Modeling Sequential Dependencies in Progressive Matrices: An Auto-Regressive Item Response Theory (AR-IRT) Approach

Area of Science:

• Psychometrics
• Cognitive Psychology
• Educational Measurement

Background:

• Traditional measurement models assume item response independence, often overlooking sequential dependencies.
• Auto-regressive models are underexplored in item response theory, particularly for cognitive ability tests.

Purpose of the Study:

• To extend binary item response models, specifically the 2-parameter logistic (2PL) model, to incorporate auto-regressive sequential dependencies.
• To investigate the impact of sequential effects on cognitive ability testing, using progressive matrices as a case study.

Main Methods:

• Development of an auto-regressive lag-1 2PL model.
• Application and comparison of the proposed model against a traditional 2PL model using a publicly available progressive matrices dataset.

Main Results:

• The auto-regressive lag-1 2PL model demonstrated superior model fit compared to the traditional 2PL model.
• The proposed model yielded more conservative discrimination parameters and standard errors, suggesting improved precision.

Conclusions:

• Sequential dependencies are likely a significant, overlooked factor in cognitive ability testing, especially in progressive matrices.
• Auto-regressive models offer a more accurate representation of response processes in sequential testing scenarios.