Correlation between two endogenous va... PreviousNext
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 dlsherry posted on Friday, October 31, 2008 - 8:03 pm
Hello. Is it possible to put a correlation (i.e., double headed arrow) between two endogenous variables in a structural equation model or a path model with Mplus? If so, how do I do this in Mplus?

Thank you.
 Linda K. Muthen posted on Saturday, November 01, 2008 - 8:17 am
As long as the parameter is identified, you would use the WITH option, for example,

y1 WITH y2;
 dlsherry posted on Tuesday, November 11, 2008 - 3:42 pm
Thank you very much for your assistance.
 Andres Fandino-Losada posted on Thursday, March 08, 2012 - 8:43 am
Dear Drs. Muthen & Muthen.
I am using Mplus 4.2, for running path analysis, all observed variables, all categorical, except for t3ksta, t3kssp, t3kemb and t3kdet. Please, see part of the input syntax:

ANALYSIS:
TYPE = GENERAL MISSING H1;
ESTIMATOR = WLSM;
PARAMETERIZATION IS THETA;
MODEL:
t5dep2 ON t4dep1 t4rdis1 t3ksta t3kssp t3kemb t3kdet;
t5rdis2 ON t5dep2 t4dep1 t4rdis1 t3kssp;
t5panx2 ON t3ksta t3kssp t3kemb t1cpls;
t5chrd2 ON t3ksta t2iedu1;
t5dep2 WITH t5panx2 t5chrd2;
t5panx2 WITH t5chrd2;
t6dlem3 ON t4ohhz1 t4rdis1 t4slec1 t1fhmd;
t6mtpr3 ON t5chrd2 t4dep1 t4slec1 t1fhmd;
t6ldff3 ON t4isps1 t4slec1;
t6isle3 ON t5chrd2 t4isps1 t4slec1;
t6dlem3 WITH t6mtpr3 t6ldff3 t6isle3;
t6mtpr3 WITH t6ldff3 t6isle3;
t7mmds3 ON t6dlem3 t5dep2 t5chrd2 t4ohhz1 t4cpls1;

In the output, some correlations between variables appear, but I have not asked for them in the MODEL (WITH terms):
t6mtpr3 WITH t5rdis2 t5panx2,
t6ldff3 WITH t5rdis2 t5panx2,
t6isle3 WITH t5rdis2 t5panx2,
t7mmds3 WITH t5rdis2 t5panx2 t6mtpr3 t6ldff3 t6isle3.

All these correlations are not significant, except for t6ldff3 WITH t5rdis2 and t7mmds3 WITH t6ldff3.
1. Why are these correlations appearing?
2. What is the meaning of the significant ones?
3. t means time, thus should I add t6ldff3 ON t5rdis2 and t7mmds3 ON t6ldff3 terms to the model?
Thank you very much.
 Linda K. Muthen posted on Friday, March 09, 2012 - 3:29 pm
The covariances between the residuals of ultimate dependent variables are estimated as the default in Mplus. There are two reasons for this:

1. They are identified.
2. They are often needed due to left-out predictors.

Your theory should dictate whether you should add these terms.
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