Estimation of the MIRID: a program and a SAS-based approach

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Item Response Theory (IRT) models are crucial for educational and psychological assessments.
• Componential IRT models, such as Rasch-MIRID and OPLM-MIRID, offer nuanced measurement capabilities.
• Efficient parameter estimation is vital for the practical application of these models.

Purpose of the Study:

• To compare the performance of the MIRID CML program with a Maximum Marginal Likelihood (MML) approach using SAS PROC NLMIXED.
• To evaluate the accuracy and efficiency of parameter estimation for both item and person parameters in two componential IRT models.
• To highlight the trade-offs between speed, flexibility, and estimation accuracy of the compared methods.

Main Methods:

• Utilized the MIRID CML program for Conditional Maximum Likelihood (CML) estimation.
• Employed SAS Version 8 PROC NLMIXED for Maximum Marginal Likelihood (MML) estimation.
• Conducted a simulation study to compare the two estimation approaches.

Main Results:

• Both MIRID CML and SAS MML approaches demonstrated comparable accuracy in estimating item parameters.
• Differences were observed in the estimation of person parameters, attributed to varying distributional assumptions.
• The SAS MML approach, while more flexible, was significantly slower than the MIRID CML program.

Conclusions:

• The MIRID CML program and SAS MML approach are both viable for estimating parameters in componential IRT models.
• The choice between methods depends on the specific research needs regarding speed, flexibility, and the importance of person parameter estimation accuracy.
• Further research may explore hybrid approaches or optimizations for MML estimation in IRT.