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Hello! I am trying to analyze across four groups a hierarchical CFA model with five firstorder latent factors and one secondorder factor. I already tested the five firstorder 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 firstorder latent factors. What might be causing this problem and how might I rectify it? Is it possible to use the factor scores from each firstorder model and use them as observed indicators of my (what was) secondorder factor? (This hiearchical structure is part of a larger model, so it is important that I estimate the "overarching" secondorder factor.) Thank you for your time! 


This is usually caused by the model not being appropriate for the data. The factor scores from a model such as this would not be trustworthy. Have you ever looked at an EFA for this data? 


Thank you, Dr. Muthen. 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 firstorder or secondorder factor scores? My firstorder 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 secondorder latent factor? Again, many thanks. 


Sorry, as a followup, might the issue be related to sample size? I have 29 observed variables (categorical and continuous) across the five firstorder 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. Thank you. 


Why don't you send the output with the error message to support@statmodel.com. 

daniel shen posted on Friday, October 17, 2008  7:44 am



Dr. Muthen, I intend to test a hierarchical CFA across multiple groups: X1 by x1x4; X2 by x5x8; X3 by x9x12; Y by X1 X2 X3; I get a message that "the starndard error of the model parameter estimates could not be computed. The model may not be identified..." Could you explain what the problem is? Thank you. 


The intercepts of the first order factors need to be fixed to zero in all groups. 

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