Testing strong factorial invariance using three-level structural equation modeling

• Main Author: Suzanne eJak
• Format: Article
• Language: English
• Published: Frontiers Media S.A. 2014-07-01
• Series: Frontiers in Psychology
• Subjects: Measurement invariance; cluster bias; multilevel SEM; measurement bias; three-level structural equation modeling
• Online Access: http://journal.frontiersin.org/Journal/10.3389/fpsyg.2014.00745/full

Within structural equation modeling, the most prevalent model to investigate measurement bias is the multigroup model. Equal factor loadings and intercepts across groups in a multigroup model represent strong factorial invariance (absence of measurement bias) across groups. Although this approach is possible in principle, it is hardly practical when the number of groups is large or when the group size is relatively small. Jak, Oort and Dolan (2013) showed how strong factorial invariance across large numbers of groups can be tested in a multilevel structural equation modeling framework, by treating group as a random instead of a fixed variable. In the present study, this model is extended for use with three-level data. The proposed method is illustrated with an investigation of strong factorial invariance across 156 school classes and 50 schools in a Dutch dyscalculia test, using three-level structural equation modeling.