Model 7.6 about statistical_rethinking_with_brms_ggplot2_and_the_tidyverse_2_ed HOT 8 CLOSED

d  <- 
  tibble(species = c("afarensis", "africanus", "habilis", "boisei", "rudolfensis", "ergaster", "sapiens"), 
         brain   = c(438, 452, 612, 521, 752, 871, 1350), 
         mass    = c(37.0, 35.5, 34.5, 41.5, 55.5, 61.0, 53.5)) %>% 
  mutate(mass_std  = (mass - mean(mass)) / sd(mass),
         brain_std = brain / max(brain))

custom_normal <- custom_family(
  "custom_normal", dpars = "mu",
  links = "identity",
  type = "real"
)

stan_funs  <- "real custom_normal_lpdf(real y, real mu) {
  return normal_lpdf(y | mu, 0.001);
}
real custom_normal_rng(real mu) {
  return normal_rng(mu, 0.001);
}
" 

stanvars <- stanvar(scode = stan_funs, block = "functions")

m7.6 <- brm(data = d,
            family = custom_normal,
            formula = brain_std ~ 1 + poly(mass_std, 6),
            prior = c(prior(normal(0.5, 1), class = Intercept),
                      prior(normal(0, 10), class = b)),
            stanvars = stanvars,
            chains = 4,
            cores = 4, 
            iter = 2000,
            warmup = 1000)


expose_functions(m7.6, vectorize = TRUE)


posterior_epred_custom_normal <- function(prep) {
  mu <- prep$dpars$mu
  mu 
}


mass_std <- seq(-1.5, 1.5, length.out = 1000)
fits <- fitted(m7.6, newdata = list(mass_std = mass_std))
fits <- data.frame(fits, 
                   mass_std = mass_std)

ggplot() + geom_line(data = fits, 
                     mapping = aes(x = mass_std, 
                                   y = Estimate),
                     colour = "blue") +
  geom_ribbon(data = fits, mapping = aes(x = mass_std,
                                         ymin = Q2.5,
                                         ymax = Q97.5),
              fill = "blue",
              alpha = 0.5) +
  geom_point(d, mapping = aes(x = mass_std,
                              y = brain_std),
             colour = "blue") +
  theme_minimal()