I want to thank all of you for helping me out with this model, you were really helpful. I have another question to ask concerning some hierarchical model predictions, but first let me describe the model more fully. The model below is designed to fit a 2 compartment pharmacokinetic model with first order absorption. Mathematically, a drug is injected into a "Muscle" compartment and then this drug slowly diffuses into the blood stream (at a rate ka) which is part of the "Central" compartment. The central compartment is an abstraction consisting of all tissues of the body which exchange fluids readily with blood. The central compartment (compartment 1) is connected to a so called "peripheral" compartment (compartment 2) which diffuses liquids and drug compounds more slowly. The flow rate from compartment 1 to compartment 2 is denoted k12 and the reverse flow is denoted k21. The elimination of drug compound from the body occurs from the central compartment and is denoted ke. The effective volume of the central compartment is denoted V. Mathematically, the expected concentration at time t in the central compartment after a dose is given at time t0 by
Y(t) = A exp( - ka (t - t0) ) + B exp( - alpha (t-t0) ) + C exp( - beta (t-t0))
Where A, B, C, alpha, and beta are complicated functions of { V, ka, ke, k12, k21}
In an experiment 4 doses were given to 17 separate monkeys on days {0, 7, 14, 21} and blood draws (and concentration measurements) for each of the monkeys were made on the 2nd, 4th and 7th days after each injection. Ok, here is my question. I have set up my model to be a hierarchical model where each monkey is allowed to have there own set of pharmacokinetic parameters {V[i], ka[i], ke[i],k12[i],k21[i]} for i = 1:17. Actually, to ensure that each of these parameters are positive I let V[i] = exp( LV[i]) and I let LV[i] ~ N (muLV, sigmaV)
Now, according to hierarchy, each of my monkey specific parameters LV[i], i=1:17, should be a draw from a common distribution N(muLV, sigmaV) which has a common mean of muLV and a common standard deviation of sigmaV. Ok, here is my question now
If I look at a summary of my output (based upon 10000 draws from posterior after adaption phase of 10000 draws) I see that the mean of LV for each monkey is roughly -20 or so...
> summary(coda)
Iterations = 10001:20000
Thinning interval = 1
Number of chains = 3
Sample size per chain = 10000
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
LV[1] -20.08109 0.199553 1.152e-03 0.0080290
LV[2] -19.98839 0.206370 1.191e-03 0.0060056
LV[3] -20.15538 0.309366 1.786e-03 0.0114883
LV[4] -20.00562 0.268906 1.553e-03 0.0137695
LV[5] -20.22493 0.311283 1.797e-03 0.0204318
LV[6] -20.06054 0.237408 1.371e-03 0.0072161
LV[7] -20.29406 0.128242 7.404e-04 0.0038551
LV[8] -20.08290 0.176014 1.016e-03 0.0041376
LV[9] -20.27580 0.189846 1.096e-03 0.0080177
LV[10] -20.39051 0.125782 7.262e-04 0.0040288
LV[11] -20.49898 0.682762 3.942e-03 0.0490074
LV[12] -20.01756 0.155996 9.006e-04 0.0040261
LV[13] -20.43970 0.166082 9.589e-04 0.0064418
LV[14] -20.07206 0.190987 1.103e-03 0.0057345
LV[15] -20.00926 0.213506 1.233e-03 0.0070148
LV[16] -20.31251 0.455545 2.630e-03 0.0312732
LV[17] -20.17079 0.150444 8.686e-04 0.0055211
However, if I look at the population mean or overall mean muLV I see that it is centered roughly at -0.02 or so:
Mean SD Naive SE Time-series SE
muLV -0.01882 0.385593 2.226e-03 0.0020359
My question is what could be driving the disconnect between the population overall mean and the individual level predictions?? Weird isn't it?
I have attached my model code, data and inits below. Thank you so much for your help.
