With statement in SEM
Message/Author
 gibbon lab posted on Thursday, March 03, 2011 - 8:31 am
Theoretically, an SEM is a combination of CFA and structural model. In mplus we use by and on statements to do that. Is it correct if the with statement (for correlations) is used when running a SEM analysis? Thanks.
 Linda K. Muthen posted on Thursday, March 03, 2011 - 8:48 am
Covariances and residual covariances can be part of an SEM model.
 gibbon lab posted on Thursday, April 21, 2011 - 2:00 pm
Hi Dr. Muthen,

If I have two well correlated independent variables, do I have to model this correlation in the model command? Here is a simple example, the model is:
y on x1 x2 x3 x4 x5,
where the independent variables x1 and x2 have correlation=0.60. Should I add
x1 with x2
in the model? If I do not specify this correlation command, does that mean I leave this correlation unspecified or assume no correlation (rho=0)?

By the way, are there any references that formulate a SEM with the three parts: measurement model, structural equation and correlations (covariances)? I would love to read it. Thanks a lot!
 Linda K. Muthen posted on Thursday, April 21, 2011 - 2:08 pm
The model is estimated conditioned on the independent variables. Their means, variances, and covariances are not model parameters. If you mention the covariance, the independent variables will be treated as dependent variables and distributional assumptions will be made about them. Not mentioning it does not mean it is zero.

See, for example, the Bollen SEM book.
 gibbon lab posted on Friday, April 22, 2011 - 11:49 am
Thanks, Dr. Muthen,

What if the correlation between x1 and x2 is 0.93? Will it be ok if I do not specify x1 with x2
in the model?

I ask this question because I am running an SEM with two exogenous variables x1 and x2 having corr=0.93. If I do not specify
x1 with x2 in the model, I have a nice result without multicolinearity problem. However, if I do specify x1 with x2 in the model, I got a multicoliearity problem which results in no convergence. What should I do?
 Linda K. Muthen posted on Friday, April 22, 2011 - 2:04 pm
You should not specify the covariance between observed exogenous variables in the MODEL command. This does not mean they are zero. Whether you mention the covariance or not does not change the fact that you have multicollinearity. The convergence problem is related to treating the variables as dependent rather than independent variables.
 gibbon lab posted on Friday, April 22, 2011 - 4:15 pm
Hi Dr. Muthen,

Without specifying x1 with x2, I did not see any sign of multicolinearity in my output. Everything looks good. Is my result valid?
 Bengt O. Muthen posted on Saturday, April 23, 2011 - 4:13 pm
Even when you don't specify x1 with x2, you will see in Sampstat that they are correlated 0.93, right?

When you do and don't specify x1 with x2, you may end up with different sample sizes as shown in the output - which may explain different results.

If this doesn't help, send your two outputs and license number to support.
 gibbon lab posted on Thursday, April 28, 2011 - 2:13 pm
Hi Dr. Muthen,

Is the with statement used to model the correlation of the original variables or their residuals? For example, I have these two regression equations:
y1=a0+a1*x1+epsilon1,
y2=b0+b1*x2+epsilon2,
where y1, y2 are manifest dependent variables, x1 and x2 are manifest independent variables, a0,b0,a1,b1 are intercepts and coefficients and epsilon1, epsilon2 are the residuals.
In mplus, does "y1 with y2" indicate that I am modeling the correlation between epsilon1 and epsilon2? Thanks a lot.
 Linda K. Muthen posted on Thursday, April 28, 2011 - 2:26 pm
In an unconditional model, WITH specifies a covariance. In a conditional model, WITH specifies a residual covariance.
 gibbon lab posted on Thursday, June 23, 2011 - 10:37 am
Hi Dr. Muthen,

I am running an SEM using Mplus 5.21. A, B and C are three independent variables in this analysis (three are also other independent variables). I specified two corrrelations using the with statement in the SEM:
A with B C;
According to the output:
corr(A,B)=0.316 with Z statistic=0.363(not sig)
corr(A,C)=0.198 with Z statistic=4.918(highly significant).

