Hello! I am trying to analyze across four groups a hierarchical CFA model with five first-order latent factors and one second-order factor.
I already tested the five first-order latent factors for configural, metric, factor variance, intercept / threshold, and factor mean invariance. I am now using the most constrained model of each that shows good fit to the data in order to estimate the hiearchical CFA.
Now that I am trying to test the hierarchical structure for configural invariance across groups, I get an error message that I have (1) a negative residual variance for a latent factor, (2) a correlation greater than 1 between two latent variables, or (3) a linear dependency among two latent variables. From my reading of TECH 4 and the model parameter estimates, I believe I have, unfortunately, satisfied all three conditions with just one of my first-order latent factors.
What might be causing this problem and how might I rectify it? Is it possible to use the factor scores from each first-order model and use them as observed indicators of my (what was) second-order factor? (This hiearchical structure is part of a larger model, so it is important that I estimate the "over-arching" second-order factor.)
No, I never looked at an EFA for these data. And, in retrospect, maybe I should have. But, since I am kind of wed to this hiearchical CFA approach at the moment (I am under the gun to finish and defend the dissertation; sorry for the lame excuse), might there be another way around this?
With respect to the factor scores not being "trustworthy" are you referring to the first-order or second-order factor scores? My first-order factors seemed to have good fit per the exact and approximate fit indices. If they are trustworthy, why not use them as my indicators of the second-order latent factor?
Sorry, as a follow-up, might the issue be related to sample size? I have 29 observed variables (categorical and continuous) across the five first-order factors. I am using the WLSMV estimator with a TYPE = COMPLEX MISSING MEANSTRUCTURE design with both a weight and cluster variable. My smallest group is approximately 550 and my largest group is approximately 1380.