Assessing Measurement Invariance with Exploratory Factor Analysis Trees: A Practical Guide

Measurement invariance (MI) describes the equivalence of measurement models of a latent variable across different groups or time. It is an important prerequisite for subsequent analyses such as group comparisons and diagnostic decisions. Therefore, establishing MI should be a key goal of psychometric research. Exploratory Factor Analysis trees (EFA trees) were developed to address MI already in early stages of measurement scale development. This tool, combining EFA and model based recursive partitioning, performs well in situations with many groups and continuous covariates. The goal of EFA trees is that they are an easy-To-use tool for assessing MI which can be applied both in questionnaire development and prior to group comparisons, especially when no specific hypotheses on the non-invariance between groups exists. To facilitate the application of EFA trees in practice, this paper provides a step-by-step tutorial of the new R package EFA tree that explains how to run the analysis and evaluate the results. A large dataset from a multi-country study is used to illustrate each step, and the results are compared with conventional methods of assessing MI. Advantages and limitations are discussed and further research ideas are presented.