Date:         Tue, 9 Sep 2003 13:33:32 -0700
Reply-To:     Dale McLerran <stringplayer_2@YAHOO.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Dale McLerran <stringplayer_2@YAHOO.COM>
Subject:      Re: Banded main diagonal structure
In-Reply-To:  <OFD3258881.5C2FFB46-ON88256D9B.00758369@epamail.epa.gov>
Content-Type: text/plain; charset=us-ascii

Mkdeo20 <mkdeo20@AOL.COM> wrote:
> When using PROC MIXED with type=un(1) in the random effects
specification. In
> the SAS (version 8.2) output "Dimensions", the number of covariance
parameters
> appears to coincide with an unstructured variance-covariance
matrix.
>
> Can someone please tell me why this is so?

Well, the fitted model is an unstructured covariance matrix
with some constraints on the off-diagonal elements.  Because
you have identified the model as having an unstructured
covariance structure, SAS reports the dimensions accordingly.
Note that you can use the GROUP= option on the RANDOM statement
to identify heterogeneity in the covariance structure, thereby
fitting a model which is identical to the banded unstructured
covariance structure.  When you fit a heterogeneous variance
structure model, the number of covariance parameters in the
dimensions table is the number of unconstrained parameters
in the banded unstructured model.  Thus, the following two
models are likelihood equivalent.


/* Banded unstructured covariance */
proc mixed data=test;
  class subject time;
  model y = ;
  random time / subject=subject type=un(1);
run;

/* Heterogeneous covariance */
proc mixed data=test;
  class subject time;
  model y = ;
  random intercept / subject=subject group=time;
run;


If the classification variable TIME has two values, then the
first model would report 4 covariance parameters in the
dimensions table, while the second model would report 3
covariance parameters in the dimensions table.  It should be
observed that although SAS reports a different number of
covariance parameters for the above two models, the AIC and
BIC statistics are reported to be the same (as are the
likelihoods from the two models).  That is, in constructing
the information criteria statistics, SAS employs the number
of unrestricted parameters, not the number of parameters
reported in the dimensions table.

Dale


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

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