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 Rita Samper posted on Tuesday, June 07, 2011 - 8:51 am

I am running a full latent variable SEM and two of my latent variables only have two oberved indicators identifying them. I was told that I can do this, but that I must set the loadings equivalent. Is this true? Is this the only way to run this model or can I leave these parameters free?

Thank you!
 Linda K. Muthen posted on Tuesday, June 07, 2011 - 9:38 am
A factor model with two indicators is not identified. If it is part of a larger model, it can borrow information from other parts of the model for identification purposes for the entire model. If you hold both factor loadings equal and set the metric by fixing the factor variance to one, it will be identified. This may be why they suggest this model.
 Rita Samper posted on Tuesday, June 07, 2011 - 2:14 pm
Thank you, Dr. Muthen! I have an additional question. I am running some analyses separately for men and women. When I run the full sample, everything loads correctly and looks great. When I run the analyses on the split sample, the measurement model looks great, but when I run the structural model one of the observed constructs no longer loads onto the latent variable it is identifying. This is the case in both samples. Does this seem possible?

Thank you.
 Linda K. Muthen posted on Tuesday, June 07, 2011 - 5:59 pm
This does seem possible. You are assuming the model that fits best in the overall sample will fit for both men and women. This is not necessarily the case. The sample statistics for men and women can be different. I would start my analysis with each group separate to see if the same measurement model fits in both groups before testing for measurement invariance and then going on to compare the structural parameters across groups.
 Rita Samper posted on Wednesday, June 08, 2011 - 8:05 am
Thank you! Sounds like I have my work cut out for me, but it's reassuring to know that this certainly is possible!
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