We began our investigation considering an SEM model in which a latent intelligence variable is regressed on a superordinate SES factor. Note that the model had convergence problems, requiring us to increase the number of iterations allowed.
Next, we regressed the intelligence factor directly on the factors that had made up the SED construct in the previous example. The program did not converge.
We considerd a MIMIC model in which we replaced the SES latent variable with the measured family income variable.
We repeated that analysis allowing the regression to vary by gender.
We noted that in the previous analysis, only the regression changed by groups, not the CFA part of the model. We further illustrated this idea by performing a CFA by gender and noting that only the covariance between factors varied by group.