Multilevel exploratory factor analysis of discrete data Measurement bias detection through factor analysis

Exploratory factor analysis (EFA) can be used to determine the dimensionality of a set of items. When data come from clustered subjects, such as pupils within schools or children within families, the hierarchical structure of the data should be taken into account. Standard multilevel EFA is only suited for the analysis of continuous data. However, with the robust weighted least squares estimation procedures that are implemented in the computer program Mplus, it has become possible to easily conduct EFA of multilevel discrete data. In the present paper, we show how multilevel EFA can be used to determine the dimensionality in discrete two-level data. Measurement invariance across clusters implies equal dimensionality across levels. We describe two procedures, one with and one without measurement invariance restrictions across clusters. Data from educational research serve as an illustrative example.