Asymptotically Correct Person Fit z-Statistics For the Rasch Testlet Model

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Established person fit statistics like $$ and $$ are limited to unidimensional or joint multidimensional item response theory (IRT) models.
• Existing methods often require joint estimation of all latent traits, posing computational challenges.

Purpose of the Study:

• To propose novel person fit statistics, $$ and $$, specifically for the Rasch testlet model.
• To extend the applicability of person fit evaluation to mixed-effects IRT models.
• To provide computational algorithms for the proposed statistics.

Main Methods:

• Development of $$ and $$ statistics based on a marginalized maximum likelihood ability estimator.
• Extension of the Lord-Wingersky algorithm for computational efficiency.
• Simulation studies to evaluate Type I error rates and power.

Main Results:

• The proposed $$ statistic demonstrates Type I error rates close to nominal levels.
• $$ shows satisfactory power in detecting aberrant responses.
• The statistics reduce to established $$ and $$ for unidimensional models.

Conclusions:

• The new statistics offer a robust method for person fit evaluation in Rasch testlet models.
• These methods enhance the assessment of response behavior in mixed-structure tests.
• The proposed statistics broaden the range of IRT models for which person fit can be assessed.