# A Psychometric Perspective on the Associations between Response Accuracy and Response Time Residuals

## TL;DR

The paper explores how response accuracy and response time residuals are connected in psychometric models, suggesting accuracy residuals may influence response time.

## Contribution

The paper introduces a novel psychometric perspective where accuracy residuals are exogenous and influence response time.

## Key findings

- Item parameter estimate heterogeneity may be a psychometric artifact from accuracy residuals.
- Response time residuals as indicators of proficiency should consider interactions with accuracy residuals.

## Abstract

We provide an alternative psychometric perspective on the empirical statistical dependencies observed between response accuracy residuals (RARs) and response time residuals (RTRs) in the context of the van der Linden model. This perspective emphasizes the RAR (or parts of the RAR) as being exogenous and having a directional influence on response time. Our simple and theoretically justifiable perspective adds to previous joint response time/accuracy models and comports with recent generalizations of the D-diffusion IRT model incorporating person-by-item interactions, and thus similarly reproduces many of the recently highlighted empirical findings concerning the associations between RARs and RTRs. Using both empirical and simulation-based results, we show how our psychometric perspective has both applied and interpretational implications. Specifically, it would suggest that (1) studies of item parameter estimate heterogeneity in relation to response times may reflect more of a psychometric artifact (due to the exogenous effects of the RARs) as opposed to providing insights about the response process (e.g., the application of different response strategies) and that (2) efforts to use RTRs as indicators of latent proficiency should attend to the anticipated interactions between the latent proficiency and RAR on response times. The validity of our psychometric perspective against alternatives likely relies on appeals to theory; the best perspective to take may vary depending on the test setting.