Factor invariance in longitudinal studies: Measuring the same construct across time

When researchers are conducting studies that require repeated measures, it is not uncommon for them to assume that the particular instrument is equally going to assess the latent construct of interest no matter how many times the instrument (test) is administered. In other words, it is not in question whether the properties of the test are likely to change or not. However, measurement invariance is not something that the instrument possesses by default. Measurement invariance has to be tested. The aim of this paper was to provide an insight into testing factorial invariance performing the confirmatory factor analysis on a set of longitudinal data. The first part of this paper is theoretical and describes different forms of invariance. The second part offers a concrete example and a step-by-step guide on how to perform confirmatory factor analysis for repeated measurements to test the invariance using statistical software R.