model {
for( i in 1 : N ) {
Y[i] ~ dnorm(pred[i], tau.y)
pred[i] <- (mu1[i] + mu2[i] + mu3[i] + mu4[i])/(pow(10,9))
mu1[i] <- dose1[i]*( A[monkey[i]]*exp( - ka[monkey[i]]*time1[i] ) + B[monkey[i]]*exp( -
alpha[monkey[i]]*time1[i] ) + C[monkey[i]]*exp( - beta[monkey[i]]*time1[i] ) )
mu2[i]<- dose2[i]*( A[monkey[i]]*exp( - ka[monkey[i]]*time2[i] ) + B[monkey[i]]*exp( - alpha
[monkey[i]]*time2[i] ) + C[monkey[i]]*exp( - beta[monkey[i]]*time2[i] ) )
mu3[i]<- dose3[i]*( A[monkey[i]]*exp( - ka[monkey[i]]*time3[i] ) + B[monkey[i]]*exp( - alpha
[monkey[i]]*time3[i] ) + C[monkey[i]]*exp( - beta[monkey[i]]*time3[i] ) )
mu4[i]<- dose4[i]*( A[monkey[i]]*exp( - ka[monkey[i]]*time4[i] ) + B[monkey[i]]*exp( - alpha
[monkey[i]]*time4[i] ) + C[monkey[i]]*exp( - beta[monkey[i]]*time4[i] ) )
}
tau.y <- pow(sigma.y, -2)
sigma.y ~ dunif(1,10)
for(j in 1:J){
alpha[j] <- ( ( k12[j] + k21[j] + ke[j] ) + sqrt( pow( ( k12[j] + k21[j] + ke[j] ) , 2) -
4* k21[j] *ke[j] ) ) /2
beta[j] <- ( ( k12[j] + k21[j] + ke[j] ) - sqrt( pow( ( k12[j] + k21[j] + ke[j] ) , 2) - 4*
k21[j] *ke[j] ) ) /2
A[j] <- ( ka[j] * ( k21[j] - ka[j] ) )/ ( V[j] * ( alpha[j] - ka[j] ) * ( beta[j] - ka[j] )
)
B[j] <- ( ka[j] * ( k21[j] - alpha[j] ) )/ ( V[j] * ( ka[j] - alpha[j] ) * ( beta[j] -
alpha[j] ) )
C[j] <- ( ka[j] * ( k21[j] - beta[j] ) )/ ( V[j] * ( ka[j] - beta[j] ) * ( alpha[j] - beta
[j] ) )
V[j] <-exp(LV[j])
ka[j] <-exp(lka[j])
ke[j] <-exp(lke[j])
k12[j]<-exp(lk12[j])
k21[j]<-exp(lk21[j])
LV[j] ~ dnorm( muLV , tauV )
lka[j] ~ dnorm( muka, tauka )
lke[j] ~ dnorm( muke, tauke )
lk12[j]~ dnorm( muk12, tauk12 )
lk21[j]~ dnorm( muk21, tauk21 )
}
tauV <- pow(sigmaV,-2)
tauka <- pow(sigmaka,-2)
tauke <- pow(sigmake,-2)
tauk12 <- pow(sigmak12,-2)
tauk21 <- pow(sigmak21,-2)
sigmaV ~ dunif(0,10)
sigmaka ~ dunif(0,10)
sigmake ~ dunif(0,10)
sigmak12 ~ dunif(0,10)
sigmak21 ~ dunif(0,10)
muLV ~ dnorm( 0.51879, 6.613 )
muka ~ dnorm( 1.175573, 0.0343 )
muke ~ dnorm( -1.910543, 11730.5 )
muk12 ~ dnorm( -2.513306, 2137.4 )
muk21 ~ dnorm( -1.731606, 296.7 )
}
# Data:
list(Y=c(9,3.9,3.2,9.8,5.6,5.1,12.2,8,10.9,10.9,9,6.5,8.7,3.1,2.8,8,6.7,1,11.5,5.8,1,7.7,6.5,4.5,3.2,1,1,1,1,1,13.4,5.1,1,4,4.9,2.4,7.3,4.1,2.8,8.1,8.9,3.2,4.1,4.9,6.9,4.1,1,9.6,6.4,11.2,12,8.4,6.5,5.2,1,9.6,7.6,6.8,13.1,10,8.4,16.3,10.5,8.8,8,5.2,8.8,4.4,2.6,1,5.3,2.6,7.2,5.3,3.5,1,1,1,1,1,1,7.9,8.4,1,14.6,11,6.1,14.6,11.9,9.6,13,11.4,7.7,7.1,6.9,3.7,10.1,7.9,2.9,1,8.3,5.3,10.3,13.7,6.9,4.2,9.9,8,5,10,8.5,5.8,10.1,9.1,13,10,7,13,11,9,13,11,9,15,13,14,4,3,7,6,6,13,10,7,14,6,6,5,11,8,5,12,7,6,8,9,14,11,5,13,8,5,10.6,7.8,5,11.4,8.2,5,4.7,1,3.6,1.8,1,1,7.8,5.7,1,9.9,5.4,5,9.3,5.7,5.7,12.5,8.2,4.9,7.8,4.3,1,8.4,5.7,3.6,10.7,7.1,4.6,9.2,13.5,8.9,4.6,10.7,6.4,3.5,9.2,8.7,7.1,9.4,8.7,4.9,4.9,1,3.4,1,1,1,9.2,4.2,1,11.4,10.2,7.1,13.3,11.7,9.4,11.5,8.6,7.1),monkey =c(1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17),time1=c(2,4,7,9,11,14,16,18,21,23,25,28,2,4,7,9,11,14,16,18,21,23,25,28,31,35,38,42,45,49,2,4,7,9,11,14,16,18,21,23,2,4,7,9,11,14,16,18,21,23,25,28,2,4,7,9,11,14,16,18,21,23,25,2,4,7,9,11,14,16,18,21,23,25,28,31,35,38,42,45,49,2,4,7,9,11,14,16,18,21,23,25,28,2,4,7,9,11,14,16,18,21,23,2,4,7,9,11,14,16,18,21,23,25,2,4,7,9,11,14,16,18,21,23,25,2,4,7,9,11,14,16,18,21,23,2,4,7,9,11,14,16,18,21,23,25,2,4,7,9,11,14,16,18,21,23,25,28,31,35,38,42,45,49,2,4,7,9,11,14,16,18,21,23,25,28,2,4,7,9,11,14,16,18,21,23,2,4,7,9,11,14,16,18,21,23,25,28,31,35,38,42,45,49,2,4,7,9,11,14,16,18,21,23,25,28
