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Anonymous posted on Wednesday, August 10, 2005  12:10 am



Hi, I've just started using MPlus. I'm testing a CFAmodel and I'd like to fix the CORRELATION between the two factors to one. "f1 WITH f2 @ 1" seems to refer to the covariance, which causes a bad model fit in my case. How can I refer to the correlation between the two factors? 


If you free the first factor loading of f1 and f2 and set the metric of the factors by fixing the factor variances to one (f1@1 f2@1;), then f1 WITH f2 @1; will refer to a correlation. 

Anonymous posted on Wednesday, August 10, 2005  8:54 am



Thank you very much !!! 

anonymous posted on Tuesday, January 16, 2007  8:29 pm



Hi, I have performed a CFA with 7 factors. These factors represent dimensions under a bigger construct, which I am not testing. I want to say that these 7 represent multiple dimensions of this construct. CFA results show that these 7 factors are correlated. I am using them then to predict a binary outcome. In my logit/probit model should I force these factor to not correlate? What would it be if I do? Thanks 


If you have significant factor correlations and you fix them to zero, this will misspecify the model. 

min soo kim posted on Friday, February 19, 2010  11:51 am



I;m testing 2 factor model CFA and tried to conduct chisquare difference test for discriminat validity. I set correlation between factors @1. F1 by x1* x2 x3; F2 by y1* y2 y3; F1@0; F2@0; F1 with F2 @1; but I got the message: NO CONVERGENCE. SERIOUS PROBLEMS IN ITERATIONS.ESTIMATED COVARIANCE MATRIX NONINVERTIBLE.CHECK YOUR STARTING VALUES. What's wrong with this? I appreciate. 


If the factor correlation is not one, fixing it at one could cause convergence problems. Instead, try the following using the Wald test. MODEL: F1 by x1* x2 x3; F2 by y1* y2 y3; F1@0; F2@0; F1 with F2 (p1); MODEL TEST: 0 = p11; 


Hi, I am interested in estimating the correlation between factors. I am a bit confused about how to get correlations, as the command output: stdyx; as I understand gives you the correlation under the STANDARDIZED MODEL RESULTS  STDYX Standardization, and than I read the correlation after "f1 with f2" Am I right? Because on another thread I read for a correlation the factor's variances need to be fixed at 1. But is that what happens automatically with the stdyx; command? Thanks in advance for your help 


You are right on both counts. Fixing factor variances at 1 makes the unstandardized estimate for f1 WITH f2 into a correlation. So it can be done that way too. 


Thank you for your answer! I have one more question: If, besides factor 1, and a regression on that factor, I add a second factor which correlates with factor 1, but is not included in the regression, the effect sizes of the regression change. This seems logical, but the exact interpretation is not clear to me. Could you clarify what happens there? 


And one more question: If I save the factor scores and use them in the exact same regression in spss I get slightly different coefficients, pvalue and explained variance, resulting in some variables gaining a significant effect. Do you know what causes these differences? (I use the WLSMV as the factor items are categorical) 


Q1. Adding a second factor may change the fit of the model,which in turn changes estimates. For instance, if that second factor was needed to predict your DV but you don't let it you have a misfit. Q2. There is a big literature on estimated factor scores not behaving like true factors. See our website's FAQ "Factor scores". 


Just to be sure, it is ok to use WLSMV for a CFA and in the same analysis regress that factor on some IV? I am not sure if the WLSMV estimator can be used for regressions as well. 


Yes, this is okay. 

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