Chapter 3: Multigroup Factor Analysis

Identification of multigroup models

The main reason for estimating a multigroup factor analysis model is typically that we wish to estimate and compare means, variances or covariances of the factors between the groups. The requirement for the identifiability of the model is then that it should be possible to uniquely identify distinct values for these parameters in the different groups.

If the measurement model has full invariance of measurement, these country-specific distributions of the factors are identified if the measurement model is such that it would be identified also for single-group factor analysis (as discussed in Chapter 2) and if the factor means and variances are fixed in one group as discussed earlier in this chapter.

The remaining question is then whether and when the multigroup model is identified if the measurement model includes some non-invariance of measurement. Here we give some conditions for this. Consider first models which have different types of partial non-invariance for all of the observed items which are used as indicators of a factor:

In the case of models for one factor, we have the following results on partial non-invariance by item:

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