),time2=c(0,0,0,2,4,7,9,11,14,16,18,21,0,0,0,2,4,7,9,11,14,16,18,21,24,28,31,35,38,42,0,0,0,2,4,7,9,11,14,16,0,0,0,2,4,7,9,11,14,16,18,21,0,0,0,2,4,7,9,11,14,16,18,0,0,0,2,4,7,9,11,14,16,18,21,24,28,31,35,38,42,0,0,0,2,4,7,9,11,14,16,18,21,0,0,0,2,4,7,9,11,14,16,0,0,0,2,4,7,9,11,14,16,18,0,0,0,2,4,7,9,11,14,16,18,0,0,0,2,4,7,9,11,14,16,0,0,0,2,4,7,9,11,14,16,18,0,0,0,2,4,7,9,11,14,16,18,21,24,28,31,35,38,42,0,0,0,2,4,7,9,11,14,16,18,21,0,0,0,2,4,7,9,11,14,16,0,0,0,2,4,7,9,11,14,16,18,21,24,28,31,35,38,42,0,0,0,2,4,7,9,11,14,16,18,21),time3=c(0,0,0,0,0,0,2,4,7,9,11,14,0,0,0,0,0,0,2,4,7,9,11,14,17,21,24,28,31,35,0,0,0,0,0,0,2,4,7,9,0,0,0,0,0,0,2,4,7,9,11,14,0,0,0,0,0,0,2,4,7,9,11,0,0,0,0,0,0,2,4,7,9,11,14,17,21,24,28,31,35,0,0,0,0,0,0,2,4,7,9,11,14,0,0,0,0,0,0,2,4,7,9,0,0,0,0,0,0,2,4,7,9,11,0,0,0,0,0,0,2,4,7,9,11,0,0,0,0,0,0,2,4,7,9,0,0,0,0,0,0,2,4,7,9,11,0,0,0,0,0,0,2,4,7,9,11,14,17,21,24,28,31,35,0,0,0,0,0,0,2,4,7,9,11,14,0,0,0,0,0,0,2,4,7,9,0,0,0,0,0,0,2,4,7,9,11,14,17,21,24,28,31,35,0,0,0,0,0,0,2,4,7,9,11,14),time4=c(0,0,0,0,0,0,0,0,0,2,4,7,0,0,0,0,0,0,0,0,0,2,4,7,10,14,17,21,24,28,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,2,4,7,0,0,0,0,0,0,0,0,0,2,4,0,0,0,0,0,0,0,0,0,2,4,7,10,14,17,21,24,28,0,0,0,0,0,0,0,0,0,2,4,7,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,2,4,0,0,0,0,0,0,0,0,0,2,4,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,2,4,0,0,0,0,0,0,0,0,0,2,4,7,10,14,17,21,24,28,0,0,0,0,0,0,0,0,0,2,4,7,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,2,4,7,10,14,17,21,24,28,0,0,0,0,0,0,0,0,0,2,4,7),dose1=c(20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20),dose2=c(0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20),dose3=c(0,0,0,0,0,0,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20),dose4=c(0,0,0,0,0,0,0,0,0,20,20,20,0,0,0,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,0,0,0,20,0,0,0,0,0,0,0,0,0,20,20,20,0,0,0,0,0,0,0,0,0,20,20,0,0,0,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,0,0,0,20,20,20,0,0,0,0,0,0,0,0,0,20,0,0,0,0,0,0,0,0,0,20,20,0,0,0,0,0,0,0,0,0,20,20,0,0,0,0,0,0,0,0,0,20,0,0,0,0,0,0,0,0,0,20,20,0,0,0,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,0,0,0,20,20,20,0,0,0,0,0,0,0,0,0,20,0,0,0,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,0,0,0,20,20,20),N = 216,J=17)
# Inits:
list(sigma.y=3.03,muLV=0.451,muka=1.37,muke=-1.988,muk12=-2.61,muk21=-1.82,sigmaV=2.85,sigmaka=1.92,sigmake=6.33,sigmak12=2.2,sigmak21=6.89,LV=c(2.3375768,2.1131326,-2.9672930,-0.7232807,5.2146430,2.3692468,1.7993847,-2.9941884,3.4077675,-0.3522470,2.6228524,-3.1021916,4.2183896,-3.6134175,3.8129013,0.1638676,2.0034773),lka=c(1.5906045,2.4214173,0.9676078,3.8440597,0.787718,-2.3277679,2.088227,1.1320029,0.3878235,4.3357967,-0.8496406,2.3591636,0.396198,4.69487,2.6023122,2.1179844,-0.3866458),lke=c(-7.