Testing Measurement Invariance Using Item Response Theory in Longitudinal Data: An Introduction

Item response theory (IRT) consists of a set of mathematical models for the probabilities of various responses to test items as a function of item and person characteristics. In longitudinal data, changes in measured variables can only be interpreted if important psychometric features of the measured variables are assumed invariant across time. Measurement invariance is invariance in the relation of a measure to the latent variable underlying it. Measurement invariance in longitudinal studies concerns invariance over time, and IRT provides a useful approach to investigating longitudinal measurement invariance. Commonly used IRT models are described, along with the representation of measurement invariance in IRT. The use of IRT for investigating invariance is then described, along with practical considerations in using IRT for this purpose. Conceptual issues, rather than technical details, are emphasized throughout.