Confirmatory factor analysis and the necessity of measurement invariance in group comparisons
Often social science researchers deal with concepts and phenomena that are latent constructs and cannot be observed directly. Examples include prejudices, skills, fears, or all kinds of attitudes in general. As an attempt to measure the unobservables, researchers use various indicators and survey items, which they see as representing the original latent construct. These items can be aggregated by several methods in order to estimate the latent constructs.
Confirmatory factor analysis (CFA) is one of the most sophisticated methods to estimate latent constructs. CFA assumes that the measured variables (items or indicators) are linear, additive functions of the unobserved (latent) factors and assumes a certain structure of the measurement model. This way, complex structures can be measured, such as the latent construct intelligence that itself consists of a couple of a couple of latent (mathematical, linguistic, musical) intelligences. However, comparing the latent constructs of different groups can be challenging. This is particularly the case for international comparisons that receive growing attention these days. The multi-group multiple indicator model offers a systematic measurement tool to tackle such problems.