influence_tv.md

Regression and Other Stories: Influence

Andrew Gelman, Jennifer Hill, Aki Vehtari 2021-04-20

• 8 Fitting regression models
  • 8.2 Influence of individual points in a fitted regression

Tidyverse version by Bill Behrman.

Plot influence of individual points in a fitted regression. See Chapter 8 in Regression and Other Stories.

---

# Packages
library(tidyverse)
library(rstanarm)

# Parameters
  # Common code
file_common <- here::here("_common.R")

#===============================================================================

# Run common code
source(file_common)

8 Fitting regression models

8.2 Influence of individual points in a fitted regression

Simulated data.

set.seed(264)

a <- 1
b <- 2
sigma <- 5

data <- 
  tibble(
    x = 2:12,
    y = rnorm(length(x), mean = a + b * x, sd = sigma)
  )

Fit linear regression to data.

set.seed(148)

fit <- stan_glm(y ~ x, data = data, refresh = 0)

Linear regression with residuals.

intercept <- coef(fit)[["(Intercept)"]]
slope <- coef(fit)[["x"]]

v <- 
  data %>% 
  mutate(pred = intercept + slope * x)

v %>% 
  ggplot(aes(x, y)) +
  geom_segment(aes(xend = x, yend = pred), color = "grey60") +
  geom_abline(slope = slope, intercept = intercept) +
  geom_point() +
  scale_x_continuous(breaks = scales::breaks_width(2)) +
  labs(title = "Linear regression with residuals")