Date:         Sun, 4 Sep 2005 13:33:23 -0700
Reply-To:     David L Cassell <davidlcassell@MSN.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         David L Cassell <davidlcassell@MSN.COM>
Subject:      Re: mixed model covariance structure constraint
In-Reply-To:  <200509012128.j81Kwmf5016271@malibu.cc.uga.edu>
Content-Type: text/plain; format=flowed

linpan1975@YAHOO.COM wrote:
>I am fitting a mixed linear model in SAS with PROC MIXED. I'd like to
>model a specific convariance structure with type=lin() in RANDOM
>statement. The following is the pseudo code.
>
>proc mixed data=test covtest ratio method=REML;
>class sex family;
>model trait = age sex /s;
>random family/type=lin(3) ldata=g;
>repeated /r;
>run;
>
>here g is a matrix preimported to SAS. I'd like to use maximum likelihood
>estimation method to find the three variance estimates for the random
>effects. But there is a constraint among these three estimates, i.e. the
>absolute value of the second variance estimate (actually covariance
>estimate) should not be greater than the product of the other two variance
>estimates. And the second variance estimate could be negative, since
>actually it is a covariance.
>
>I checked the SAS manual for PROC MIXED, but could not find the answer.
>Has anyone met this before? Or is SAS able to do this? Any thoughts would
>be great appreciated. thanks in advance.

Okay, I think you need to explain this a lot more.  I have several
questions.
Feel free to write back to SAS-L (not to me personally), and then your
answers should drive further discussion.

[1] Why do you think you should be using the TYPE=LIN(k) covariance
structure?  Why not TYPE=UN or something else?  See more below.

[2] If you're using TYPE=LIN(k) , then you need to *specify* the
covariance structure yourself using the LDATA= option.  That ought to
take care of your covariance modeling problems right there.  Why doesn't
it?

[3] If all you want is a 2x2 block like this:

  s1**2        s1*s2*rho
  s1*s2*rho    s2**2

( where -1 < rho < 1 )
then why are you making this so hard?  You could get this through
TYPE=ANTE(1) or TYPE=UNR or .....  After all, you're *guaranteed*
that you'll get the square of the covariance is less than the product
of the two diagonal elements, or it won't even be positive definite!
Now are you sure you need the TYPE=LIN(3) model?

[4] I'm just not sure you have specified your model properly.  What
are you trying to do, and what led to your current PROC MIXED
statements?

HTH,
David
--
David L. Cassell
mathematical statistician
Design Pathways
3115 NW Norwood Pl.
Corvallis OR 97330

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