How could this happen? The bigger correlation is not significant, but the smaller one is highly significant?

The output says "THE MODEL ESTIMATION TERMINATED NORMALLY". Did not see any warning message.
 Linda K. Muthen posted on Thursday, June 23, 2011 - 11:32 am
Significance is determined by the ratio of the parameter estimate to the standard error of the parameter estimate. Check the sizes of the standard errors.
 gibbon lab posted on Thursday, June 23, 2011 - 1:14 pm
The Z statistic I mentioned is the ratio of the parameter estimate to the standard error of the parameter estimate.
 Linda K. Muthen posted on Thursday, June 23, 2011 - 1:18 pm
That's right. Although the two parameter estimates are close to the same size, the standard errors are not. This results in different signficance. One parameter is more precisely estimated than the other.
 Andrew Whitehead posted on Tuesday, July 26, 2011 - 8:23 am
Why, when we do or don't specify x1 with x2, are there different sample sizes? Also, when I specify x1 with x2 and request output: stdyx, I receive standard errors and significance tests in the standardized section of the output. But, when I don't specify x1 with x2, I only receive the standadized estimate with no SEs or significance tests when I request output: stdyx.

Thank you for the help on these two issues!
 Andrew Whitehead posted on Tuesday, July 26, 2011 - 8:51 am
I should have mentioned that I am using the wlsmv estimator.
 Linda K. Muthen posted on Tuesday, July 26, 2011 - 12:46 pm
Please send the outputs and your license number to support@statmodel.com so I can understand what you are saying.
 Daniel Lee posted on Monday, February 06, 2017 - 1:26 pm
Hi Dr. Muthen,

I was under the assumption that a standardized "with" command for two variables (e.g., depression, anxiety), should equate to the bi-variate correlation. I am clearly wrong b/c it does not. I was wondering if you can help me understand why the bi-variate correlation between depression and anxiety would differ from the standardized with command between depression and anxiety.

Thank you!
 Bengt O. Muthen posted on Monday, February 06, 2017 - 3:35 pm
I think you are comparing a sample correlation with a model-estimated correlation. If the model doesn't fit well, these can differ. If that's not getting at your question, send outputs to Support along with your license number.
 Daniel Lee posted on Monday, February 06, 2017 - 6:10 pm
Makes perfect sense. thank you!
 Daniel Lee posted on Monday, February 06, 2017 - 6:25 pm
I actually have a quick follow-up question: if two mediators are correlated at .74 (sample correlation), but they operate very differently (e.g., mediator 1 is associated to the outcome and has significant indirect effect, while mediator 2 does not), is it problematic to include both mediators due to the strong correlation?
 Bengt O. Muthen posted on Tuesday, February 07, 2017 - 5:55 pm
It could be. But if M2 does not affect Y, then it need not be included.
 Felice K. posted on Wednesday, July 05, 2017 - 3:00 am
Dear Dr. Muthen,

what's the difference between an unconditional modell (nested structure of the data, no level 1- and no level 2- predictors) with and without "WITH-Command" on both levels?

I suppose, that the WITH-command indicates, that the dependent variables are correlated. If we use no "WITH-Command", we suppose that they aren't, right?

Thank you for answering my question.
 Linda K. Muthen posted on Wednesday, July 05, 2017 - 1:50 pm
In an unconditional model, WITH statement refer to covariances. Covariances are the default in some cases. You need to check the output.
 Kristine posted on Friday, November 10, 2017 - 10:47 am
Hello!

What is the Greek symbol for the latent variable covariance parameter estimates (i.e., "Standardized Model Results" when using the WITH statement on a conditional model)?

Thank you!
 Bengt O. Muthen posted on Friday, November 10, 2017 - 4:47 pm
Psi.