Logistic response models with item interactions.

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Conditional independence is a core assumption in traditional item response theory (IRT).
• Clustered items (e.g., testlets) often exhibit local dependence, violating this assumption.
• Existing IRT models may not adequately capture these dependencies.

Purpose of the Study:

• To investigate a logistic item response model capable of handling locally dependent item responses.
• To evaluate the model's performance in scenarios with clustered item content.
• To provide a framework for more accurate measurement in the presence of local dependence.

Main Methods:

• Development of a logistic item response model incorporating main effect and interaction parameters.
• Parameters are modeled as linear functions of the latent trait.
• Maximum likelihood estimation algorithm and information matrix are detailed.
• Parameter identifiability and over-fitting are addressed.

Main Results:

• The proposed model effectively accounts for local item dependence.
• Simulation studies demonstrate the model's ability to mitigate over-fitting.
• Real-data examples from sample surveys and ability testing highlight practical applicability.

Conclusions:

• The logistic item response model offers a viable solution for data with local item dependence.
• This approach enhances the accuracy of latent trait estimation in clustered item contexts.
• The findings have implications for survey design and educational/psychological assessment.