In a new paper in the European Journal of Psychological Assessment, Timo Gnambs and I examined the soundness of reporting measurement invariance (MI) testing in the context of multigroup confirmatory factor analysis (MGCFA). Of course, there are several good primers on MI testing (e.g., Cheung & Rensvold, 2002; Wicherts & Dolan, 2010) and textbooks that elaborate on the theoretical base (e.g., Millsap, 2011), but a clearly written tutorial with example syntax how to implement MI practically was still missing. In the first part of the paper, we demonstrate that a sobering large amount of reported degrees of freedom (df) do not match with the df recalculated based on information given in the articles. More specifically, we both reviewed 128 studies including 302 measurement invariance MGCFA testing procedures from six leading peer-reviewed journals that focus on psychological assessment and on a regular base. Overall, about a quarter of all articles included at least one discrepancy with some systematic differences between the journals. However, it was interesting to see that the metric and scalar step of invariance testing were more frequently affected.
In 2009, I wrote a small chapter that was part of an EU conference book on the transition to computer-based assessment. Now and then I’m coming back to this piece of work - in my teaching and my publications (e.g., the EJPA paper on testing reasoning ability across different devices). Now I want to make it publically available. Hopefully, it will be interesting to some of you. The chapter is the (unaltered) preprint version of the book chapter, so if you want to cite it, please use the following citation: