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.

Measurement Invariance Syntax

Online tool to check degrees of freedom in MGCFA

We encourage authors and reviewers to routinely use our online tool where you can enter the number of indicators, latent variables, groups, etc. to double-check the degrees of freedom of your reported models. In this context, we welcome the recent effort of journals in psychology to include soundness checks on manuscript submission such as statcheck to improve the accuracy of statistical reporting.

Online tool to check df in MGCFA

Ant Colony Optimization script

Ant Colony Optimization (ACO) mimics the foraging behavior of ants and is a popular optimization algorithm in computational sciences. Ants use pheromone tracks to find the shortest route from the nest to the food source, which generally accumulate faster on shorter routes which in turn attract more ants. Routes are constantly optimized until an efficient route is found. Due to its great flexibility the same principles can also be applied to psychological settings, for example, in the construction of short scales.

We have used ACO in several publications: Jankowsky et al. (2020), Olaru et al. (2018), Olaru et al. (2019), Schroeders et al. (2016), Schroeders et al. (2016). A recent version of the syntax can be found here, which is described in more detail in Olaru et al. (2019).

Ant Colony Optimization script