title: Testing strong factorial invariance using three-level structural equation modeling.
abstract: 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 et al. (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.
authors.affiliation: Department of Methods and Statistics, Faculty of Social Sciences, Utrecht University Utrecht, Netherlands.
authors.forename: Suzanne
authors.initials: S
authors.lastname: Jak
keywords: cluster bias; measurement bias; measurement invariance; multilevel SEM; three-level structural equation modeling