Posterior distribution and heterogeneity in Bayesian three-level meta-analysis with brms

Interfaces brms
1

Hi,

As a beginner, I am trying to do a Bayesian three-level meta-analysis with brms. Following the https://doing-meta.guide/bayesian-ma , here is the code for my main model.

#Main model
main.model <- brm(yi|se(seTE)~ 0 + Intercept + (1|es_id) + (1|study),
                  data = dat,
                  save_pars = save_pars(all = TRUE),
                  prior = c(prior(normal(0, 1), class = b),
                            prior(cauchy(0, 0.5), class = sd)),
                  iter = 5000, control = list(adapt_delta = .999, max_treedepth = 15))
summary(main.model)


Family: gaussian 
  Links: mu = identity 
Formula: yi | se(seTE) ~ 0 + Intercept + (1 | es_id) + (1 | study) 
   Data: dat (Number of observations: 40) 
  Draws: 4 chains, each with iter = 5000; warmup = 2500; thin = 1;
         total post-warmup draws = 10000

Multilevel Hyperparameters:
~es_id (Number of levels: 40) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.24      0.07     0.11     0.37 1.00     2875     3366

~study (Number of levels: 17) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.11      0.08     0.00     0.30 1.00     2052     3909

Regression Coefficients:
          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept     0.17      0.07     0.04     0.31 1.00     6212     6615

Further Distributional Parameters:
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     0.00      0.00     0.00     0.00   NA       NA       NA

Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

My questions are: What are the code for

  1. within-study variance and between-study variance and their CrI.
  2. plots of posterior distribution of g, τ(2) and τ(3) in the main model.
  3. Heterogeneity I2 statistics for different levels (Cheung, 2014).

Best,

data_YYH.csv (1.1 KB)

Yuan