The methodology for assessing FI is based upon multiple group confirmatory factor analysis (MGCFA), a variant of multiple groups SEM. The MGCFA model is expressed as:

xg g g= + +τ η εΛg (5.1)

The parameters in this model are the same as in equation (3.1), with the addition of the group subscript, g, indicating that each of the parameters can differ by group. Invariance testing for the parameters in (5.1) is done sequentially using MGCFA models with increasing constraints with respect to group equality on the model parameters. The weakest type of invariance under the FI umbrella is commonly referred to as configural invariance (CI). Under CI, the researcher assumes only that the number of latent variables and the correspondence of observed indicators to the latent variables is the same for all groups in the population. In other words, when CI holds, the basic factor structure is equivalent across groups, but no assumptions are made about equality of the model parameters. This situation would correspond to (5.1).