A minimal Bayesian multi-level model. 12 groups.

minimal_mlm.R

library(brms)
library(tidybayes)

N <- 1e3
number_of_groups <- 12
group_means <- rnorm(number_of_groups)

tibble(obs = seq_len(N)) %>%
  mutate(group = sample(seq_len(number_of_groups), n(), replace = TRUE),
         contribution = group_means[group],
         discrepancy = rnorm(n()),
         y = contribution + discrepancy) -> x

brm(y ~ (1|group) - 1, data = x, cores = 4, control = list(adapt_delta = 0.99)) -> bfit

x %>%
  add_fitted_draws(bfit) %>%
  ungroup() %>%
  group_by(group) %>%
  sample_n(1e4) %>%
  ggplot(aes(x = .value, y = factor(group))) +
  geom_halfeyeh() +
  geom_vline(aes(xintercept = contribution), color = "red", size = 1) +
  facet_wrap(~ group, ncol = 1, scales = "free_y") +
  ylab("") +
  ggtitle("Inference for each group's hidden estimate (red lines)") +
  xlab("red line = our hidden estimate we're trying to infer, each distribution is our guess.")