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

Abstract

Measurement models traditionally make the assumption that item responses are independent from one another, conditional upon the common factor. They typically explore for violations of this assumption using various methods, but rarely do they account for the possibility that an item predicts the next. Extending the development of auto-regressive models in the context of personality and judgment tests, we propose to extend binary item response models—using, as an example, the 2-parameter logistic (2PL) model—to include auto-regressive sequential dependencies. We motivate such models and illustrate them in the context of a publicly available progressive matrices dataset. We find an auto-regressive lag-1 2PL model to outperform a traditional 2PL model in fit as well as to provide more conservative discrimination parameters and standard errors. We conclude that sequential effects are likely overlooked in the context of cognitive ability testing in general and progressive matrices tests in particular. We discuss extensions, notably models with multiple lag effects and variable lag effects.