Expanding the Lognormal Response Time Model Using Profile Similarity Metrics to Improve the Detection of Anomalous Testing Behavior

The Lognormal Response Time (LNRT) model measures the speed of test-takers relative to the normative time demands of items on a test. The resulting speed parameters and model residuals are often analyzed for evidence of anomalous test-taking behavior associated with fast and poorly fitting response time patterns. Extending this model, we demonstrate the connection between the existing LNRT model parameters and the “level” component of profile similarity, and we define two new parameters for the LNRT model representing profile “dispersion” and “shape.” We show that while the LNRT model measures level (speed), profile dispersion and shape are conflated in model residuals, and that distinguishing them provides meaningful and useful parameters for identifying anomalous testing behavior. Results from data in a situation where many test-takers gained preknowledge of test items revealed that profile shape, not currently measured in the LNRT model, was the most sensitive response time index to the abnormal test-taking behavior patterns. Results strongly support expanding the LNRT model to measure not only each test-taker's level of speed, but also the dispersion and shape of their response time profiles.