Date:         Wed, 31 Oct 2001 15:34:59 -0500
Reply-To:     Paige Miller <paige.miller@KODAK.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Paige Miller <paige.miller@KODAK.COM>
Organization: Eastman Kodak Company
Subject:      Re: Multivariate Variance Components in SAS
Content-Type: text/plain; charset=us-ascii

Perhaps there are a multiplicity of meanings of "multivariate variance
components", and so the options you mention are not what I was looking
for (sigh).

From the PROC MIXED documentation:

<--quoting from the PROC MIXED Documentation-->
The standard linear model, as used by the GLM procedure, is one of the
most common statistical models:

y = X*beta + epsilon

In this expression, y represents a vector of observed data, beta is an
unknown vector of fixed-effects parameters with known design matrix X,
and epsilon is an unknown random error vector modeling the statistical
noise around X*beta.

The mixed model generalizes the standard linear model as follows:

y = X*beta + Z*gamma + epsilon

Here, gamma is an unknown vector of random-effects parameters with known
design matrix Z, and epsilon is an unknown random error vector whose
elements are no longer required to be independent and homogeneous.
...
The variance of y is thus

     V = ZGZ' + R
<--End of quote from PROC MIXED manual-->

The options in SAS that you point to allow you to specify the structure
of R, and thus the model estimation does not have to assume that the
errors are independent and identical.

The multivariate variance components I was hoping to estimate come from
the situation where y is a matrix and not a vector. Each row of y
represent multiple measurements made on each observation (object) in the
study.

--
Paige Miller
Eastman Kodak Company
paige.miller@kodak.com

"It's nothing until I call it!" -- Bill Klem, NL Umpire
"When you get the choice to sit it out or dance,
   I hope you dance" -- Lee Ann Womack

Dale McLerran wrote:
>
> Paige,
>
> PROC MIXED is able to handle multivariate problems.  Take a look
> at the Kroneker product variance structures available when you
> use the repeated statement.  These structures have type specifications
> UN@CS, UN@AR(1), or UN@UN.  If you must use a random statement,
> then I am sure that there would be some method of model specification
> which could handle multivariate models.  However, without knowing
> anything more about the problem other than that you have a
> multivariate response, it is really next to impossible to give
> anything more concrete.
>
> Dale
>
> >Date:         Wed, 31 Oct 2001 12:53:11 -0500
> >Reply-To: Paige Miller <paige.miller@KODAK.COM>
> > Paige Miller <paige.miller@KODAK.COM>      Multivariate Variance Components in SAS SAS-L@LISTSERV.UGA.EDU
> >Anyone know how one can compute multivariate variance components in SAS
> >8?
> >Obviously, the univariate case is handled via PROC MIXED or PROC
> >VARCOMP, but neither produce multivariate variance-covariance component
> >matrices.