Assessing linearity in logistic regression

Background

https://chatgpt.com/share/6851c5ad-9c08-8013-ad26-d03c0de42079

Simulate some data

n <- 1000
p <- 3
X1 <- matrix(rnorm(n * p), ncol = p)
X2 <- X1
X2[, 1] <- X2[, 1] ^ 2
beta <- rep(1, p)
y_logit <- X2 %*% beta
p <- plogis(y_logit)
outcome <- rbinom(n * p, 1, p)

Fit a model

fm1 <- glm(outcome ~ X1, family = binomial())
fm2 <- glm(outcome ~ X2, family = binomial())

Partial residual plots

library(faraway)
prplot(fm1, 1)

prplot

function (g, i) 
{
    xl <- attributes(g$terms)$term.labels[i]
    yl <- paste("beta*", xl, "+res", sep = "")
    x <- model.matrix(g)[, i + 1]
    plot(x, g$coeff[i + 1] * x + g$res, xlab = xl, ylab = yl)
    abline(0, g$coeff[i + 1])
    invisible()
}
<bytecode: 0x10fbf0978>
<environment: namespace:faraway>

library('tidyverse')

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prplot2 <- function (g, i) 
{
    xl <- attributes(g$terms)$term.labels[i]
    yl <- paste("beta*", xl, "+res", sep = "")
    x <- model.matrix(g)[, i + 1]
    y <- g$coeff[i + 1] * x + g$res
    tibble(x = x, y = y) |> 
      ggplot(aes(x, y)) + geom_point() + geom_smooth()
}

prplot2(fm1, 1)

`geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

prplot2(fm2, 1)

`geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

Binned plot

library(arm)

Loading required package: MASS

Attaching package: 'MASS'

The following object is masked from 'package:dplyr':

    select

Loading required package: Matrix

Attaching package: 'Matrix'

The following objects are masked from 'package:tidyr':

    expand, pack, unpack

Loading required package: lme4

arm (Version 1.14-4, built: 2024-4-1)

Working directory is /Users/seb/Documents/Projects/00_websites/sbloggel/posts/2025-07-30-assessing-linearity-in-logistic-regression

Attaching package: 'arm'

The following objects are masked from 'package:faraway':

    fround, logit, pfround

binnedplot(predict(fm1), residuals(fm1, type = "response"))

binnedplot(predict(fm2), residuals(fm2, type = "response"))