Comparison of procedures used to test measurement invariance in longitudinal factor analysis

In this paper we hope to further advance the use of structural equation modelling to test longitudinal measurement invariance. To achieve this we discuss two different procedures to test invariance. We illustrate the differences by applying both procedures to an example of longitudinal data from lung cancer patients. One procedure relies on the modification indices (MI) and expected parameter changes (EPC) to assess the tenability of the equality constraints imposed on parameters across two measurement occasions. However, as Saris, Satorra and Van der Veld (2009) have suggested that this procedure can be improved upon by taking the power of the MI into account, our first procedure will include MI, EPC, and power. In the second procedure, we rely on global tests and standardised observed parameter changes (SOPC) rather than expected changes. Both procedures guard against chance findings, though they do so in very different ways that can lead to different results.