### Chapter 15 Bayes Rules! R examples:

# Cherry Blossom data:

# Load packages
library(bayesrules)
library(tidyverse)
library(rstanarm)
library(broom.mixed)

# Load data
data(cherry_blossom_sample)
running <- cherry_blossom_sample %>% 
  select(runner, age, net)
nrow(running)

# Boxplots:

ggplot(running, aes(x = runner, y = net)) + 
  geom_boxplot()


## Complete pooling:

# Scatterplot of race time against age:

ggplot(running, aes(y = net, x = age)) + 
  geom_point()

# Regression model:  Y=net time, X=age:

complete_pooled_model <- stan_glm(
  net ~ age, 
  data = running, family = gaussian, 
  prior_intercept = normal(0, 2.5, autoscale = TRUE),
  prior = normal(0, 2.5, autoscale = TRUE), 
  prior_aux = exponential(1, autoscale = TRUE),
  chains = 4, iter = 5000*2, seed = 84735)

# Posterior summary statistics
tidy(complete_pooled_model, conf.int = TRUE, conf.level = 0.80)

# Plotting regression line from pooled model (blue)
# and regression lines from models for individual runners (gray)

# Plot of the posterior median model
ggplot(running, aes(x = age, y = net, group = runner)) + 
  geom_smooth(method = "lm", se = FALSE, color = "gray", size = 0.5) + 
  geom_abline(aes(intercept = 75.2, slope = 0.268), color = "blue")

# Looking at data for runners 1, 20, and 22:

# Select an example subset
examples <- running %>% 
  filter(runner %in% c("1", "20", "22"))

ggplot(examples, aes(x = age, y = net)) + 
  geom_point() + 
  facet_wrap(~ runner) + 
  geom_abline(aes(intercept = 75.2242, slope = 0.2678), 
              color = "blue")

# Model with no pooling (three examples):

ggplot(examples, aes(x = age, y = net)) + 
  geom_point() + 
  geom_smooth(method = "lm", se = FALSE, fullrange = TRUE) + 
  facet_wrap(~ runner) + 
  xlim(52, 62)