

CFA Testing Model Constraints 

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Hello Drs. Muthen, I am running a 2 factor CFA. One factor has ordinal indicators and the other has binary indicators. I set the variance of the factors = 1 (F1@1 F2@1) and let the F1 with F2 be freely estimated. The model runs fine and converges (and fits!) with no errors. The correlation of F1 with F2 is close to 1 (about .97). So I want to test if it is one by running the model again and adding the command F1 with F2@1. When I do that, I get an error that PSI is non positive definite. This does not seem to make sense to me because everything in PSI is constrained (the error message does include the warning of PSI including values greater than or equal to 1). It seems that this is a plausible constraint based upon other submissions to the discussion list. It seems strange that this issue should when there are less parameters to estimate. Any ideas what might be going on? Perhaps an error message is being invoked by default? 


A correlation of one makes the psi matrix nonpositive definite. You can use MODEL TEST to test if the correlation is equal to one. See the user's guide for the MODEL TEST command. 

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