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
}