Built-in models:Meta-analysis of correlation

! Model

Let \(r_i\), \(n_i\), and \(a_i\) be the sample correlation, sample size, and power for study \(i,i=1,\ldots,m\). A random-effects meta-analysis model based on Fisher z-transformation can be written as below:

{{%%

\[
z_i = \frac{1}{2}\log\left[ \frac{1+r_i}{1-r_i}\right]
\]

\[
z_i \sim N(\zeta_i, \phi_i)
\]

\[
\zeta_i \sim N(\beta, \tau)
\]

\[
\phi_i = \frac{1}{a_i(n_i-3)}
\]
%%}}

! BUGS code
{{
model{
for (i in 1:m){
z[i] <- .5*log((1+r[i])/(1-r[i]))
pre.phi[i] <- (n[i]-3)*a[i]
z[i] ~ dnorm(zeta[i], pre.phi[i])
zeta[i] ~ dnorm(\beta, pre.tau)
rho[i] <- (exp(2*zeta[i])-1)/((exp(2*zeta[i])+1))
}
beta ~ dnorm(0, 1.0E-6)
rho.beta <- (exp(2*beta)-1)/((exp(2*beta)+1))
pre.tau ~ dgamma(.001,.001)
tau <- 1/pre.tau
}
}}