345367,2.383361,-6.350776,3.713401,1.563373,11.179944,11.01133,8.637848,-3.441219,-6.579666,3.101094,-8.668811,1.101745,-1.731504,-10.413856,-2.427511,-10.42432),lk12=c(-1.668994,-1.9942154,-0.9190348,0.1852387,-2.883629,-0.7384197,-1.2938703,-3.537769,-2.5941325,-0.1249434,-1.9240245,-2.2275114,-3.1574265,-2.3539842,-4.7286449,-5.8670984,-0.4284762),lk21=c(-3.5060777,-4.1271651,-3.364257,-5.801624,-13.3371005,8.3216115,1.2069363,-7.4143348,7.3379469,-7.6311012,7.3515466,5.3150512,-5.407578,-1.9711796,-0.1472733,-4.6044567,5.0966538))
-----Original Message-----
From: Megan Pledger [mailto:[log in to unmask]]
Sent: Monday, December 05, 2011 6:33 PM
To: King, David B*
Subject: RE: Question on Initialing Nodes
You need to have a Y in your inits with an NA where you have data and an intial value where you don't have data e.g.
# Inits:
list(sigma.y=3.03,muLV=0.451,muka=1.37,muke=-1.988,muk12=-2.61,muk21=-1.82,sigmaV=2.85,sigmaka=1.92,sigmake=6.33,sigmak21=6.89,LV=c(2.3375768,2.1131326,-2.9672930,-0.7232807,5.2146430,2.3692468,1.7993847,-2.9941884,3.4077675,-0.3522470,2.6228524,-3.1021916,4.2183896,-3.6134175,3.8129013,0.1638676,2.0034773),lka=c(1.5906045,2.4214173,0.9676078,3.8440597,0.787718,-2.3277679,2.088227,1.1320029,0.3878235,4.3357967,-0.8496406,2.3591636,0.396198,4.69487,2.6023122,2.1179844,-0.3866458),lke=c(-7.345367,2.383361,-6.350776,3.713401,1.563373,11.179944,11.01133,8.637848,-3.441219,-6.579666,3.101094,-8.668811,1.101745,-1.731504,-10.413856,-2.427511,-10.42432),lk12=c(-1.668994,-1.9942154,-0.9190348,0.1852387,-2.883629,-0.7384197,-1.2938703,-3.537769,-2.5941325,-0.1249434,-1.9240245,-2.2275114,-3.1574265,-2.3539842,-4.7286449,-5.8670984,-0.4284762),lk21=c(-3.5060777,-4.1271651,-3.364257,-5.801624,-13.3371005,8.3216115,1.2069363,-7.4143348,7.3379469,-7.6311012,7.3515466,5.3150512,-5.407578,-1.9711796,-0.1472733,-4.6044567,5.0966538),
Y=c(NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 5.53255424111375, NA, NA, 4.5030676555029, NA, NA, NA, NA, 6.17399747067961, 4.26909984454993, 4.85749854299164, 5.69968646403738, 4.52972366293811, NA, NA, 4.90056996541565, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 4.61843493638795, NA, NA, NA, NA, NA, NA, NA, 5.58567071135453, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 4.68755621628236, NA, NA, NA, NA, NA, 6.06682179191973, 4.94513090989767, 6.08347211472557, 4.33514355771155, 5.02722933691986, 5.143317987005, NA, NA, 4.86154307364941, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 3.74068460642984, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 4.86676301354203, NA, NA, 5.11845649127266, 5.01281010814806, NA, NA, 6.59071263298828, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 5.23845328956075, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 5.68465109321842, NA, 5.71986103577618, 4.41598712876517, 5.36800789235565, NA, NA, 3.98859284601011, NA, NA, NA, NA, NA, NA, NA, NA, NA))
After that there were still some missing initial values but I generated them with the gen inits button and then clicked model>save state to get the values before the first interation which in my case were.
