Chapter 4 Checklist for Measurement Invariance with MGCFA

In this section we describe the necessary steps for invariance testing.

4.1 Start by having a model

  • Any statistical model is only as good as the theory it is built on.

  • Run CFA in each group to detect any large deviations.

4.2 Test the configural model

  • Run a MGCFA without cross group equality constraints

  • The model should show a good fit.

There are two approaches of model identification: marker indicator or reference group (see Little et al., 2006)

4.3 Test the metric model

  • Fix the factor loadings to be equal across groups

  • Compare the model fit to the configural model

4.4 Test the scalar model

  • In addition to the factor loadings, constrained the intercepts to be equal across groups

  • Compare the model fit to the metric model

4.5 Got noninvariance? It happens often.

Several options:

	- exclude groups
	
	- remove items

	- distinguish several subgroups of countries

Still not getting invariance?

Conclude that the construct has different meaning across groups

Alternatively, consider the decision tree presented in Figure 3.7.