Evaluating Reasonableness Tests for Longitudinal Measurement Invariance in Structural Equation Modeling using Confirmatory Factor Analysis

Researchers are typically interested in comparing groups of people and/or comparing people across time. If researchers are to conclude differences are due to group dynamics or time, we must establish that the measure(s) we are using are actually invariant across groups or time. Some statistical methods (ANOVA and regression) make this assumption without direct evaluation. Conducting analyses in the Structural Equation Modeling (SEM) framework using Confirmatory Factor Analysis (CFA) is one way the assumption of measurement invariance can be evaluated directly. Many researchers have studied multiple group invariance and current invariance testing recommendations are based on multiple group studies and simulations. There is a lack of literature on testing invariance in longitudinal designs. Current guidelines recommend researchers apply the same guidelines from multiple group to longitudinal designs. Longitudinal designs are more complicated and may need different recommendations. The current study evaluates measurement invariance in longitudinal CFA in order to ascertain if the current guidelines based off the multiple group case are acceptable when applied to the longitudinal framework