Three new corrections for standardized person-fit statistics for tests with polytomous items

Area of Science:

• Psychometrics
• Educational Measurement
• Statistics

Background:

• Person-fit statistics are crucial for identifying unusual response patterns in testing.
• Standardized person-fit statistics ($$) for polytomous items often assume known ability and infinite items, which are unrealistic.
• Violations of these assumptions can degrade the quality of person-fit results.

Purpose of the Study:

• To propose three novel corrections for the $$ statistic.
• To address the limitations of estimated ability parameters and finite item pools in polytomous tests.
• To enhance the accuracy of person-fit assessment in educational and psychological testing.

Main Methods:

• Development of three new corrections for the $$ statistic, extending methods for dichotomous items.
• Conducting a simulation study to evaluate the performance of the proposed corrections.
• Comparison of new corrections against the original $$ statistic and an existing correction by Sinharay (2016).

Main Results:

• The three proposed corrections demonstrated superior performance compared to the original $$ statistic.
• The new corrections also outperformed an existing correction for $$ in the simulated scenarios.
• The proposed methods effectively account for estimated ability and finite item numbers.

Conclusions:

• The newly developed corrections offer a promising advancement for person-fit analysis with polytomous items.
• These corrections provide more reliable person-fit results in practical testing situations.
• The findings suggest improved methods for detecting aberrant response behaviors in standardized tests.