# 心理学データ解析応用/伴走サイトコード -----------------------------------------------------
#  Programmed by kosugitti
#  Licence ; Creative Commons BY-SA license (CC BY-SA) version 4.0
## Lesson 8. Kappa coefficients. rstan Version

# 準備 ----------------------------------------------------------------------

rm(list = ls())
library(tidyverse)
library(bayesplot)
library(rstan)
options(mc.cores = parallel::detectCores())
rstan_options(auto_write = TRUE)
## MAP関数
map_estimation <- function(z) {
  density(z)$x[which.max(density(z)$y)]
}
## MCMCサンプルをデータフレームにする関数
MCMCtoDF <- function(fit) {
  fit %>%
    rstan::extract() %>%
    as.data.frame() %>%
    tibble::as_tibble() %>%
    tibble::rowid_to_column("iter") %>%
    dplyr::select(-lp__) %>%
    tidyr::pivot_longer(-iter) -> MCMCsample
  return(MCMCsample)
}

## MCMCデータフレームを要約する関数
MCMCsummary <- function(MCMCsample) {
  MCMCsample %>%
    dplyr::group_by(name) %>%
    dplyr::summarise(
      EAP = mean(value),
      MED = median(value),
      MAP = map_estimation(value),
      SD = sd(value),
      L95 = quantile(value, prob = 0.025),
      U95 = quantile(value, prob = 0.975),
      Rhat = posterior::rhat_basic(value)
    ) %>%
    mutate(across(where(is.numeric), ~ num(., digits = 3)))
}

# モデル ---------------------------------------------------------------------

model <- rstan::stan_model("rstan/categorical1.stan")
fit <- rstan::sampling(model,
  data = list(K = 3, X = c(51, 45, 27)),
  chains = 4,
  iter = 6000,
  warmup = 1000
)


fit %>%
  MCMCtoDF() %>%
  MCMCsummary()

# Kappa係数
### 定義に則って計算した場合
a <- 55
b <- 16
c <- 14
d <- 35
n <- a + b + c + d
p0 <- (a + d) / n
pe <- ((a + b) * (a + c) + (b + d) * (c + d)) / n / n
(p0 - pe) / (1 - pe)


### モデルによる推定
model <- rstan::stan_model("rstan/kappa.stan")
dataSet <- list(Y = c(55, 16, 14, 35))
fit <- sampling(model,
  data = dataSet,
  chains = 4,
  iter = 5000,
  warmup = 1000
)

fit %>%
  MCMCtoDF() %>%
  MCMCsummary()