Tutorial in Longitudinal Measurement Invariance and Cross-lagged Panel Models Using Lavaan

In longitudinal studies involving multiple latent variables, researchers often seek to predict how iterations of latent variables measured at early time points predict iterations measured at later time points. Cross-lagged panel modeling, a form of structural equation modeling, is a useful way to conceptualize and test these relationships. However, prior to making causal claims, researchers must first ensure that the measured constructs are equivalent between time points. To do this, they test for measurement invariance, constructing and comparing a series of increasingly strict and parsimonious models, each making more constraints across time than the last. This comparison process, though challenging, is an important prerequisite to interpretation of results. Fortunately, testing for measurement invariance in cross-lagged panel models has become easier, thanks to the wide availability of R and its packages. This paper serves as a tutorial in testing for measurement invariance and cross-lagged panel models using the lavaan package. Using real data from an openly available study on perfectionism and drinking problems, we provide a step-by-step guide of how to test for longitudinal measurement invariance, conduct cross-lagged panel models, and interpret the results. Original data source with materials: https://osf.io/gduy4/. Project website with data/syntax for the tutorial: https://osf.io/hwkem/.