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A Posterior Predictive Model Checking Method Assuming Posterior Normality for Item Response Theory.

Megan Kuhfeld¹

¹The University of Texas at Austin, USA.

Applied Psychological Measurement

|February 23, 2019

Summary

This study introduces a new Bayesian posterior predictive model checking (PPMC) method to detect local dependence in item response theory (IRT) models. The PPMC-N approach offers a straightforward way to assess model fit and parameter uncertainty.

Keywords:

item response theory model fit assessment posterior predictive model checking

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Area of Science:

Psychometrics
Statistical Modeling
Educational Measurement

Background:

Unidimensional item response theory (IRT) models rely on the assumption of local independence.
Violations of local independence can lead to inaccurate model estimations and interpretations.
Bayesian posterior predictive model checking (PPMC) is a valuable tool for assessing model fit and detecting violations of assumptions in IRT.

Purpose of the Study:

To propose and evaluate a novel PPMC method for assessing local dependence in unidimensional IRT models.
To address the challenge of parameter uncertainty in model fit assessment within IRT.
To provide a straightforward approach for detecting local dependence.

Main Methods:

The study proposes a PPMC method, termed "PPMC assuming posterior normality" (PPMC-N), for IRT models estimated via full-information maximum likelihood.
The PPMC-N method accounts for parameter uncertainty in model fit assessment.
A simulation study was conducted to compare the performance of PPMC-N with a standard Bayesian PPMC approach.

Main Results:

The proposed PPMC-N method demonstrated comparability with the Bayesian PPMC approach in detecting local dependence.
The simulation study confirmed the effectiveness of PPMC-N in identifying local dependence in dichotomous IRT models.
PPMC-N offers a practical and efficient way to evaluate local independence assumptions.

Conclusions:

The PPMC-N method is a viable and effective tool for assessing local dependence in unidimensional IRT models.
This approach enhances the reliability of IRT model applications by addressing violations of local independence.
The findings support the use of PPMC-N for robust model fit assessment in psychometric research.