Second-Order Probability Matching Priors for the Person Parameter in Unidimensional IRT Models

Area of Science:

• Psychometrics
• Statistical modeling
• Social sciences

Background:

• Accurate confidence intervals (CIs) for person parameters are crucial in item response theory (IRT) applications.
• Standard interval estimation procedures (e.g., Wald, Bayesian CIs) rely on asymptotic normality and perform poorly with short tests common in social science.
• There is a need for refined methods that provide reliable frequentist coverage for person parameters in IRT, especially in resource-limited research settings.

Purpose of the Study:

• To propose a novel construction of second-order probability matching priors for person parameters in unidimensional IRT models.
• To develop confidence intervals (CIs) that achieve accurate frequentist coverage, even for short tests.
• To offer an efficient computational method for these improved CIs across various unidimensional IRT models.

Main Methods:

• Development of second-order probability matching priors for the person parameter in unidimensional IRT.
• Establishment of the probability matching property through posterior distribution function expansion and a shrinkage argument.
• Efficient computation of CIs derived from the proposed priors for diverse IRT models.

Main Results:

• The proposed probability matching priors yield confidence intervals with accurate coverage, outperforming asymptotic methods for short tests.
• The method demonstrates robust performance in a simulation study and a real-data example involving a mixed-format test.
• The proposed CIs can be efficiently computed, making them practical for applied researchers.

Conclusions:

• The novel probability matching prior construction provides a valuable tool for accurate interval estimation of person parameters in IRT, particularly when test length is limited.
• This method addresses a critical limitation of existing asymptotic CIs, enhancing the reliability of findings in social science research.
• The proposed approach offers an efficient and accurate alternative for computing confidence intervals in various unidimensional IRT models.