```Date: Tue, 9 Sep 2003 13:33:32 -0700 Reply-To: Dale McLerran Sender: "SAS(r) Discussion" From: Dale McLerran Subject: Re: Banded main diagonal structure In-Reply-To: Content-Type: text/plain; charset=us-ascii Mkdeo20 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 --------------------------------------- __________________________________ Do you Yahoo!? Yahoo! SiteBuilder - Free, easy-to-use web site design software http://sitebuilder.yahoo.com ```

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