probs-odds-logits.R

library(tidyverse)
library(patchwork)
library(latex2exp)

logit_df <- tibble(x = seq(0, 100, length.out = 101),
                   logits = seq(-4, 4, length.out = 101)) |> 
  mutate(odds = exp(logits)) |> 
  mutate(probs = plogis(logits))

p1 <- ggplot(logit_df, aes(x = x, y = probs)) +
  geom_line(size = 1, color = "darkred") +
  labs(title = "Probabilities", 
       subtitle = "Can't be modeled linearly; too curvy and bound between 0–1",
       x = NULL,
       y = TeX("$\\pi$")) +
  theme_minimal() +
  theme(plot.title = element_text(face = "bold"),
        axis.title.y = element_text(angle = 0, hjust = 0),
        panel.grid.minor = element_blank())

p2 <- ggplot(logit_df, aes(x = x, y = odds)) +
  geom_line(size = 1, color = "goldenrod") +
  labs(title = "Odds", 
       subtitle = "No longer bound between 0–1, but still too curvy for linear models",
       x = NULL,
       y = TeX("$\\frac{\\pi}{1 - \\pi}$")) +
  theme_minimal() +
  theme(plot.title = element_text(face = "bold"),
        axis.title.y = element_text(angle = 0, hjust = 0),
        panel.grid.minor = element_blank())

p3 <- ggplot(logit_df, aes(x = x, y = logits)) +
  geom_line(size = 1, color = "dodgerblue") +
  labs(title = "Log odds (logits)", 
       subtitle = "Linear models are comfy and happy here",
       x = NULL,
       y = TeX("$log \\left( \\frac{\\pi}{1 - \\pi} \\right)$")) +
  theme_minimal() +
  theme(plot.title = element_text(face = "bold"),
        axis.title.y = element_text(angle = 0, hjust = 0),
        panel.grid.minor = element_blank())

p1 / p2 / p3

ggsave("~/logit.png", width = 6, height = 7, dpi = 600)