Parsimonious asymmetric item response theory modeling with the complementary log-log link.

Area of Science:

• Psychometrics
• Statistical Modeling
• Educational Measurement

Background:

• Traditional item response theory (IRT) models commonly assume symmetric error distributions and link functions (logit, probit).
• These assumptions can limit the accurate modeling of response probabilities in certain psychometric applications.
• There is a need for alternative models that accommodate asymmetric response patterns.

Purpose of the Study:

• To investigate the one-parameter complementary log-log model (CLLM) as an alternative to traditional IRT models.
• To evaluate the psychometric properties and practical utility of the CLLM.
• To demonstrate the CLLM's applicability in scenarios with asymmetric response distributions.

Main Methods:

• The study employed simulation studies to assess the performance of the CLLM.
• Key aspects investigated included model estimability with small sample sizes, item-weighted scoring capabilities, and the handling of guessing.
• The CLLM was also applied to empirical data to validate simulation findings.

Main Results:

• The complementary log-log model (CLLM) proved to be estimable even with small sample sizes.
• The CLLM demonstrated the ability to facilitate item-weighted scoring.
• The model effectively accounted for the effect of guessing, a significant psychometric property, despite its single-parameter nature.

Conclusions:

• The one-parameter complementary log-log model (CLLM) is a viable and psychometrically sound alternative to traditional IRT models.
• The CLLM offers advantages in handling asymmetric response distributions and guessing.
• This research contributes to the ongoing development of more flexible and complex psychometric models.