao Jiang2, Frank Rijmen2
1Financial Industry Regulatory Authority.
Psychometrika
|February 25, 2026
Summary
New person fit statistics, lzt and lzt*, are introduced for the Rasch testlet model, offering improved detection of aberrant responses in item response theory (IRT) analysis.
Area of Science:
- Psychometrics
- Educational Measurement
- Item Response Theory
Background:
- Established person fit statistics like lz and lz* are limited to unidimensional or joint multidimensional IRT models.
- Existing methods often require simultaneous estimation of all latent traits, posing computational challenges.
Purpose of the Study:
- To propose new person fit statistics, lzt and lzt*, specifically for the Rasch testlet model.
- To extend the applicability of person fit evaluation to a broader range of IRT models, including those with testlet structures.
Main Methods:
- Development of lzt and lzt* statistics based on a marginalized maximum likelihood ability estimator.
- Extension of the Lord-Wingersky algorithm for the computation of the lzt* statistic.
- Simulation studies to evaluate Type I error rates and power for detecting aberrant responses.
Main Results:
- The proposed lzt* statistic demonstrates close-to-nominal Type I error rates and satisfactory power in simulations.
- lzt and lzt* statistics generalize to lz and lz* for unidimensional models, validating their broader applicability.
- A real data application illustrates the utility of the new statistics for mixed-structure tests.
Conclusions:
- The lzt and lzt* statistics provide a valuable tool for assessing person fit within the Rasch testlet model.
- These statistics enhance the evaluation of response behavior across a wider spectrum of IRT models.
- The proposed methods are effective for identifying aberrant responses in complex testing structures.
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