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a[i, 1:2]~dmnorm(mu.a[1:2], Siga[1:2,1:2])
So I tried the Wishart alternative according to the Winbugs web site FAQs section:
a[i,1] ~ dnorm(mu.a1,tau5)
a[i,2] ~ dnorm(mu.a2[i],tau6)
mu.a2[i] <- lambda0 + lambda1*(a[i,1] - mean(a[i,1]))
It did run, but the distribution of the correlation of a[i,1] and a[i,2] became bimodal (either 1 or -1).
Any suggestion/insight? Thanks in advance for your help.
Minya
model
{
alpha[1]~dnorm (mu.alpha1, tau1)
alpha[2]~dnorm (mu.alpha2, tau2)
mu.alpha1~dnorm(0, 0.001)
mu.alpha2~dnorm(0, 0.001)
tau1~dgamma(.01,.01)
tau2~dgamma(.01,.01)
beta[1]~dnorm (mu.beta1, tau3)
beta[2]~dnorm (mu.beta2, tau4)
mu.beta1~dnorm(0, 0.001)
mu.beta2~dnorm(0, 0.001)
tau3~dgamma(.01,.01)
tau4~dgamma(.01,.01)
Galpha[1]~dnorm (Gmu.alpha1, Gtau1)
Galpha[2]~dnorm (Gmu.alpha2, Gtau2)
Gmu.alpha1~dnorm(0, 0.001)
Gmu.alpha2~dnorm(0, 0.001)
Gtau1~dgamma(.01,.01)
Gtau2~dgamma(.01,.01)
Gbeta[1]~dnorm (Gmu.beta1, Gtau3)
Gbeta[2]~dnorm (Gmu.beta2, Gtau4)
Gmu.beta1~dnorm(0, 0.001)
Gmu.beta2~dnorm(0, 0.001)
Gtau3~dgamma(.01,.01)
Gtau4~dgamma(.01,.01)
for (i in 1:1551){
a[i, 1:2]~dmnorm(mu.a[1:2], Siga[1:2,1:2])
T[i,1]<-a[i,1]
T[i,2]<-a[i,1]
T[i,3]<-a[i,1]
mu[i,1]<-alpha[1] +beta[1]*T[i,1]
mu[i,2]<-alpha[1] +beta[1]*T[i,2]
mu[i,3]<-alpha[1] +beta[1]*T[i,3]
mu[i,4]<-alpha[2] +beta[2]*T[i,1]
mu[i,5]<-alpha[2] +beta[2]*T[i,2]
mu[i,6]<-alpha[2] +beta[2]*T[i,3]
mulab[i,1]<-T[i,1]
mulab[i,2]<-T[i,2]
mulab[i,3]<-T[i,3]
alpharesponse[i,1:6]~ dmnorm (mu[i,1:6],Sigma1[1:6, 1:6])
lab[i,1:3]~dmnorm(mulab[i,1:3], Sigmavallab[1:3, 1:3])
}
for (i in 1552:I){
a[i, 1:2]~dmnorm(mu.a[1:2], Siga[1:2,1:2])
T[i,1]<-a[i,1]
T[i,2]<-a[i,1]+a[i,2]
T[i,3]<-a[i,1]+a[i,2]
mu[i,1]<-Galpha[1] +Gbeta[1]*T[i,1]
mu[i,2]<-Galpha[1] +Gbeta[1]*T[i,2]
mu[i,3]<-Galpha[1] +Gbeta[1]*T[i,3]
mu[i,4]<-Galpha[2] +Gbeta[2]*T[i,1]
mu[i,5]<-Galpha[2] +Gbeta[2]*T[i,2]
mu[i,6]<-Galpha[2] +Gbeta[2]*T[i,3]
mulab[i,1]<-T[i,1]
mulab[i,2]<-T[i,2]
mulab[i,3]<-T[i,3]
alpharesponse[i,1:6]~ dmnorm (mu[i,1:6],Sigma2[1:6, 1:6])
lab[i,1:3]~dmnorm(mulab[i,1:3], Sigmavallab[1:3, 1:3])
}
Sigma1[1:6, 1:6]~dwish(Sigval[,],6)
Sigma2[1:6, 1:6]~dwish(Sigval2[,],6)
Sigmalab1~dgamma(.01,.01)
Sigmalab2~dgamma(.01,.01)
Sigmalab3~dgamma(.01,.01)
Sigmavallab[1,1]<-Sigmalab1*Sigvallab[1,1]
Sigmavallab[2,2]<-Sigmalab2*Sigvallab[2,2]
Sigmavallab[3,3]<-Sigmalab3*Sigvallab[3,3]
Sigmavallab[1,2]<-Sigvallab[1,2]*sqrt(Sigmalab1)*sqrt(Sigmalab2)
Sigmavallab[1,3]<-Sigvallab[1,3]*sqrt(Sigmalab1)*sqrt(Sigmalab3)
Sigmavallab[2,1]<-Sigvallab[1,2]
Sigmavallab[2,3]<-Sigvallab[2,3]*sqrt(Sigmalab2)*sqrt(Sigmalab3)
Sigmavallab[3,1]<-Sigvallab[1,3]
Sigmavallab[3,2]<-Sigvallab[2,3]
Siga[1:2, 1:2]~dwish(Sigaval[,],2)
mu.a[1:2]~ dmnorm(amean[1:2], aSig[1:2,1:2])
invSigma1[1:6, 1:6]<-inverse(Sigma1[1:6, 1:6])
invSigma2[1:6, 1:6]<-inverse(Sigma2[1:6, 1:6])
invSigmalab[1:3, 1:3]<-inverse(Sigmavallab[1:3, 1:3])
}
### inits
list(
tau1=100,
tau2=100,
tau3=100,
tau4=100,
mu.a=c(0,0),
Siga=structure(.Data=c(1,0,0,1),.Dim=c(2,2)),
Gtau1=100,
Gtau2=100,
Gtau3=100,
Gtau4=100,
Sigmalab1=1,
Sigmalab2=1,
Sigmalab3=1
)
####data
list(I=3088,
Sigaval=structure(.Data=c(1,0,0,1),.Dim=c(2,2)),
aSig=structure(.Data=c(1,0,0,1),.Dim=c(2,2)), amean=c(0,0),
Sigval=structure(.Data=c(1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1),.Dim=c(6,6)),
Sigval2=structure(.Data=c(1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1),.Dim=c(6,6)),
Sigvallab=structure(.Data=c( 1.0185185, -0.0925926, -0.0925926, -0.0925926 , 1.0185185, -0.0925926 , -0.0925926, -0.0925926, 1.0185185),.Dim=c(3,3)),
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