Testing measurement Invariance in a CFA framework – State of the art

In recent years, several studies have stressed out the importance to guarantee the comparability of theoretical constructs (i.e. measurement invariance) in the compared units (e.g., groups or time points) in order to conduct comparative analyses (e.g. Harkness, Van de Vijver, & Mohler, 2003; Meredith, 1993; Vandenberg, & Lance, 2000). If one does not test for measurement invariance (MI) or ignores lack of invariance, differences between groups in the latent constructs cannot be unambiguously attributed to ‘real’ differences or to differences in the measurement attributes. One approach to test for MI is in a confirmatory factor analysis (CFA) framework. In this framework, MI is usually tested with a series of model comparisons that define more and more stringent equality constraints. The presentation will be about new developments in the MI-CFA framework. Among other things, the presentation tries to answer the following questions:
• Which scale setting method to use (marker variable, fixed factor or effect coding method) when testing for MI?
• Should a top-down- or bottom-up-approach be used?
• How to test MI with a large number of groups (>30)?
• What are the possibilities to evaluate whether MI exists (e.g., statistical significance of the ∆² after Bonferroni adjustment, changes in approximate fit statistics, magnitude of difference between the parameter estimates)?
• How to determine confidence intervals for fit indices?
• Can MI be graphically analyzed?
• How can be dealt with non-invariance?
These questions will be tried to answered by an application to a real world dataset (N ~ 40.000), with a one-factor/five indicator model of a well-being scale tested in 35 groups.