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A family of score-based tests has been proposed in recent years for assessing the invariance of model parameters in several models of item response theory (IRT). These tests were originally developed in a maximum likelihood framework. This study discusses analogous tests for Bayesian maximum-aposteriori estimates and multiple-group IRT models. We propose two families of statistical tests, which are based on an approximation using a pooled variance method, or on a simulation approach based ondoi:10.5167/uzh-223810 fatcat:uzqj4svst5dwxpirkvk2qfuj4e