Nested Model Error
Message/Author
 Tracy Witte posted on Sunday, February 28, 2010 - 11:22 am
I'm doing a CFA with skewed data; therefore, I'm using the MLMV estimator. The 2-factor solution has adequate fit to the data; however, the correlation between the factors is around 0.9. Thus, I'm interested in determining whether the two-factor solution offers any improvement in fit compared to the one-factor solution. My problem is that when I fix the covariance between the factors to "1;" I get an error message stating that the estimated covariance matrix is non-invertible. I don't get this error message when I just run the model with 1 latent variable, so I'm not sure if there's something wrong with my syntax. When I use the DIFFTEST to compare the solution with 1 factor to the solution with 2 factors, I get a message stating that the models aren't nested. Here's my syntax:

MODEL: sdi by m1 m2 m3 m4 m5 m6 m7 m13 m14 m22 m23;
RPP by m2 m15 m17 m20 m21 m25 m26;
SDI with RPP@1;
 Linda K. Muthen posted on Monday, March 01, 2010 - 9:28 am
Note that you are fixing the covariance to one not the correlation. To test if the correlation is one use the following MODEL command and MODEL test:

MODEL: sdi by m1* m2 m3 m4 m5 m6 m7 m13 m14 m22 m23;
RPP by m2* m15 m17 m20 m21 m25 m26;
sdi@1 rpp@1;
sdi WITH rpp (p1);

MODEL TEST:
0 = p1 - 1;
 Tracy Witte posted on Monday, March 01, 2010 - 9:45 am
I thought that I would want to fix the covariance at 1 to determine if the 2-factor solution has a better fit than the 1-factor solution. Is there an error in my syntax for fixing the covariance at 1? Will using the syntax you provided allow me to compare the model fit of the 1-factor vs. 2-factor solution?
 Linda K. Muthen posted on Monday, March 01, 2010 - 11:23 am
There is not an error in your syntax but when you fix a parameter to a value that is not its true value, this can result in convergence problems.

The syntax I provided tests that the correlation is one. Because you said the correlation between your factors was .9, I assumed that you wanted to test a correlation of one not a covariance of one.
 Tracy Witte posted on Monday, March 01, 2010 - 3:49 pm
Thank you so much for your time! What I'm trying to do is compare the fit of a model with 1 latent variable to the fit of a model with 2 latent variables. My understanding is that these models are nested within each other. If I fix the covariance between the latent variables to "1," isn't this equivalent to a model with 1 latent variable?

What I ultimately want to do is a chi-square difference test between the 2-factor and 1-factor models to see if having 2 factors improves model fit. However, I'm not able to get the one-factor model to run...
 Linda K. Muthen posted on Monday, March 01, 2010 - 5:24 pm
I think the question is why won't the one-factor model run. Please send the full output and your license number to support@statmodel.com.