movies.Rmd

# 人们会给爱情片打高分？ {#movies}


```{r}
library(tidyverse)
library(tidybayes)
library(bayesplot)
library(rstan)
library(loo)
library(broom.mixed)
rstan_options(auto_write = TRUE)
options(mc.cores = parallel::detectCores())
theme_set(bayesplot::theme_default())
```



```{r}
movies_clean <- ggplot2movies::movies %>% 
  select(title, year, rating, Action, Romance) %>%
  filter(!(Action == 1 & Romance == 1)) %>% # 既是爱情片又是动作片的，删去
  mutate(genre = case_when(
    Action == 1 ~ "Action",
    Romance == 1 ~ "Romance",
    TRUE ~ "Neither"
  )) %>%
  filter(genre != "Neither") %>%
  mutate(genre = factor(genre)) %>% 
  mutate(genre_numeric = as.numeric(genre)) %>% # action = 1, comedy = 2
  select(-Action, -Romance) %>%
  group_by(genre) %>%
  slice_sample(n = 200) %>%  # 每种题材的电影**随机**选取若干，每次运行结果会不同
  ungroup()

movies_clean
```


```{r}
movies_clean %>%
  ggplot(aes(x = genre, y = rating, color = genre)) +
  geom_boxplot() +
  geom_jitter() +
  scale_x_discrete(
    expand = expansion(mult = c(0.5, 0.5))
  ) +
  theme(legend.position = "none") 
```





```{r}
group_diffs <- movies_clean %>% 
  group_by(genre) %>% 
  summarize(avg_rating = mean(rating, na.rm = TRUE)) %>% 
  mutate(diff_means = avg_rating - lag(avg_rating))
group_diffs

```





## normal

先假定rating评分，服从正态分布，同时不同的电影题材 genre，分组考虑

```{r, warning=FALSE, message=FALSE}
stan_program <- '
data {
  int<lower=1> N;                            // Sample size
  int<lower=2> n_groups;                     // Number of groups
  vector[N] y;                               // Outcome variable
  int<lower=1, upper=n_groups> group_id[N];  // Group variable
}
transformed data {
  real mean_y;
  mean_y = mean(y); 
}
parameters {
  vector[2] mu;                    // Estimated group means for each
  vector<lower=0>[2] sigma;        // Estimated group sd for each
}
model {
  mu ~ normal(mean_y, 2);
  sigma ~ cauchy(0, 1);

  for (n in 1:N){
    y[n] ~ normal(mu[group_id[n]], sigma[group_id[n]]);
  }
}

generated quantities {
  real mu_diff;
  real cohen_d;
  real cles;

  mu_diff = mu[2] - mu[1];
  cohen_d = mu_diff / sqrt(sum(sigma)/2);
  cles = normal_cdf(mu_diff / sqrt(sum(sigma)), 0, 1);
}

'

stan_data <- movies_clean %>% 
  select(genre, rating, genre_numeric) %>% 
  tidybayes::compose_data(
  N        = nrow(.), 
  n_groups = n_distinct(genre), 
  group_id = genre_numeric, 
  y        = rating
  )

stan_best_normal <- stan(model_code = stan_program, data = stan_data)
```




```{r, fig.width= 5, fig.height= 5}
stan_best_normal %>% 
  tidybayes::spread_draws(mu_diff) %>%
  ggplot(aes(x = mu_diff)) +
  tidybayes::geom_halfeyeh() +
  geom_vline(xintercept = 0)
```





```{r, fig.width= 5, fig.height= 2.5}
stan_best_normal %>% 
  tidybayes::spread_draws(mu_diff) %>%
  
	ggplot(aes(x = mu_diff)) +
  stat_eye(side = "right", 
           fill = "skyblue",
  		     point_interval = mode_hdi, 
  		     .width = c(0.95, 0.5),
    	     interval_colour = "red", 
    	     point_colour = "red",
  		     width = 15.5, 
  		     height = 0.1
  		     ) +
  geom_vline(xintercept = 0, linetype = "dashed", size = 1) +

  coord_cartesian(xlim = c(-1, 2)) +
	labs(x = "mu_diff", y = NULL)
```






## 参考

- John Kruschke’s Bayesian Estimation Supersedes the t Test (BEST) method

- <https://github.com/andrewheiss/diff-means-half-dozen-ways/blob/master/imdb_best.stan>

- <https://github.com/m-clark/Miscellaneous-R-Code/blob/master/ModelFitting/Bayesian/rstant_testBEST.R>