Re: Fixed elements within a block covariance matrix

From: Leonid Gibiansky - lgibiansky@emmes.com Subject: Re: [NMusers] Fixed elements within a block covariance matrix Date: 1/14/2004 9:44 AM One can check correlation structure via simulation, but I am not quite sure why should one do it. I guess, we can trust NONMEM to simulate according to the variance-covariance model, and then, for the OMEGA matrix X11 X13 X33 0 X23 X22 Eta1 and Eta2 will not be correlated in any way (implicit or explicit). If simulations show correlation (X12 not equal to zero), then one need to increase the sample size of the simulations. Correlation coefficient X21 should decay to zero with the sample size, if the model is implemented correctly. Example Eta1=a1*cov1+e1 Eta2=a2*cov2+e2 Eta3=a3*cov1+a4*cov2+e3 is not quite correct unless means of cov1 and cov2 are equal to zero (since means of etas should be zero). But the idea holds. If Eta1=a11*e1 Eta2=a22*e2 Eta3=a13*e1+a23*e2+a33*e3 where e1, e2, and e3 are independent [then mean(ei*ej) = 0 if i not equal j] with variance 1 [ mean(ei*ei) = 1 ] then X11=mean(Eta12)=a112 X12=mean(Eta1*Eta2) = 0 (since e1 and e2 are independent) X13=mean(Eta1*Eta3) = a11*a13 X22 = a222 X23 = a22*a23 X33 = a132+a232+a332 Leonid