Response-time models are of increasing interest in educational and psychological testing. This paper focuses on the lognormal model for response times (van der Linden, 2006), which is one of the most popular response-time models, and suggests a simple person-fit statistic for the model. The distribution of the statistic under the null hypothesis…

In standard item response theory (IRT) applications, the latent variable is typically assumed to be normally distributed. If the normality assumption is violated, the item parameter estimates can become biased. Summed score likelihood based statistics may be useful for testing latent variable distribution fit. We develop Satorra-Bentler type…