Correlations between factors PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
 Anonymous posted on Wednesday, August 10, 2005 - 12:10 am
I've just started using MPlus. I'm testing a CFA-model 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?
 Linda K. Muthen posted on Wednesday, August 10, 2005 - 8:24 am
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

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?

 Linda K. Muthen posted on Wednesday, January 17, 2007 - 9:08 am
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 chi-square difference test for discriminat validity.

I set correlation between factors @1.

F1 by x1* x2 x3;
F2 by y1* y2 y3;
F1 with F2 @1;

but I got the message:

What's wrong with this?

I appreciate.
 Linda K. Muthen posted on Friday, February 19, 2010 - 6:32 pm
If the factor correlation is not one, fixing it at one could cause convergence problems. Instead, try the following using the Wald test.

F1 by x1* x2 x3;
F2 by y1* y2 y3;
F1 with F2 (p1);

0 = p1-1;
 Joanna Jones posted on Tuesday, July 01, 2014 - 3:25 pm

I am interested in estimating the correlation between factors.

I am a bit confused about how to get correlations, as the command


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
 Bengt O. Muthen posted on Tuesday, July 01, 2014 - 5:15 pm
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.
 Joanna Jones posted on Wednesday, July 02, 2014 - 1:49 pm
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?
 Joanna Jones posted on Wednesday, July 02, 2014 - 2:41 pm
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, p-value 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)
 Bengt O. Muthen posted on Wednesday, July 02, 2014 - 5:08 pm
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".
 Joanna Jones posted on Tuesday, July 15, 2014 - 1:37 pm
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.
 Linda K. Muthen posted on Tuesday, July 15, 2014 - 1:47 pm
Yes, this is okay.
 Nicolette Waschl posted on Wednesday, October 01, 2014 - 9:12 pm

As I understand it, obtaining a factor correlation >1 means the model is not viable. I have two questions regarding this:

1) If I am comparing a two-factor model that demonstrates a correlation >1 between factors with a one-factor model that fits the data, does this mean it is correct to say that the one-factor model fits the data better?

2) Would it be appropriate to constrain the factor correlation to 1 or less between the two factors for comparison purposes, or will this inevitably result in an error? I have tried this, but still end up with an error saying that psi is not positive definite.

 Linda K. Muthen posted on Thursday, October 02, 2014 - 6:49 am
1. You can't interpret the results from the two-factor model. I would not use it as a comparison.

2. I would not do this.
 Eric Thibodeau posted on Wednesday, January 07, 2015 - 3:15 pm

I'm doing an SEM. I have two factors, each with four indicators, and some dependent variables. I expect a correlation between my factors. Should I add a "with" statement?

f1 with f2;

Or is that not necessary?


 Bengt O. Muthen posted on Wednesday, January 07, 2015 - 4:29 pm
In most cases that correlation is included as the default because that is the most common specification. Check the output to see if it is reported (either under Model results or TECH1).
 HavilahRenee posted on Monday, March 02, 2015 - 8:28 am
I have a very simple question. I completed several CFAs. I need to add the correlations between factors to a report that I am working on. There are about 100 models. Is there a way to save the correlations into a file? Obviously, having to open each output file and do a copy and paste into Excel or Word is quite tedious. Thanks.
 Linda K. Muthen posted on Monday, March 02, 2015 - 9:52 am
You can save the results using the RESULTS option of the SAVEDATA command but that is probably just as tedious. See in the left margin of the homepage Using Mplus with R.
 Alice  posted on Tuesday, November 10, 2015 - 5:05 pm
Dear. Professors,
Iím wondering about the meaning for the three different models.

1. Second-order model (f1 by u1-u10; f2 by u11-u20; f3 by u21-u30; f3 by f1 f2 f3)
2. First-order model with correlated factors (f1 by u1-u10; f2 by u11-u20; f3 by u21-u30)
3. First-order model with correlated factors and correlated factor-residuals (f1 by u1-u10; f2 by u11-u20; f3 by u21-u30; f1 WITH f2; f1 WITH f3; f2 WITH f3)

What does #3 means - the residual variance of f1 correlates with the residual variance of f2 and the residual variance of f3? How does this differ from #1 and #2?

Iím trying to replace model #1 with #2 or #3 because the tests that had estimation problems using #1 showed no problem when using #2 and #3. Which one will be conceptually closer to #1?

Thanks for your help in advance!
 Bengt O. Muthen posted on Tuesday, November 10, 2015 - 5:20 pm
Model 1 is the same as 2 and 3 because you have only 3 factors. We need to see your outputs to see what's happening - send to Support along with your license number.
 Alice  posted on Wednesday, November 11, 2015 - 6:37 am
Okay I will. Thanks!
 Dave MŲwisch  posted on Thursday, February 04, 2016 - 2:22 am
Is there a possibility to check the p-values of correlations among manifest variables?

Thanks for your help in advance!
 Linda K. Muthen posted on Thursday, February 04, 2016 - 10:40 am
Are they continuous or categorical?
 Dave MŲwisch  posted on Saturday, February 06, 2016 - 2:54 am
They are continuous and it is a Two level-model. But I only need the correlations and p-values for variables at level 1.
 Linda K. Muthen posted on Saturday, February 06, 2016 - 6:23 am
Try TWOLEVEL BASIC; with no MODEL command and the H1SE option of the OUTPUT command.
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