Multigroup measurement invariance testing (in R und Mplus) Measurement invariance (MI) is a key concept in psychological assessment and a fundamental prerequisite for meaningful comparisons across groups. In the prevalent approach, multi-group confirmatory factor analysis (MGCFA), specific measurement parameters are constrained to equality across groups, to test for (a) configural MI, (b) metric MI, (c) scalar MI, and (d) strict MI. In the online supplement to Schroeders & Gnambs (2018), we provide example syntax for all steps of MI in lavaan and Mplus for different ways of scaling latent variables: Identification by (a) marker variable, (b) reference group, and (c) effects coding.
Reference. Schroeders, U., Wilhelm, O., & Olaru, G. (2016). Meta-heuristics in short scale construction: Ant Colony Optimization and Genetic Algorithm. PLOS ONE, 11, e0167110. doi:10.1371/journal.pone.0167110 Abstract. The advent of large-scale assessment, but also the more frequent use of longitudinal and multivariate approaches to measurement in psychological, educational, and sociological research, caused an increased demand for psychometrically sound short scales. Shortening scales economizes on valuable administration time, but might result in inadequate measures because reducing an item set could: a) change the internal structure of the measure, b) result in poorer reliability and measurement precision, c) deliver measures that cannot effectively discriminate between persons on the intended ability spectrum, and d) reduce test-criterion relations.