Date:         Thu, 4 Sep 2008 22:28:40 -0700
Reply-To:     stringplayer_2@yahoo.com
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Dale McLerran <stringplayer_2@YAHOO.COM>
Subject:      Re: PROC MIXED - Estimated G matrix is not positive definite.
In-Reply-To:  <6843c444-ed2e-4c66-8dd7-e5c8f93adc67@z66g2000hsc.googlegroups.com>
Content-Type: text/plain; charset=us-ascii

--- On Thu, 9/4/08, Ryan <Ryan.Andrew.Black@GMAIL.COM> wrote:

> From: Ryan <Ryan.Andrew.Black@GMAIL.COM>
> Subject: PROC MIXED - Estimated G matrix is not positive definite.
> To: SAS-L@LISTSERV.UGA.EDU
> Date: Thursday, September 4, 2008, 2:04 PM
> Hi,
>
> I'm getting the following message: "Estimated G
> matrix is not positive
> definite" when I run the following:
>
> proc mixed data=mydata;
>      class ID;
>      model Y= / s ;
>          random intercept / subject=ID;
>    run;
>
> ----------
> Does this occur when the within variability is much larger
> than the
> between variability? The whole point of this analysis is to
> measure
> the covariance parameter estimates (residual and
> intercept). Is it
> reasonable to just interpret the random intercept as being
> 0?
>
> Thoughts?
>
> Ryan

Ryan,

The non positive definite G matrix here means that your variance
estimate for the random subject effect is zero.  If you were to
fit a random effects model using method of moments (specifying
METHOD=TYPE3 and changing your RANDOM statement to read just
RANDOM ID; or simply using the GLM procedure with a RANDOM
statement), then you would likely find that the between subjects
variance component estimate using moment methods has a negative
value.  This all means that there is less variation between the
subject means than would be expected given the within-subject
(residual or error) variance.

Let me note, too, that you could remove the constraint that the
between-subject variance estimate should be non-negative.  If
you run the code

 proc mixed data=mydata nobound;
      class ID;
      model Y= / s ;
      random intercept / subject=ID;
    run;

then even when using REML I would be willing to bet that you will
observe that the between subjects variance component estimate is
actually negative.  With REML (and ML) estimation, the default
behavior is to constrain the variance component estimates to be
positive (as is required for a variance).

Dale

---------------------------------------
Dale McLerran
Fred Hutchinson Cancer Research Center
mailto: dmclerra@NO_SPAMfhcrc.org
Ph:  (206) 667-2926
Fax: (206) 667-5977
---------------------------------------