How to Obtain Asymptotic Covariance M... PreviousNext
Mplus Discussion > Growth Modeling of Longitudinal Data >
 Johnny Wu posted on Thursday, April 23, 2009 - 11:14 am
Hi Dr Muthen,

I am conducting an LGM and want to probe for an interaction between x1 and x2 in predicting intercept and slope.

I am following Preacher's advice on how to examine interactions.

I need the asymptotic covariances for the required coefficients. Is there a way to obtain the ACOV matrix in MPLUS?

Thank you very much

 Bengt O. Muthen posted on Thursday, April 23, 2009 - 11:32 am
Request TECH3 in the OUTPUT command.
 Johnny Wu posted on Thursday, April 23, 2009 - 12:54 pm
Thank you very much.

Another question: How can exogenous predictors interact with time to predict growth factors, within the LGM framework?

You see, because on Preacher's website, time is treated as an predictor. Hence, a two-way interaction regressing slope on x1 with x2, would be a three-way interaction regression slope on x1 with x2 and time.

How do I obtain the regression coefficient for time?
 Bengt O. Muthen posted on Thursday, April 23, 2009 - 1:41 pm
It sounds like Preacher's approach to growth modeling is via two-level analysis with a random slope for a time variable - see the Mplus UG example 9.16. You get the same effect by letting the x1*x2 interaction variable influence the slope growth factor in the regular Mplus single-level wide approach to growth: the slope growth factor multiplies time to create the product of the 3 variables.
 Kostas Fanti posted on Tuesday, August 23, 2011 - 2:39 am
I have a related question. I used TECH3 to request for an asymptotic covariance matrix, but Mplus did not provide the covariance between the growth terms and the predictors. How should I proceed?

Thank you

 Linda K. Muthen posted on Tuesday, August 23, 2011 - 11:55 am
TECH3 gives covariances among the parameter estimates. The growth factors and covariates are variables. It would be difficult to get that without changing your model. Why not regress the growth factors on the covariates.
 Fabien Long posted on Monday, January 20, 2014 - 3:38 am
Dear Dr. Muthen,

I have a related question. I am using Preacher's online tool to graph a multilevel interaction effect ( and I find myself unable to find the required asymptotic covariances using the tech3 output.

Elsewhere, it was stated that the order of the tech1 values can be used to interpret tech3. However, while the order of my tech1 output is Y, X1, X2, X1*X2, there is a 6*6 matrix in the tech3 output.

Is there a reference that explains how to interpret the respective tech3 values? Also, does tech3 contain the covariances between the predictors and the intercept y00?

Thank you for your help and your time!
 Linda K. Muthen posted on Monday, January 20, 2014 - 6:56 am
Please send the output and your license number to
 Lauren Molloy Elreda posted on Thursday, March 02, 2017 - 9:48 am
Dr. Muthen,

I am interested in the answers to the last two questions that last poster raised. Specifically, does tech3 contain the covariances between the coefficients for the predictors and the intercept? If so, where? If not, is there another way to obtain these?

Also, I am unclear as to how to interpret the values in the tech3 output matrix. For instance:


What does the "D-06" in the above value mean?

Thank you in advance for your time and help!
 Bengt O. Muthen posted on Friday, March 03, 2017 - 5:11 pm
Yes, Tech3 provides that information. The rows and columns are ordered according to their parameter numbers given in Tech1.

As for D-06, google scientific notation.

For instance,



 Claire Huang posted on Thursday, December 14, 2017 - 1:06 am
Dear Professor Muthen,
If we sqrt the diagonal of TECH3's asymptotic covariance matrix, should the numbers equal to S.E. reported in TECH1 for each coefficient estimates?
 Bengt O. Muthen posted on Thursday, December 14, 2017 - 12:29 pm
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