Re: FW: OMEGA HAS A NONZERO BLOCK

From:Leonid Gibiansky Subject: Re: FW: [NMusers] OMEGA HAS A NONZERO BLOCK Date:Fri, 04 Oct 2002 09:06:16 -0400 Ken, Nick, Here are my 2c for this discussion: As Ken pointed out, with the original parameterization there were 10 parameters responsible for the OMEGA matrix. NONMEM solution evidences that those parameters are related (determinant of the matrix is zero). Therefore, correct parameterization should contain 9 parameters. Restricting this to 7 parameters, as Ken suggested, introduces two additional restrictions that were not evident from the solution. Therefore my guess is that re-parametrized solution will not be, in general, equivalent to the original one. For practical purposes, the simplest way is to try and see what happens. If one wants to do a rigorous search for the correct correlation, I would propose the following solution (for the 4 by 4 case) CORR1=THETA(1)*ETA(1) CORR2=THETA(2)*ETA(1)+THETA(3)*ETA(2) CORR3=THETA(4)*ETA(1)+THETA(5)*ETA(2)+THETA(6)*ETA(3) CORR4=THETA(7)*ETA(1)+THETA(8)*ETA(2)+THETA(9)*ETA(3)+THETA(10)*ETA(4) CL= *EXP(CORR1) Q = *EXP(CORR2) V1= *EXP(CORR3) V2= *EXP(CORR4) Here I assume that OMEGA matrix for ETAs is fixed to unit matrix. This has 10 parameters and should be equivalent to the original problem, and least it gave the same solution in all the cases that I tested. Coefficients of the OMEGA matrix are easily expressed via THETA1 - THETA10. Then one can continue with the regular procedure to exclude parameters one by one. Leonid