From: Brett Houk <bhouk@amgen.com>
Subject: [NMusers] Omega Block off Diagonals
Date: 6/27/2003 12:33 PM

Users,
I am currently running a placebo effect mixture model (responders and
non-responders) with Omega Block (3) and getting off diagonal elements
coming up as negative.  Has anyone seen this result previously, and/or does
anyone have any insight as to the meaning of such a result?  I will past the
control stream and final parameter est. below.
Thanks,
Brett

$PROB PLACEBO MIXTURE MODEL 
$INPUT C ID TIME DV
$DATA data.csv IGNORE=C
$PRED 
 CALLFL = 1
 EST = MIXEST
 TVE0=THETA(1)
 E0=TVE0*EXP(ETA(1))
 IF (MIXNUM.EQ.2) THEN
 EMAX = THETA(3)*EXP(ETA(3))
 ELSE
 EMAX = THETA(2)*EXP(ETA(2))
 ENDIF  
 TVIT=THETA(4)
 IT50=TVIT*EXP(ETA(4))
 TVHL=THETA(5)
 HILL=TVHL
 F=E0*(1-(EMAX*(TIMW**HILL))/((IT50**HILL)+(TIMW**HILL)))
 IPRED=F
 W=(THETA(6)**2+F*F*THETA(7)**2)**0.5
 IRES=DV-IPRED
 IWRES=IRES/W
 Y=F+W*EPS(1)
$MIX
 NSPOP= 2
 P(1) = THETA(8)
 P(2) = 1 - THETA(8)
$OMEGA BLOCK (3)
 0.2 
 0.01 0.2
 0.01 0.01 0.2
$OMEGA BLOCK (1)
 0.2
$THETA
 (18.1)             ;THETA(1) TVE0 typical value of E0
 (-0.02)              ;THETA(2) Emax for population 1
 (0.135)              ;THETA(3) Emax for population 2
 (0, 5.28)              ;THETA(4) TVIT typical value for IT50
 (0, 1.98)            ;THETA(5) TVHL typical value of Hill Factor
 (0, 2.42)             ;THETA(6) Additive error term
 (0, 0.001)            ;THETA(8) Proportional error term
 (0, 0.765, 1)         ;THETA(7) Proportion of population in Pop1
$SIGMA
 1 FIX; Eps(1)
$COV
$EST NOABORT MAXEVAL=9999 POSTHOC
****************************************************************************
******************************
THETA - VECTOR OF FIXED EFFECTS PARAMETERS   *********
            TH 1      TH 2      TH 3      TH 4      TH 5      TH 6      TH 7
TH 8
         1.84E+01  1.08E-02  8.80E-02  5.33E+00  1.98E+00  2.43E+00
4.89E-08  7.47E-01

 OMEGA - COV MATRIX FOR RANDOM EFFECTS - ETAS  ********
            ETA1      ETA2      ETA3      ETA4 
 ETA1
+        1.88E-01
 ETA2
+       -3.30E+00  2.56E+02
 ETA3
+        1.04E+00 -4.19E+01  6.84E+01
 ETA4
+        0.00E+00  0.00E+00  0.00E+00  9.37E+01
_______________________________________________________

From: Leonid Gibiansky <lgibiansky@emmes.com>
Subject: Re: [NMusers] Omega Block off Diagonals
Date: 6/27/2003 12:55 PM

There is nothing unusual in these results. This just means that the correlation between
the parameters is negative. Elements of OMEGA matrix are defined as OMEGA_i_j=mean(eta_i * eta_j).
Negative correlation roughly means that when eta_1 is positive, eta_2 is more often negative
than positive. If eta1 is random effect on CL and eta2 is random effect on V, this means that
individuals with higher CL tend to have smaller V.

Leonid 
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