First order autoregressive error cova...
Message/Author
 Jaime Maerten-Rivera posted on Wednesday, February 10, 2010 - 1:14 pm
I am running an LGM and want to check a first order autoregressive covariance structure. This would mean that the elements on the main diagonal of the covariance matrix are homoscedastic (with variance ó2) and pairs of errors have identical covariances in bands parallel to the leading diagonal. These covariances are the product of the residual variance, ó2, and an error autocorrelation parameter, ñ. Since ñ is always fractional, the error covariances in the bands of decline the further out from the leading diagonal.

In other words, the error covariance structure would look like the following matrix:
ó2 ó2ñ ó2ñ2 ó2ñ3
ó2ñ ó2 ó2ñ ó2ñ2
ó2ñ2 ó2ñ ó2 ó2ñ
ó2ñ3 ó2ñ2 ó2ñ ó2

Does anyone know how to set up this covariance structure using MPlus? That is, how to get ñ and set up all of the parameters to estimate as above?
 Linda K. Muthen posted on Wednesday, February 10, 2010 - 2:58 pm
We show how to do this in Example 6.17.
 Jaime Maerten-Rivera posted on Friday, February 12, 2010 - 10:26 am
Thanks so much for your help.
 Jaime Maerten-Rivera posted on Saturday, February 13, 2010 - 4:13 pm
I have a couple of follow-up questions.

1) How does the program know how to compute the corr variable? Is that predefined in the program?

2) The model that I am examining is actually a piecewise growth model with two slopes. Does the first-order auto correlated residuals model get specified differently? Is it a separate autocorrelation for each of the slopes? Do you know of any literature on this?

3) Is there a way to get MPlus to output the fitted error covariance matrix and correlation matrix?

Thanks for any info you can give me.
 Bengt O. Muthen posted on Sunday, February 14, 2010 - 9:32 am
1} Corr is a parameter that is implicitly defined in the sense that the parameters p1-p3 are expressed in terms of only 2 parameters, resvar and corr as seen in Model constraint. So corr puts a restriction on p1-p3. The analogy is that parameters are defined by putting restrictions on a covariance matrix for the analysis variables.

2) The autocorrs are for the residuals so no change is caused by piecewise.

3) You get the components printed for such a cov/corr matrix. On the diagonal of the cov matrix is resvar, one step below the diagonal you have resvar*corr, two steps below you have resvar*corr*corr, etc. The corr matrix has 1's on the diagonal, one step below the diagonal you have corr, two steps you have corr*corr, etc.
 Jaime Maerten-Rivera posted on Friday, February 26, 2010 - 11:02 am
When I ask for the RESIDUAL output, I get a table for the "Model Estimated Covariances/Correlations/Residual Correlations", but in the table only the covariances appear. Is there a way to get the correlations, or to compute them myself?
 Bengt O. Muthen posted on Saturday, February 27, 2010 - 6:31 am
You will have to compute them yourself.