I am trying to use esem multiple group analysis like one-way anova to do bivariate analyses with my factors. I have about 20 categorical variables that I want to do bivariate analyses on. Later I would like to do multivariable analyses with the factors and the classification variables. The problem is that each grouping variable gives me a different version of the factors. I have to make different modifications to achieve partial invariance with each grouping variable. With some grouping variables I canít achieve partial invariance at all and with other grouping variables the interpretation of the factors is different than the interpretation in the total sample. Am I using the technique appropriately? Any suggestions on a better way to approach this? Or should I just conclude that my factors are too unstable to work with?
I don't think such a critique of EFA is valid. It may instead be that EFA is often applied to measurements that have not been well designed and piloted to measure a certain set of hypothesized constructs.
I am sure the literature contains many studies where the measurement structure holds up. Perhaps you find some in the work by Marsh et al at