```Dear BUGS users,
I wonder if anyone else has tried this:
I am trying to fit a joint model for longitudinal and binary data.
(as opposed to the usual joint models for longitudinal and survival data.)
The longitudinal data are measured with error.

In the generated data below, there are 100 individuals, and
a continuous variable (Y) is measured at 8 different times (longitudinal data)
while a binary variable (R) is measured once.
The continuous measurements include true measure (U) and
measurement error (e): Y=U+e
The binary variable follows a logit model: logit(R) =  G0 + G1*U.

The model is correct, since the data are generated, and the
true value of G1 is 1.6.

When I put a non-informative prior on the parameters,
the posterior distribution of the parameter of interest (G1)
is so variable as to be practically useless.  Here is the output
from a not particularly vague prior on G1 (G1~dnorm(0, .02)).

mean      sd      MC_error  val2.5pc  median   val97.5pc   start  sample
G0  -0.08904  0.3394  0.008596  -0.789   -0.08988   0.6018     10000  10001
G1  -0.439    6.725   0.229     -13.18   -0.7294   13.5        10000  10001

It gets worse the lower the precision of the prior on G1.
Is there any obvious reason for this? Is this model just doomed,
or have I done something silly?

Thanks,

Julie Horrocks
University of Guelph

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model{
for (i in 1:N) {
for (j in 1:M) {
Y[i,j] ~ dnorm(muy[i, j], tauz)
muy[i, j]<-U1[i]
}
U1[i] ~ dnorm(muu,tau1)
r[i]~dbin(p[i],1)

logit(p[i])<-G0+G1*U1[i]
}

sigmaz<- sqrt(1/tauz )

#priors

tauz~dgamma(0.1, 0.1)
sigma1~dunif(0,1)
G0~dnorm(0,0.000001)
G1~dnorm(1.6, .02)
muu~dnorm(0,1.0E-6)
}

list(N = 100, M = 8, Y = structure(.Data=c(-0.262313843855381,
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-0.0135981310993740, 1.09097945900444, 0.0346151682731844, -0.197802459374791,
-1.47514497226055, 0.407207984279559, -0.309004451018228, -0.36725925131416,
1.30945036479418, 0.765328207381141, 1.30184900895539, 1.62183617798371,
0.564485540193846, -0.892685774787704, -0.41708531390867, -1.82656464269386,
0.254683325636118, -0.304363230935357, -0.349802115911927, -0.91133574351325,
-1.23231058438745, -0.308931641851249, 0.298146719690391, 0.430237494557323,
1.42949014693376, 0.93109091891645, 0.56110944691244, -0.268290089653620,
-0.651203391833492, -0.299477176380969, 1.00123461378704, -0.132486843148446,
1.37848452519519, -0.431433999132537, -1.55023463925404, -1.36465421332819,
0.0339502755094938, 0.397492874858985, 0.383095985651148, 0.00568678112217202,
0.617176121879459, 0.150103498407917, -0.351107961069875, 0.215606643314364,
-0.852552887011086, -0.892052149513662, -0.195285146867997, -0.46025895465704,
-0.375836754636786, 0.153241148807489, 0.754634996062549, -0.322830422102971,
-1.12570002174003, -0.371595866755367, -0.675509053412837, 0.97407630412936,
0.199279992105377, 0.145756186739396, -1.45985395704062, 0.634084076326643,
-0.839175345416791, -0.811343569105302, -1.53394510038748, -1.06507227404272,
1.08274843159052, 0.307840840323339, -0.135123087179747, -0.315506811176714,
-0.292291579345138, 0.601793929269907, 1.68835971398503, -0.418231348707417,
-0.527953059264142, -1.34171700632720, 0.877855944027478, 2.07116931866773,
0.125286188715722, 0.821505571498239, -0.620181753764083), .Dim = c(100,
8)), r = c(1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1,
1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1,
1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1,
1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0,
1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0))

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