Page 427 - Applied Statistics with R

17.2. BINARY RESPONSE 427

Again, we could re-write this to better match the function we’re using to simu-
late the data:

∣ X = x ∼ Bern( )
i

i

1
= (x ) = 1 + − (x i )

i
(x ) = 1 + −4
i

In this model, as increases, the log odds decrease.

set.seed(1)
example_data = sim_logistic_data(sample_size = 50, beta_0 = 1, beta_1 = -4)

We again simulate some observations form this model, then fit logistic regression.

fit_glm = glm(y ~ x, data = example_data, family = binomial)

plot(y ~ x, data = example_data,
pch = 20, ylab = "Estimated Probability",
main = "Logistic Regression, Decreasing Probability")
grid()
curve(predict(fit_glm, data.frame(x), type = "response"),
add = TRUE, col = "dodgerblue", lty = 2)
curve(boot::inv.logit(1 - 4 * x), add = TRUE, col = "darkorange", lty = 1)
legend("bottomleft", c("True Probability", "Estimated Probability", "Data"), lty = c(1, 2, 0),
pch = c(NA, NA, 20), lwd = 2, col = c("darkorange", "dodgerblue", "black"))