How Important is the Choice of Bandwidth in Kernel Equating?

Area of Science:

• Educational Measurement
• Psychometrics
• Statistical Modeling

Background:

• Kernel equating is a statistical method used to adjust test scores from different assessments.
• The smoothness of score distributions in kernel equating is controlled by a parameter called bandwidth.
• Existing bandwidth selection methods for kernel equating lack comprehensive comparative analysis.

Purpose of the Study:

• To compare four established bandwidth selection methods for kernel equating.
• To evaluate two additional cross-validation-based bandwidth selection methods.
• To assess the impact of sample size, test length, and score distributions on equating accuracy.

Main Methods:

• A simulation study was conducted using both equivalent and non-equivalent group designs.
• Variations in sample size, test length, and score distributions were implemented.
• The performance of six bandwidth selection methods was evaluated using mean squared error.

Main Results:

• Sample size and test length were identified as significant factors influencing equating accuracy and precision.
• All evaluated bandwidth selection methods demonstrated similar performance regarding mean squared error.
• Differences in equated scores across methods were minimal, suggesting bandwidth choice is not critical.

Conclusions:

• The choice of bandwidth selection method is not a critical factor in kernel equating accuracy.
• Sample size and test length are more influential parameters for achieving precise test score equating.
• Findings were further supported by an empirical analysis using college admissions test data.