Survey weighted regression

Modeling
14

It does not.

Instead, one has to calculate the standard deviation for the effect of each study outside Stan (see e.g. the compute.es R package, or equation 2 here) and provide it as data.

Then, the following model estimates the effect size such that the study weight depends on the studies effect sizes and associated standard deviations.

data {
  int N;            // number of studies
  vector[N] y;      // study effect sizes
  vector[N] sigmas; // standard deviations of study effect sizes
}
parameters {
  real mu;
}
model {
  mu ~ normal(0,2);
  y ~ normal(mu,sigmas);
}

Here, weighting is “implicit”, because larger studies have smaller variances, as you can see from the equation for the variance of Cohen’s d:

\sigma^2_d=\frac{n_a+n_b}{n_a*n_b}+\frac{d^2}{2(n_a+n_b)}
where n_a and n_b are sample sizes of the groups compared to obtain d. (details)

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