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 Alyson Zalta posted on Wednesday, March 16, 2011 - 7:13 pm
Hello,
I am running an SEM model with a single latent variable. The latent variable has three indicators that have intercorrelations of r= .55, .26, & .63. When I try to run the measurement model, I get the following error message.

WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE DASSS.

How should I interpret this error message? I do not see a problem with multicollinearity when I test for it in Stata (the condition index is less than 10). I see that I am getting a negative residual for the one variable listed as the problem variable. But I don't understand why this would be happening. Any guidance would be much appreciated!
 Linda K. Muthen posted on Wednesday, March 16, 2011 - 7:17 pm
The problem is the negative residual variance for DASSS. This makes the model inadmissible. It seems that these three variables are not good indicators of the factor.
 Alyson Zalta posted on Wednesday, March 16, 2011 - 8:17 pm
I see. That is very surprising to me because these are all measures of anxiety. And when I run the structural model, the standardized paths for the three indicators are .55, .98, and .64. Is there any way to figure out why these measures are not making a good factor? Thank you for your help!!
 Bengt O. Muthen posted on Wednesday, March 16, 2011 - 9:23 pm
We would have to see your model to say - please send input, output, data, and license number to suppport@statmodel.com.
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