different parameterizations of OMEGA matrix vs. chance of getting flip-flop estimates

Dear NONMEM Users, One of the tricks people often use is to specify the SD(ETA) as a THETA and fix the OMEGA to be 1, which is a trick I often use when I determine which parameter should I put an ETA on. Most of the time, I will get the same results whether I use this trick, or just the normal way of specifying the OMEGA matrix. So my understanding is that these two approaches are equivalent. Today I run into some problem - I got a flip-flop estimate. All other aspects of the codes are the same, including same initial values and estimation method. In this one compartment first order absorption and first order elimination model, the estimation of CL and residual error magnitude SIGMA is not impacted by the method used, but V and Ka are totally different (as a result of flip-flop), and accordingly, their OMEGA estimate. Has anyone encountered similar situation? What kind of difference does these two approaches make in terms of searching for the minimizer? I'd appreciate if someone can help me to understand what's going on here. Here are my codes and NONMEM outcome: Approach 1 (the usual way): $SUBROUTINES ADVAN2 TRANS2 $PK TVCL=THETA(1) CL=TVCL*EXP(ETA(1)) TVV=THETA(2) V=TVV*EXP(ETA(2)) TVKA=THETA(3) KA=TVKA*EXP(ETA(3)) S2=V $ERROR DEL=0 IF(F.LE.0) DEL=1 W1=1 IPRED=0 IF(F.GT.0) IPRED=LOG(F) IRES=DV-IPRED W2=THETA(4) IWRES=IRES/(W1*DEL+W2) Y=IPRED + W2*ERR(1) $OMEGA DIAGONAL(3) 0.1 0.1 0.1 $SIGMA 1 FIX $THETA (0, 31) ; 1 [THETA1, TVCL] (0, 300) ; 2 [THETA2, TVV] (0,2) ; 3 [THETA3, TVKA] (0,0.2) ; 4 [THETA4, SD(EPISILON)] $EST METHOD=1 INTERACTION PRINT=5 MAX=9999 SIG=3 NOABORT MSFO=103.MSF $COV PRINT=E The results: THETA OMEGA SIGMA THETA1 27.68 (0.03513) OMEGA(1,1) 0.371 (0.2428) SIGMA(1,1) 1 (........) THETA2 298.9 (0.01969) OMEGA(2,2) 0.1585 (0.2042) THETA3 0.8336 (0.05652) OMEGA(3,3) 0.6265 (0.1491) THETA4 0.4441 (0.03294) Approach 2 (using the trick): $SUBROUTINES ADVAN2 TRANS2 $PK TVCL=THETA(1) CL=TVCL*EXP(THETA(5)*ETA(1)) TVV=THETA(2) V=TVV*EXP(THETA(6)*ETA(2)) TVKA=THETA(3) KA=TVKA*EXP(THETA(7)*ETA(3)) S2=V $ERROR DEL=0 IF(F.LE.0) DEL=1 W1=1 IPRED=0 IF(F.GT.0) IPRED=LOG(F) IRES=DV-IPRED W2=THETA(4) IWRES=IRES/(W1*DEL+W2) Y=IPRED + W2*ERR(1) $OMEGA DIAGONAL(3) 1 FIX 1 FIX 1 FIX $SIGMA 1 FIX $THETA (0, 31) ; 1 [THETA1, TVCL] (0, 300) ; 2 [THETA2, TVV] (0,2) ; 3 [THETA3, TVKA] (0,0.2) ; 4 [THETA4, SD(EPISILON)] (0,0.01) ; 5 [THETA5, IIV ON CL, SD(ETA1) (0,0.01) ; 6 [THETA6, IIV ON V, SD(ETA2)] (0,0.01) ; 7 [THETA7, IIV ON KA, SD(ETA3)] $EST METHOD=1 INTERACTION PRINT=5 MAX=9999 SIG=3 NOABORT MSFO=104.MSF $COV PRINT=E Results: THETA OMEGA SIGMA THETA1 27.68 (0.03569) OMEGA(1,1) 1 (........) SIGMA(1,1) 1 (........) THETA2 33.57 (0.06407) OMEGA(2,2) 1 (........) THETA3 0.09296 (0.03003) OMEGA(3,3) 1 (........) THETA4 0.4442 (0.03295) THETA5 0.4001 (0.117) THETA6 0.6873 (0.08321) THETA7 0.3336 (0.1125) Yaming Hang, Ph.D. Pharmacometrics Biogen Idec 14 Cambridge Center Cambridge, MA 02142 Office: 781-464-1741 Fax: 617-679-2804 Email: [email protected]<mailto:[email protected]>