Score-Based Tests with Fixed Effects Person Parameters in Item Response Theory: Detecting Model Misspecification Including Differential Item Functioning

We develop an approximation to score-based tests for item response theory models that treat the person parameters as fixed effects, which are important for large data and item counts where typical approaches can be too slow. Our approximation allows computationally inexpensive tests for differential item function and other model misspecifications in sufficiently long tests, in that score contributions are leveraged and comparison models are not required. We outline the theoretical framework and adapt it to two recently proposed consistent methods of parameter estimation, constrained joint maximum likelihood estimation and a joint maximum a posteriori approach. A key benefit of the approach is that, in contrast to earlier score-based test approaches, the prior for person parameters does not need to be specified precisely. We use simulations to evaluate the new method for detecting violations of measurement invariance in the two-parametric logistic test model. The new approximation is sensitive to violations of measurement invariance while having a sufficiently low Type I error rate in large samples and tests. We demonstrate the new method in an empirical data set examining reading performance, from the Mindsteps online learning platform.