Maximum Likelihood Score Estimation Method With Fences for Short-Length Tests and Computerized Adaptive Tests.

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Maximum Likelihood Estimation (MLE) faces limitations with specific response patterns (all 0s or 1s) in test score estimation.
• Existing MLE with Truncation (MLET) and Bayesian methods (MAP, EAP) have drawbacks, including inability to handle certain patterns or score scale shrinkage.

Purpose of the Study:

• To introduce and evaluate a novel method, MLE with Fences (MLEF), for robust test score estimation.
• To address the shortcomings of MLE, MLET, MAP, and EAP in handling problematic response patterns and score scale shrinkage.

Main Methods:

• Developed MLEF by incorporating imaginary "fence" items with fixed responses to ensure a workable log-likelihood function.
• Compared MLEF performance against MLET, MAP, and EAP using simulated or real-world test data with diverse response patterns.

Main Results:

• MLEF successfully handles all response patterns, including those problematic for MLET.
• MLEF avoids the score scale shrinkage observed with MAP and EAP methods.
• MLEF provides accurate theta estimates without bias towards the prior distribution's center.

Conclusions:

• MLEF is a viable and superior alternative to existing methods for test score estimation, especially in Computerized Adaptive Testing (CAT).
• The MLEF approach enhances the reliability and accuracy of ability estimation across various testing scenarios.