Covariances of exogenous variables PreviousNext
Mplus Discussion > Categorical Data Modeling >
 Jochen Mayerl posted on Wednesday, December 04, 2002 - 3:32 am
I am trying to estimate a multiple group model with two continous latent variables measured by categorical indicators (WLSMV) and two exogenous observed variables.

I have a problem concerning the covariance between the two exogenous variables. If I do NOT explicitly specify the WITH-statement in the MODEL command, no covariance is estimated and the model fit statistics are very good (Chi-Square=23,321, df=20, p=0,2733; CFI=0,996; RMSEA=0,033). If I modify this model and specify the covariance in the MODEL command, the goodness of fit is worse (Chi-Square=58,744, df=43, p=0,0552; CFI=0,981; RMSEA=0,049). The estimated covariance is significant.

How can I explain this drop in goodness of fit when specifying the covariance between the exogenous variables? And why is the covariance between the exogenous variables not specified as default?
 Linda K. Muthen posted on Wednesday, December 04, 2002 - 9:52 am
When you specify the covariance between the exogenous variables, they are no longer considered to be independent variables in the model. Instead, they are considered to be dependent variables. The model is estimated with y being conditioned on x. By turning them into y variables, you change the conditioning variables. You should not do this. Although not printed, the covariance among the exogenous variables is the sample covariance which you can obtain from SAMPSTAT.
 Anonymous posted on Tuesday, June 21, 2005 - 2:14 pm
I am estimating a model using observed variables. I notice that if I explicitly add covariances among the exogenous variables (using the WITH command), it does not change any of the model statistics. In Mplus, are these covariances automatically estimated and why? Is it common to set these paths to zero(based on theoretical reasons) or should they be left alone? Can you recommend any good references or other discussions on this subject? Thank you.
 Linda K. Muthen posted on Wednesday, June 22, 2005 - 12:18 am
Exogenous variables are correlated as the defalt. In general if you run a model without a parameter specfied and the parameter is estimated, then this is an Mplus default. You can also read about the defaults in the user's guide. I would let them be correlated as the default unless you have strong substantive reasons that they should not be.
 Cecily Na posted on Wednesday, December 15, 2010 - 2:09 pm
Dear Linda,
Could you tell me what is the syntax command for reading a covaraince matrix? Do I type in the covariance matrix or do I save it in a file and tell Mplus to read the covariance file? How do I type in directly the covariance matrix?
Thanks a lot!
 Linda K. Muthen posted on Wednesday, December 15, 2010 - 5:18 pm
See the DATA command in the user's guide and Example 13.1.
 Anonymous  posted on Thursday, February 08, 2018 - 10:25 am

Do observed exogenous variables in path models have to covary? I was reading a chapter by Kline where he says no, however, it seems to be standard practice to covary exogenous variables unless there is a theoretical reason not to do so. I have been having issues with model identification, so I was considering removing exogenous covariances. These variables do not have to covary (and in many cases the covariances are very small).

Any feedback or suggested readings is sincerely appreciated. Thank you.
 Anonymous  posted on Thursday, February 08, 2018 - 10:29 am

Do observed exogenous variables always have to covary in a path model? I was reading a chapter by Kline and he says no, however, it seems to be standard practice for exogenous variables to covary-unless there is a theoretical reason not to do so. I am having issues with model identification and I was considering removing covariances. I should note that the covariances are among control variables and not my key predictor in my model.

Any feedback or suggested reading is appreciated. Thank you.
 Bengt O. Muthen posted on Thursday, February 08, 2018 - 4:12 pm
Assuming that you are thinking of observed exogenous variables, they should be correlated typically. That's what Mplus does as the default- that is, the exogenous variable part is not part of the model parameters that are estimated but handled just like regular regression (the exogenous part can be obtained by Sampstat).
 Steven John posted on Wednesday, July 04, 2018 - 2:01 am
Dear Muthéns'

I was running a SEM model where I regressed:

Y1 Y2 Y3 Y4 ON X1 X2 X3 X4;

(Y are latent, X manifest)

I compared the results of this model with those where I specified WITH statements between all X variables. I got slightly different estimates and improved fit. I expected identical results as X-variables are correlated as default in such regression. I however noted that the model without WITH statements had some missing which may be the reason for the divergence?

I'm unsure whether I should specify covariances using WITH in my input or not, and what the difference would be - to me the models are the same when I draw them. Should I exclude WITH statements and use sampstat for this information instead?

 Bengt O. Muthen posted on Wednesday, July 04, 2018 - 4:35 pm
Q1: Yes, the different N's is the reason.

Q2: Using WITH brings the x's into the model and you make normality assumptions about the variables having missing data. So it is not longer the same model. See our RMA book, chapter 10.
 Talea Cornelius posted on Monday, August 13, 2018 - 9:44 am

What happens if I specify that MPlus estimate the means and variances of my continuous covariates (which have missing data), but I do not request that MPlus estimate the variances of my binary covariates (which don't have missing data)? Will these still covary?
 Bengt O. Muthen posted on Monday, August 13, 2018 - 9:50 am
No, they won't covary. So you have to mention all covariates. But that message is harmless/ignorable in the binary covariate case.
 Margarita  posted on Wednesday, September 11, 2019 - 5:27 am
Hi Dr. Muthen,

When the variances of exogenous do get mentioned (to use FIML), is the regression in Mplus still estimated based on their covariances, or does the fact that they become dependent changes things? I wonder if the covariances between exogenous once they are brought into the model need to remain as parameters, or is it safe to remove them (set them to zero) in order to simplify the model?

Thank you,
 Bengt O. Muthen posted on Wednesday, September 11, 2019 - 1:24 pm
Q1: Still the same regression.

Q2: The covariances need to be in the model - otherwise the model is mis-specified.
 Daniel Lee posted on Wednesday, October 02, 2019 - 9:11 am
Hi Dr. Muthen,

If I have no missing data, would covarying my exogenous variables produce the same results as keeping my exogenous variables independent? If not, can you point me to some literature around regression models that covary exogenous variables.

Thank you.
 Bengt O. Muthen posted on Wednesday, October 02, 2019 - 12:26 pm
Yes. This is explained in Chapter 10 of our RMA book.
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