Joint modeling with generalized item response theory model family and response time model: Enhancing model structural...

Area of Science:

• Psychometrics
• Educational Measurement
• Statistical Modeling

Background:

• Traditional hierarchical models often overlook response times (RTs) as auxiliary data.
• Integrating RTs can improve the accuracy of latent trait estimation in item response theory (IRT) models.
• Existing models may not fully capture the complex, nonlinear relationship between examinee speed and ability.

Purpose of the Study:

• To propose a novel joint hierarchical model integrating IRT and log-normal RT models.
• To enhance the accuracy of latent trait estimation by incorporating RTs.
• To investigate nonlinear relationships between speed and ability and optimize IRT models using flexible link functions.

Main Methods:

• Developed a joint hierarchical model combining IRT and log-normal response time (RT) models.
• Integrated generalized logit-linked IRT with a log-normal random quadratic variable speed model for nonlinear relationships.
• Explored identical and distinct link functions across items for model optimization.
• Utilized Bayesian model comparison for evaluating model fit.

Main Results:

• The proposed joint hierarchical model yields more accurate estimates of ability, item difficulty, and discrimination parameters compared to traditional models.
• Bayesian model comparison indicates superior fit for the new joint model over existing IRT and RT combination models.
• The model demonstrates effectiveness, particularly with data exhibiting symmetric and asymmetric link functions.

Conclusions:

• The joint hierarchical model offers a significant advancement in analyzing item responses and response times.
• Incorporating response times and flexible link functions improves the precision of psychometric estimations.
• The methodology is validated through a comprehensive analysis of PISA 2015 science examination data.