Hi all, I am trying to write the winbugs code using stan, the winbugs code looks like below

```
model;
{
for(j in 1:9){ # j indexes trial
# (1) fixed effect based on normal approximation
y1[j]<- y[j]
y1[j] ~ dnorm(theta[1,j],sigma2.inv[j])
theta[1,j] ~ dunif(-10,10)
# (2) pooled effect based on normal approximation
y2[j]<- y[j]
y2[j] ~ dnorm(theta[2,j],sigma2.inv[j])
theta[2,j] <- mu[2]
# (3) random effect based on normal approximation
y3[j]<- y[j]
y3[j] ~ dnorm(theta[3,j],sigma2.inv[j])
theta[3,j] ~ dnorm(mu[3],tau2.inv[3])
# (4) random, exact binomial, indep uniform
rt4[j] <- rt[j]; rc4[j] <- rc[j]
rt4[j] ~ dbin(pt4[j],nt[j])
rc4[j] ~ dbin(pc4[j],nc[j])
logit(pt4[j]) <- theta[4,j] + logit(pc4[j])
pc4[j] ~ dunif(0,1)
theta[4,j] ~ dnorm(mu[4],tau2.inv[4])
# (5) random, exact binomial, indep on logodds
rt5[j] <- rt[j]; rc5[j] <- rc[j]
rt5[j] ~ dbin(pt5[j],nt[j])
rc5[j] ~ dbin(pc5[j],nc[j])
logit(pt5[j]) <- theta[5,j] + phi5[j]
logit(pc5[j]) <- phi5[j]
phi5[j] ~ dunif(-10,10)
theta[5,j] ~ dnorm(mu[5],tau2.inv[5])
}
phi.mean ~ dunif(-10,10) # uniform on control group mean
phi.sd ~ dunif(0,50)# Prior: Uniform(0,50) on tau
phi.prec <- 1/(phi.sd*phi.sd)
for(i in 1:5){
mu[i] ~ dunif(-10,10) # uniform on overall mean
tau[i] ~ dunif(0,50)# Prior: Uniform(0,50) on tau
tau2.inv[i] <- 1/(tau[i] * tau[i])
}
# j again indexes study number
for(j in 1:9)
{
dummy[j]<-id[j]+date[j] # just to mention all data # log-odds ratios
y[j] <- log(((rt[j] + 0.5)/(nt[j] - rt[j] + 0.5))/((rc[j] + 0.5)/(nc[j] - rc[j] + 0.5)))
# variances & precisions
sigma2[j] <- 1/(rt[j] + 0.5) + 1/(nt[j] - rt[j] + 0.5) + 1/(rc[j] + 0.5) + 1/(nc[j] - rc[j] + 0.5)
sigma2.inv[j] <- 1/sigma2[j]
}
}
```

Here is the stan code I have

```
dat<-read.table(header = TRUE, text = "
id[] date[] nt[] rt[] nc[] rc[]
1 1976 175 1 175 1
2 1976 242 2 241 1
3 1978 253 0 251 1
4 1979 463 3 232 0
5 1981 445 1 482 0
6 1985 485 0 493 1
7 1985 6530 14 6554 14
8 1987 122 17 124 18
9 1993 746 2 682 9
")
names(dat) <- gsub(".", "", names(dat), fixed = TRUE)
dataList = list(
Ntotal = 9,
nt=dat$nt,
rt=dat$rt,
nc=dat$nc,
rc=dat$rc,
rt4=dat$rt,
rc4=dat$rc,
rt5=dat$rt,
rc5=dat$rc,
y=log(((dat$rt + 0.5)/(dat$nt - dat$rt + 0.5))/((dat$rc + 0.5)/(dat$nc - dat$rc + 0.5))),
y1=log(((dat$rt + 0.5)/(dat$nt - dat$rt + 0.5))/((dat$rc + 0.5)/(dat$nc - dat$rc + 0.5))),
y2=log(((dat$rt + 0.5)/(dat$nt - dat$rt + 0.5))/((dat$rc + 0.5)/(dat$nc - dat$rc + 0.5))),
y3=log(((dat$rt + 0.5)/(dat$nt - dat$rt + 0.5))/((dat$rc + 0.5)/(dat$nc - dat$rc + 0.5)))
)
################Stan###############
modelString1 = "
data{
int<lower=0> Ntotal;
int<lower=0> nt[Ntotal];
int<lower=0> rt[Ntotal];
int<lower=0> nc[Ntotal];
int<lower=0> rc[Ntotal];
int<lower=0> rt4[Ntotal];
int<lower=0> rc4[Ntotal];
int<lower=0> rt5[Ntotal];
int<lower=0> rc5[Ntotal];
real y[Ntotal];
real y1[Ntotal];
real y2[Ntotal];
real y3[Ntotal];
}
transformed data {
vector<lower=0>[9] sigma2;
for(j in 1:9){
sigma2[j] = 1/(rt[j] + 0.5) + 1/(nt[j] - rt[j] + 0.5) + 1/(rc[j] + 0.5) + 1/(nc[j] - rc[j] + 0.5);
}
}
parameters {
real<lower=-10,upper=10> phimean;
real<lower=0,upper=50> phisd;
real<lower=-10,upper=10> theta1[Ntotal];
real<lower=-10,upper=10> theta2[Ntotal];
real<lower=0,upper=1> pc4[Ntotal];
real<lower=-10,upper=10> phi5[Ntotal];
real<lower=0,upper=50> tau4;
real<lower=0,upper=50> tau5;
real<lower=0,upper=50> tau3;
real<lower=-10,upper=10> mu4;
real<lower=-10,upper=10> mu5;
real<lower=-10,upper=10> mu3;
vector[Ntotal] theta3;
vector[Ntotal] theta4;
vector[Ntotal] theta5;
}
model
{
vector[Ntotal] pt4;
vector[Ntotal] pt5;
vector[Ntotal] pc5;
for(j in 1:9){
//# (1) fixed effect based on normal approximation
target += normal_lpdf(y1[j] | theta1[j],sqrt(sigma2[j]));
//# (2) pooled effect based on normal approximation
target += normal_lpdf(y2[j] | theta2[j],sqrt(sigma2[j]));
//# (3) random effect based on normal approximation
target += normal_lpdf(y3[j] | theta3[j],sqrt(sigma2[j]));
target += normal_lpdf(theta3[j] | mu3,tau3);
//# (4) random, exact binomial, indep uniform
pt4[j] = theta4[j] + logit(pc4[j]);
rt4[j] ~ binomial_logit(nt[j],pt4[j]);
rc4[j] ~ binomial(nc[j],pc4[j]);
target += normal_lpdf(theta4[j] | mu4,tau4);
//# (5) random, exact binomial, indep on logodds
pt5[j] = theta5[j] + phi5[j];
pc5[j] = phi5[j];
rt5[j] ~ binomial_logit(nt[j],pt5[j]);
rc5[j] ~ binomial_logit(nc[j],pc5[j]);
target += normal_lpdf(theta5[j] | mu5,tau5);
}
}
"
writeLines( modelString1 , con="TEMPmodel.stan" )
stanModel <- stan(
data = dataList ,
file = "TEMPmodel.stan",
chains = 4,
warmup = 5000,
iter = 25000,
control = list(adapt_delta = 0.999)
)
stanModel
```

I am not sure why I have so many warnings below:

2: There were 1078 divergent transitions after warmup. See

http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup

to find out why this is a problem and how to eliminate them.

3: There were 19942 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See

http://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded

4: Examine the pairs() plot to diagnose sampling problems

Any help is appreciated!!!