list(
LV = c(
2.3375768,2.1131326,-2.967293,-0.7232807,5.214643,
2.3692468,1.7993847,-2.9941884,3.4077675,-0.352247,
2.6228524,-3.1021916,4.2183896,-3.6134175,3.8129013,
0.1638676,2.0034773),
Y = c(
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA,5.53255424111375, NA, NA,
4.5030676555029, NA, NA, NA, NA,
6.17399747067961,4.26909984454993,4.85749854299164,5.69968646403738,4.52972366293811,
NA, NA,4.90056996541565, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA,4.61843493638795, NA, NA, NA,
NA, NA, NA, NA,5.58567071135453,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA,4.68755621628236,
NA, NA, NA, NA, NA,
6.06682179191973,4.94513090989767,6.08347211472557,4.33514355771155,5.02722933691986,
5.143317987005, NA, NA,4.86154307364941, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA,3.74068460642984,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA,4.86676301354203,
NA, NA,5.11845649127266,5.01281010814806, NA,
NA,6.59071263298828, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA,5.23845328956075, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA,5.68465109321842,
NA,5.71986103577618,4.41598712876517,5.36800789235565, NA,
NA,3.98859284601011, NA, NA, NA,
NA, NA, NA, NA, NA,
NA),
lk12 = c(
-1.668994,-1.9942154,-0.9190348,0.1852387,-2.883629,
-0.7384197,-1.2938703,-3.537769,-2.5941325,-0.1249434,
-1.9240245,-2.2275114,-3.1574265,-2.3539842,-4.7286449,
-5.8670984,-0.4284762),
lk21 = c(
-3.5060777,-4.1271651,-3.364257,-5.801624,-13.3371005,
8.321611499999999,1.2069363,-7.4143348,7.3379469,-7.6311012,
7.3515466,5.3150512,-5.407578,-1.9711796,-0.1472733,
-4.6044567,5.0966538),
lka = c(
1.5906045,2.4214173,0.9676078,3.8440597,0.787718,
-2.3277679,2.088227,1.1320029,0.3878235,4.3357967,
-0.8496406,2.3591636,0.396198,4.69487,2.6023122,
2.1179844,-0.3866458),
lke = c(
-7.345367,2.383361,-6.350776,3.713401,1.563373,
11.179944,11.01133,8.637848,-3.441219,-6.579666,
3.101094,-8.668811,1.101745,-1.731504,-10.413856,
-2.427511,-10.42432),
muLV = 0.451,
muk12 = -2.61,
muk21 = -1.82,
muka = 1.37,
muke = -1.988,
sigma.y = 3.03,
sigmaV = 2.85,
sigmak12 = 7.79985268963494,
sigmak21 = 6.89,
sigmaka = 1.92,
sigmake = 6.33)
cheers,
Megan
________________________________________
From: (The BUGS software mailing list) [[log in to unmask]] on behalf of King, David B* [[log in to unmask]]
Sent: 02 December 2011 04:52
To: [log in to unmask]
Subject: [BUGS] Question on Initialing Nodes
Hello Bugs help group. I am attempting to fit a 2 compartment pharmacokinetic model on some data where Monkey's were given 4 separate injections of mercury to 17 monkey's and the blood concentration was observed over the course of many days. The pharmacokinetic model is non-linear in the parameters and there were missing Y observations observed. There are 5 variables in my particular 2 compartment model: V, ka, ke, k12, and k21. Because there were 4 separate doses at different days, we basically utilize the superposition principle which adds the response.
Here is my question, when I run the code below the model compiles ok. However, the program says "initial values loaded but chain contains unitialized variables". Is this an error message due to the fact that some of the Y observations are missing? Is there a way to look at the nodes and tell which ones are unitialized?
Thanks for your kind assistance.
