The Asymptotic Power of the Lagrange Multiplier Tests for Misspecified IRT Models

This article studies the power of Lagrange Multiplier Test and Generalized to detect measurement non-invariance in Item Response Theory (IRT) models for binary data. We study performance these two tests under correct model specification incorrect distribution latent variable. The asymptotic each test alternative hypothesis depends on a noncentrality parameter that is used compute power. present different procedures consequently tests. methods evaluated through simulation study. They turn out be very similar classic empirical but less time consuming. Moreover, results highlight more powerful than all conditions.