# st: How to estimate a model with exponential covariance structure, reproducing a code from SAS

 From Amado David Quezada Sanchez To "'statalist@hsphsun2.harvard.edu'" Subject st: How to estimate a model with exponential covariance structure, reproducing a code from SAS Date Mon, 15 Feb 2010 10:36:41 -0600

```Dear statalisters,

I have been using xtmixed to replicate some examples from Fitzmaurice/Laird/Ware book "Applied
Logitudinal Analysis"

Those examples require a specified covariance. I have had no problem with unstructured and with
ar(1) covariance structures. For example, in order to replicate the following SAS code

PROC MIXED;
CLASS id group time;
MODEL y=group time group*time/S CHISQ;
REPEATED time/TYPE=UN SUBJECT=id R RCORR;

I executed this in Stata 11:

xi: xtmixed y i.gpo*i.t || id:, nocons var residuals(unstructured, t(t))

I obtained the very same results as the book. Now I'm trying to replicate an example for which an
exponential covariance structure has to be specified:

PROC MIXED;
CLASS id group time;
MODEL y=group time group*time/S CHISQ;
REPEATED time/TYPE=SP(EXP)(ctime) SUBJECT=id R RCORR;

Where ctime is a copy from the variable time. As the authors say, this variable is used to construct
"distances" or time separation between repeated measures.

How could I fit this in Stata11?

For the exponential covariance model, we have:

Corr(Yj,Yk)=rho^(tj-tk)

That is, correlation between responses depend on time separation. The feature that distinguishes an
exponential covariance model from the autoregressive one is its ability to be used with unequally
spaced responses. In this example we have that characteristic since time=0,4,6,8,12.

This structure can be expressed so it includes an exponential component, that's the reason for its name.

Thank you,
Dave Q.

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```