Regarding Item Parameter Invariance for the Rasch and the 2-Parameter Logistic Models: An Investigation under Finite Non-Representative Sample Calibrations

Abstract

ABSTRACT The property of item parameter invariance in item response theory (IRT) plays a pivotal role in the applications of IRT such as test equating. The scope of parameter invariance when using estimates from finite biased samples in the applications of IRT does not appear to be clearly documented in the IRT literature. This article provides information on the extent to which item parameter invariance is observed in samples with the Rasch and 2-parameter model calibrations through simulations, where the behaviors of item parameter estimates were examined under 12 different types of convenient sampling scenarios. The results indicated that the property of item invariance in IRT for dichotomously scored data could hold for the sample item parameter estimates, regardless of biased samples, when the model holds in the data, the number of items in a test is not small, and the sample size is large.