Bootstrapping

Based on Chapter 8 of ModernDive. Code for Quiz 12.

Load the R packages we will use.

What is the average age of members that have served in congress?

set.seed(4346)

congress_age_100 <- congress_age  %>% 
  rep_sample_n(size=100)

Construct the confidence interval 1. Use specify to indicate the variable from congress_age_100 that you are interested in

congress_age_100  %>% 
  specify(response = age)
Response: age (numeric)
# A tibble: 100 × 1
     age
   <dbl>
 1  58  
 2  27.3
 3  59.4
 4  47.8
 5  36.4
 6  62.3
 7  52.5
 8  55.5
 9  44  
10  48  
# … with 90 more rows
2. generate 1000 replicates of your sample of 100
Response: age (numeric) # A tibble: 100,000 × 2 # Groups: replicate [1,000] replicate age <int> <dbl> 1 1 55.2 2 1 40.8 3 1 55.7 4 1 52.5 5 1 54.5 6 1 35.8 7 1 44.5 8 1 47.9 9 1 40.8 10 1 37.4 # … with 99,990 more rows

3. calculate the mean for each replicate

bootstrap_distribution_mean_age  <- congress_age_100  %>% 
  specify(response = age)  %>% 
  generate(reps = 1000, type = "bootstrap")  %>% 
  calculate(stat = "mean")

bootstrap_distribution_mean_age
Response: age (numeric)
# A tibble: 1,000 × 2
   replicate  stat
       <int> <dbl>
 1         1  51.3
 2         2  48.2
 3         3  49.7
 4         4  50.5
 5         5  51.6
 6         6  47.9
 7         7  49.5
 8         8  50.0
 9         9  51.0
10        10  51.0
# … with 990 more rows

The bootstrap_distribution_mean_age has 1000 means

4. visualize the bootstrap distribution

visualize(bootstrap_distribution_mean_age) 

Calculate the 95% confidence interval using the percentile method

congress_ci_percentile  <- bootstrap_distribution_mean_age %>% 
  get_confidence_interval(type = "percentile", level = 0.95)

congress_ci_percentile
# A tibble: 1 × 2
  lower_ci upper_ci
     <dbl>    <dbl>
1     48.5     52.7

- Calculate the observed point estimate of the mean and assign it to obs_mean_age

obs_mean_age  <-  congress_age_100  %>% 
  specify(response = age)  %>% 
  calculate(stat = "mean")  %>% 
  pull()

obs_mean_age
[1] 50.533
visualize(bootstrap_distribution_mean_age) +
  shade_confidence_interval(endpoints = congress_ci_percentile) +
  geom_vline(xintercept = obs_mean_age, color = "hotpink", size = 1 )

pop_mean_age  <- congress_age  %>% 
  summarize(pop_mean= mean(age))  %>% pull()

pop_mean_age
[1] 53.31373
visualize(bootstrap_distribution_mean_age) +
  shade_confidence_interval(endpoints = congress_ci_percentile) + 
   geom_vline(xintercept = obs_mean_age, color = "hotpink", size = 1) +
   geom_vline(xintercept = pop_mean_age, color = "purple", size = 3)

Save the previous plot to preview.png and add to the yaml chunk at the top

ggsave(filename = "preview.png", 
       path = here::here("_posts", "2022-04-25-bootstrapping"))