

Covariances of exogenous variables 

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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 WITHstatement in the MODEL command, no covariance is estimated and the model fit statistics are very good (ChiSquare=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 (ChiSquare=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? 


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  8:14 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. 


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  8:09 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! 


See the DATA command in the user's guide and Example 13.1. 

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