Re: comparing theta's

From: Lewis Sheiner <lewis@c255.ucsf.edu> Date: Thu, 25 Mar 1999 08:33:20 -0800 Subject: Re: comparing theta's Peter, I think Pascal's answer is the most complete, but if you are (as your note implies) interested only in the thetas and are willing to (1) condition on the estimates of omega and the cov matrix, and (2) approximate the covariance matrix by a diagonal one, then you essentially model the thetas as randomly varying from group to group and see if this is compatible with the SE data. That is, use a model like Y(j,k) = THETA(j) + ETA(j) + SE(j,k)*EPS(j) where j=1,m (thetas); k=1,3 (groups="individuals"); SE(j,k) is the std error from the analysis that estimated Y(j,k), the jth "theta" from the kth "group". Allow OMEGA to be full m x m; set SIGMA fixed to the identity matrix (assumption (2)). Test equality of thetas across groups by seeing if you can fix the corresponding OMEGA(j,j)=0 without raising the Obj fn too much. Or anyway, something like that ... -- Lewis B Sheiner Professor, Lab. Med., Bioph. Sci, Med. Box 0626 - UCSF San Francisco, CA 94143 415-476-1965 (voice) 415-476-2796 (fax) lewis@c255.ucsf.edu