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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 2factor 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 twofactor solution offers any improvement in fit compared to the onefactor 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 noninvertible. 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; 


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; 


I thought that I would want to fix the covariance at 1 to determine if the 2factor solution has a better fit than the 1factor 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 1factor vs. 2factor solution? 


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. 


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 chisquare difference test between the 2factor and 1factor models to see if having 2 factors improves model fit. However, I'm not able to get the onefactor model to run... 


I think the question is why won't the onefactor model run. Please send the full output and your license number to support@statmodel.com. 

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