Kindly,
David King
model {
for( i in 1 : N ) {
Y[i] ~ dnorm(pred[i], tau.y)
pred[i] <- mu1[i] + mu2[i] + mu3[i] + mu4[i] mu1[i] <- dose1[i]*( A[monkey[i]]*exp( - ka[monkey[i]]*time1[i] ) + B[monkey[i]]*exp( - alpha[monkey[i]]*time1[i] ) + C[monkey[i]]*exp( - beta[monkey[i]]*time1[i] ) )
mu2[i]<- dose2[i]*( A[monkey[i]]*exp( - ka[monkey[i]]*time2[i] ) + B[monkey[i]]*exp( - alpha[monkey[i]]*time2[i] ) + C[monkey[i]]*exp( - beta[monkey[i]]*time2[i] ) )
mu3[i]<- dose3[i]*( A[monkey[i]]*exp( - ka[monkey[i]]*time3[i] ) + B[monkey[i]]*exp( - alpha[monkey[i]]*time3[i] ) + C[monkey[i]]*exp( - beta[monkey[i]]*time3[i] ) )
mu4[i]<- dose4[i]*( A[monkey[i]]*exp( - ka[monkey[i]]*time4[i] ) + B[monkey[i]]*exp( - alpha[monkey[i]]*time4[i] ) + C[monkey[i]]*exp( - beta[monkey[i]]*time4[i] ) ) } tau.y <- pow(sigma.y, -2) sigma.y ~ dunif(0,100)
for(j in 1:J){
alpha[j] <- ( ( k12[j] + k21[j] + ke[j] ) + sqrt( pow( ( k12[j] + k21[j] + ke[j] ) , 2) - 4* k21[j] *ke[j] ) ) /2 beta[j] <- ( ( k12[j] + k21[j] + ke[j] ) + sqrt( pow( ( k12[j] + k21[j] + ke[j] ) , 2) - 4* k21[j] *ke[j] ) ) /2 A[j] <- ( ka[j] * ( k21[j] - ka[j] ) )/ ( V[j] * ( alpha[j] - ka[j] ) * ( beta[j] - ka[j] ) ) B[j] <- ( ka[j] * ( k21[j] - alpha[j] ) )/ ( V[j] * ( ka[j] - alpha[j] ) * ( beta[j] - alpha[j] ) ) C[j] <- ( ka[j] * ( k21[j] - beta[j] ) )/ ( V[j] * ( ka[j] - beta[j] ) * ( alpha[j] - beta[j] ) ) V[j] <-exp(LV[j]) ka[j] <-exp(lka[j]) ke[j] <-exp(lke[j])
k12[j]<-exp(lk12[j])
k21[j]<-exp(lk21[j])
LV[j] ~ dnorm( muLV , tauV )
lka[j] ~ dnorm( muka, tauka )
lke[j] ~ dnorm( muke, tauke )
lk12[j]~ dnorm( muk12, tauk12 )
lk21[j]~ dnorm( muk21, tauk21 )
}
tauV <- pow(sigmaV,-2)
tauka <- pow(sigmaka,-2)
tauke <- pow(sigmake,-2)
tauk12 <- pow(sigmak12,-2)
tauk21 <- pow(sigmak21,-2)
sigmaV ~ dunif(0,10)
sigmaka ~ dunif(0,10)
sigmake ~ dunif(0,10)
sigmak12 ~ dunif(0,10)
sigmak21 ~ dunif(0,10)
muLV ~ dnorm( 0.51879, 0.01 )
muka ~ dnorm( 1.175573, 0.01 )
muke ~ dnorm( -1.910543, 0.01 )
muk12 ~ dnorm( -2.513306, 0.01 )
muk21 ~ dnorm( -1.731606, 0.01 )
}
# Data:
list(Y=c(9,3.9,3.2,9.8,5.6,5.1,12.2,8,10.9,10.9,9,6.5,8.7,3.1,2.8,8,6.7,NA,11.5,5.8,NA,7.7,6.5,4.5,3.2,NA,NA,NA,NA,NA,13.4,5.1,NA,4,4.9,2.4,7.3,4.1,2.8,8.1,8.9,3.2,4.1,4.9,6.9,4.1,NA,9.6,6.4,11.2,12,8.4,6.5,5.2,NA,9.6,7.6,6.8,13.1,10,8.4,16.3,10.5,8.8,8,5.2,8.8,4.4,2.6,NA,5.3,2.6,7.2,5.3,3.5,NA,NA,NA,NA,NA,NA,7.9,8.4,NA,14.6,11,6.1,14.6,11.9,9.6,13,11.4,7.7,7.1,6.9,3.7,10.1,7.9,2.9,NA,8.3,5.3,10.3,13.7,6.9,4.2,9.9,8,5,10,8.5,5.8,10.1,9.1,13,10,7,13,11,9,13,11,9,15,13,14,4,3,7,6,6,13,10,7,14,6,6,5,11,8,5,12,7,6,8,9,14,11,5,13,8,5,10.6,7.8,5,11.4,8.2,5,4.7,NA,3.6,1.8,NA,NA,7.8,5.7,NA,9.9,5.4,5,9.3,5.7,5.7,12.5,8.2,4.9,7.8,4.3,NA,8.4,5.7,3.6,10.7,7.1,4.6,9.2,13.5,8.9,4.6,10.7,6.4,3.5,9.2,8.7,7.1,9.4,8.7,4.9,4.9,NA,3.4,NA,NA,NA,9.2,4.2,NA,11.4,10.2,7.1,13.3,11.7,9.4,11.5,8.6,7.1),monkey =c(1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17),time1=c(2,4,7,9,11,14,16,18,21,23,25,28,2,4,7,9,11,14,16,18,21,23,25,28,31,35,38,42,45,49,2,4,7,9,11,14,16,18,21,23,2,4,7,9,11,14,16,18,21,23,25,28,2,4,7,9,11,14,16,18,21,23,25,2,4,7,9,11,14,16,18,21,23,25,28,31,35,38,42,45,49,2,4,7,9,11,14,16,18,21,23,25,28,2,4,7,9,11,14,16,18,21,23,2,4,7,9,11,14,16,18,21,23,25,2,4,7,9,11,14,16,18,21,23,25,2,4,7,9,11,14,16,18,21,23,2,4,7,9,11,14,16,18,21,23,25,2,4,7,9,11,14,16,18,21,23,25,28,31,35,38,42,45,49,2,4,7,9,11,14,16,18,21,23,25,28,2,4,7,9,11,14,16,18,21,23,2,4,7,9,11,14,16,18,21,23,25,28,31,35,38,42,45,49,2,4,7,9,11,14,16,18,21,23,25,28
