12.8 Posterior Prediction

Consider the state of Minnesota, a historically Democrat state with 73.3% of residents residing in urban areas and 4 anti-discrimination laws.

equality %>% 
  filter(state == "minnesota")

## # A tibble: 1 × 6
##   state     region  gop_2016  laws historical percent_urban
##   <fct>     <fct>      <dbl> <dbl> <fct>              <dbl>
## 1 minnesota midwest     44.9     4 dem                 73.3

# Calculate posterior predictions
set.seed(84735)
mn_prediction <- posterior_predict(
  equality_model, newdata = data.frame(percent_urban = 73.3, 
                                       historical = "dem"))

mcmc_hist(mn_prediction, binwidth = 1) + 
  geom_vline(color = "purple", xintercept = 4, linewidth = 4) + 
  xlab("Predicted number of laws in Minnesota")

The posterior distribution leads to a credible interval with values near (10, 30) for the number of anti-discriminatory laws, but Minnesota has 4 such laws.