Jay,

I can't say that I know what a proper formula as I have not seen anything about this in anything I have read, but let's think about the definition of the influence function. The influence function is a measure of the distance of the observed covariate vector from the centroid of the data. Now, in the mixed model, where there is a fixed effects covariate vector and a random effects covariate vector, each having different influence on the response, we might want to measure the distance of the fixed effect covariate vector from the center of the fixed effect data, and measure the distance of the random effects covariate vector from the center of the random effects data. Each of these distances could then be weighted by the variance due to the fixed effects components and the variance due to the random effects component (in a random intercept model). Thus, we might compute

v(f)ii = xi'(X'X)xi v(r)ii = zi'(Z'Z)xi

where xi is the i-th observation covariate vector and X is the entire covariate vector matrix.

Then, the expected variance of the residual would be the sum

V(resid) = V(f)*(1-v(f)ii) + V(r)*(1-v(r)ii)

where V(f) is the variance due to the fixed effects and V(r) is the variance due to the random effects. Thus, one could take

(Y(i) - xi'*beta - zi'*gamma)/sqrt(V(resid))

as a studentized residual.

As I say, this is entirely off the cuff. I have not formally worked out the math, but I believe that it should be correct. Let me know if you find anything else, or if you see anything off in what I have suggested above.

Dale

>Date: Fri, 26 Oct 2001 15:52:17 -0400 >Reply-To: Jay Weedon <jweedon@EARTHLINK.NET> > Jay Weedon <jweedon@EARTHLINK.NET> Standardized residuals for Proc Mixed SAS-L@LISTSERV.UGA.EDU >Does anyone know of an algorithm to generate standardized or >studentized residuals appropriate for proc mixed? > >TIA, >Jay Weedon.

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

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