),time2=c(0,0,0,2,4,7,9,11,14,16,18,21,0,0,0,2,4,7,9,11,14,16,18,21,24,28,31,35,38,42,0,0,0,2,4,7,9,11,14,16,0,0,0,2,4,7,9,11,14,16,18,21,0,0,0,2,4,7,9,11,14,16,18,0,0,0,2,4,7,9,11,14,16,18,21,24,28,31,35,38,42,0,0,0,2,4,7,9,11,14,16,18,21,0,0,0,2,4,7,9,11,14,16,0,0,0,2,4,7,9,11,14,16,18,0,0,0,2,4,7,9,11,14,16,18,0,0,0,2,4,7,9,11,14,16,0,0,0,2,4,7,9,11,14,16,18,0,0,0,2,4,7,9,11,14,16,18,21,24,28,31,35,38,42,0,0,0,2,4,7,9,11,14,16,18,21,0,0,0,2,4,7,9,11,14,16,0,0,0,2,4,7,9,11,14,16,18,21,24,28,31,35,38,42,0,0,0,2,4,7,9,11,14,16,18,21),time3=c(0,0,0,0,0,0,2,4,7,9,11,14,0,0,0,0,0,0,2,4,7,9,11,14,17,21,24,28,31,35,0,0,0,0,0,0,2,4,7,9,0,0,0,0,0,0,2,4,7,9,11,14,0,0,0,0,0,0,2,4,7,9,11,0,0,0,0,0,0,2,4,7,9,11,14,17,21,24,28,31,35,0,0,0,0,0,0,2,4,7,9,11,14,0,0,0,0,0,0,2,4,7,9,0,0,0,0,0,0,2,4,7,9,11,0,0,0,0,0,0,2,4,7,9,11,0,0,0,0,0,0,2,4,7,9,0,0,0,0,0,0,2,4,7,9,11,0,0,0,0,0,0,2,4,7,9,11,14,17,21,24,28,31,35,0,0,0,0,0,0,2,4,7,9,11,14,0,0,0,0,0,0,2,4,7,9,0,0,0,0,0,0,2,4,7,9,11,14,17,21,24,28,31,35,0,0,0,0,0,0,2,4,7,9,11,14),time4=c(0,0,0,0,0,0,0,0,0,2,4,7,0,0,0,0,0,0,0,0,0,2,4,7,10,14,17,21,24,28,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,2,4,7,0,0,0,0,0,0,0,0,0,2,4,0,0,0,0,0,0,0,0,0,2,4,7,10,14,17,21,24,28,0,0,0,0,0,0,0,0,0,2,4,7,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,2,4,0,0,0,0,0,0,0,0,0,2,4,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,2,4,0,0,0,0,0,0,0,0,0,2,4,7,10,14,17,21,24,28,0,0,0,0,0,0,0,0,0,2,4,7,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,2,4,7,10,14,17,21,24,28,0,0,0,0,0,0,0,0,0,2,4,7),dose1=c(20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20),dose2=c(0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,20,20,20,20,20,20,20,20,20),dose3=c(0,0,0,0,0,0,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,20,20,20,20,20,20),dose4=c(0,0,0,0,0,0,0,0,0,20,20,20,0,0,0,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,0,0,0,20,0,0,0,0,0,0,0,0,0,20,20,20,0,0,0,0,0,0,0,0,0,20,20,0,0,0,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,0,0,0,20,20,20,0,0,0,0,0,0,0,0,0,20,0,0,0,0,0,0,0,0,0,20,20,0,0,0,0,0,0,0,0,0,20,20,0,0,0,0,0,0,0,0,0,20,0,0,0,0,0,0,0,0,0,20,20,0,0,0,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,0,0,0,20,20,20,0,0,0,0,0,0,0,0,0,20,0,0,0,0,0,0,0,0,0,20,20,20,20,20,20,20,20,20,0,0,0,0,0,0,0,0,0,20,20,20),N = 216,J=17)
# Inits:
list(sigma.y=3.03,muLV=0.451,muka=1.37,muke=-1.988,muk12=-2.61,muk21=-1.82,sigmaV=2.85,sigmaka=1.92,sigmake=6.33,sigmak21=6.89,LV=c(2.3375768,2.1131326,-2.9672930,-0.7232807,5.2146430,2.3692468,1.7993847,-2.9941884,3.4077675,-0.3522470,2.6228524,-3.1021916,4.2183896,-3.6134175,3.8129013,0.1638676,2.0034773),lka=c(1.5906045,2.4214173,0.9676078,3.8440597,0.787718,-2.3277679,2.088227,1.1320029,0.3878235,4.3357967,-0.8496406,2.3591636,0.396198,4.69487,2.6023122,2.1179844,-0.3866458),lke=c(-7.345367,2.383361,-6.350776,3.713401,1.563373,11.179944,11.01133,8.637848,-3.441219,-6.579666,3.101094,-8.668811,1.101745,-1.731504,-10.413856,-2.427511,-10.42432),lk12=c(-1.668994,-1.9942154,-0.9190348,0.1852387,-2.883629,-0.7384197,-1.2938703,-3.537769,-2.5941325,-0.1249434,-1.9240245,-2.2275114,-3.1574265,-2.3539842,-4.7286449,-5.8670984,-0.4284762),lk21=c(-3.5060777,-4.1271651,-3.364257,-5.801624,-13.3371005,8.3216115,1.2069363,-7.4143348,7.3379469,-7.6311012,7.3515466,5.3150512,-5.407578,-1.9711796,-0.1472733,-4.6044567,5.0966538))
-----Original Message-----
From: (The BUGS software mailing list) [mailto:[log in to unmask]] On Behalf Of Aaron Mackey
Sent: Wednesday, November 02, 2011 3:13 PM
To: [log in to unmask]
Subject: Re: [BUGS] General question about data error and Bayesian updates
I've done this in the past by using both the observed (actually estimated, as you say) mean (y[i]) and variance (prec[i]) as the
"data":
y[i] ~ dnorm(mu, prec[i])
thus, your final posterior estimate of mu will incorporate the varying "uncertainty" associated with each data value.
-Aaron
On Mon, Oct 24, 2011 at 2:11 PM, Robert Stewart <[log in to unmask]> wrote:
> Hello-
> I am still on the Bayesian learning curve and was curious if someone could point me to a good reference on how to deal with the fact that the data you wish to update your prior with has measurement errors in it. I want to account for the errors somehow in the posterior.
>
> Shedding just a little more light on it - each of my "data" are actually themselves the outcomes of a simple model. The data I am gathering can't be directly sensed but must be inferred from ancillary data that you can sense. The outcome of the simple model is really a PDF where you can use say the median or mean as your "data". I would rather use the entire PDF somehow. I've seen Hierarchical models but they are dealing with the Prior. Not me - I want to update my prior (which is by the way hierarchical) with my "pdf data".
>
> Shedding just a little more light on it - At the end of the day. I intend to use some statistic of the posterior distribution (e.g. expected value) as my final answer. I was thinking if I drew X simulations of all my N "data" giving me X simulations of the posterior update, then I would get a X simulations of that statistic and i would have successfully propogated my uncertainty through the system.
>
> I realize this is not a BUGS question necessarily, but the community is quite strong so I thought I'd try....
>
> Thanks in advance for any advice or directions you can offer, Robert
>
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For help with crashes and error messages, first mail [log in to unmask]
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Before mailing, please check the archive at www.jiscmail.ac.uk/lists/bugs.html
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