After you fit a logistic model, check it: the binary outcome, the linearity of the logit, influential points (Cook’s distance), and multicollinearity (VIF) — each with the fix when it fails
Check the assumptions of a logistic regression in R: a binary outcome, a linear relationship between each continuous predictor and the logit, no influential observations, and no multicollinearity. Inspect logit-linearity scatter plots, Cook’s distance and standardized residuals, and VIF — with the workaround for each violation. Run it all live.
car::vif() (> 5 is problematic).Fitting a logistic regression gives you odds ratios and p-values — but those are only trustworthy if the model’s assumptions hold. Logistic regression has its own diagnostic checklist, related to but different from linear regression’s.
This lesson walks through the four assumptions, how to check each in R, and — the practical part — what to do when one fails.
We reuse the diabetes model from the logistic regression lesson — glm() on the clinical predictors — and grab its predicted probabilities:
data("PimaIndiansDiabetes2", package = "mlbench")
diabetes_data <- na.omit(PimaIndiansDiabetes2)
model <- glm(diabetes ~ ., data = diabetes_data, family = binomial)
probabilities <- predict(model, type = "response")
head(probabilities) 4 5 7 9 14 15
0.02711452 0.89756363 0.03763559 0.85210016 0.79074609 0.71308818 pos/neg). ✔ by design.Assumption 1 is automatic; the next three need checking.
Logistic regression assumes each continuous predictor is linear against the logit (log-odds), not the probability. Compute the logit from the predicted probabilities and plot each predictor against it, with a loess smoother. We reshape to long form with base R (no tidyverse):
library(ggpubr)
data("PimaIndiansDiabetes2", package = "mlbench")
diabetes_data <- na.omit(PimaIndiansDiabetes2)
model <- glm(diabetes ~ ., data = diabetes_data, family = binomial)
probabilities <- predict(model, type = "response")
# numeric predictors + the logit, reshaped long with base R
num <- diabetes_data[sapply(diabetes_data, is.numeric)]
logit <- log(probabilities / (1 - probabilities))
long <- data.frame(
logit = rep(logit, ncol(num)),
predictor = rep(names(num), each = nrow(num)),
value = unlist(num)
)
ggscatter(long, x = "logit", y = "value", size = 0.5, alpha = 0.4,
add = "loess", add.params = list(color = "#3a86d4")) +
facet_wrap(~ predictor, scales = "free_y")
Read each panel: a roughly straight loess curve means the predictor is linear in the logit. Here glucose, mass, pregnant, pressure, triceps look linear, while age and pedigree bend — they may need a transformation.
Verdict here: most predictors are linear in the logit; age and pedigree are not. If a predictor is non-linear, the fix is a non-linear term — log-transform it, add a polynomial (poly(x, 2)), or use a spline — then re-check the panel.
Extreme points can distort the fit. Screen with Cook’s distance — plot(model, which = 4) labels the largest:
data("PimaIndiansDiabetes2", package = "mlbench")
diabetes_data <- na.omit(PimaIndiansDiabetes2)
model <- glm(diabetes ~ ., data = diabetes_data, family = binomial)
plot(model, which = 4, id.n = 3)
A large Cook’s distance only flags a point — it’s influential only if its standardized residual is also extreme (|value| > 3). Plot the standardized residuals by index, coloured by outcome:
library(ggpubr)
data("PimaIndiansDiabetes2", package = "mlbench")
diabetes_data <- na.omit(PimaIndiansDiabetes2)
model <- glm(diabetes ~ ., data = diabetes_data, family = binomial)
resid.df <- data.frame(
index = seq_len(nrow(diabetes_data)),
std_resid = rstandard(model),
diabetes = diabetes_data$diabetes
)
ggscatter(resid.df, x = "index", y = "std_resid", color = "diabetes",
palette = "jco", size = 1, alpha = 0.6,
ylab = "Standardized residual") +
geom_hline(yintercept = c(-3, 3), linetype = "dashed")
Verdict here: the largest standardized residual is ~2.8 — none exceeds ±3, so there are no influential outliers. If a point did exceed 3, options are: investigate it (data error?), remove the record, transform the predictor, or use a robust method.
Strongly correlated predictors make logistic coefficients unstable — the same VIF check as linear regression. car::vif(); anything above 5 is problematic:
library(car)
data("PimaIndiansDiabetes2", package = "mlbench")
diabetes_data <- na.omit(PimaIndiansDiabetes2)
model <- glm(diabetes ~ ., data = diabetes_data, family = binomial)
sort(vif(model), decreasing = TRUE) age pregnant mass triceps insulin glucose pressure pedigree
1.974053 1.892387 1.832416 1.638865 1.384038 1.378937 1.191287 1.031715 Verdict here: every VIF is well below 5 (the largest is ≈ 2) — no multicollinearity. If one exceeded 5, remove the redundant predictor (see multicollinearity & VIF).
| Assumption | Check | Good sign | Fix if violated |
|---|---|---|---|
| Binary outcome | the response | exactly two classes | use multinomial/ordinal models instead |
| Linearity of logit | predictor-vs-logit + loess | straight loess | transform / polynomial / spline the predictor |
| No influential points | Cook’s distance + std. residual | |std. resid| < 3 | investigate / remove / transform |
| No multicollinearity | car::vif() |
VIF < 5 | remove the redundant predictor |
Logistic regression assumptions were checked. Most continuous predictors were linear in the logit (age and pedigree showed mild departures); no observations exceeded a standardized residual of 3 (no influential outliers); and all variance inflation factors were below 2 (no multicollinearity).
The logit of the fitted probability is \(\text{logit}(p) = \log\!\dfrac{p}{1-p}\), which the model assumes is linear in each continuous predictor — that’s why you plot predictors against the logit, not the probability. The standardized (Pearson) residual rescales each raw residual by its standard error so extremes are comparable; Cook’s distance combines residual size and leverage to measure each point’s influence on the fit (same idea as in linear regression, adapted to the GLM). VIF is unchanged from linear regression — it’s computed on the predictor design matrix.
Re-check the VIF after dropping a predictor, or inspect the logit-linearity for a single variable. The sandbox boots on first Run.
Ask Prova “check the assumptions of my logistic regression and tell me which one is violated and how to fix it” — it inspects logit-linearity, influence and VIF, and answers with code you can run on your own model. The runtime is the judge. Ask Prova →
You checked linearity against the probability, not the logit. Logistic regression assumes linearity in the log-odds — plot each continuous predictor against the logit, not the raw probability or the 0/1 outcome.
You treated a labelled Cook’s-distance point as an automatic outlier. plot(model, which = 4) labels the largest values, but a point is influential only if its standardized residual is also extreme (|value| > 3). Check both.
You forgot categorical predictors don’t need the linearity check. The logit-linearity assumption applies only to continuous predictors; factors are dummy-coded and exempt.
Four: a binary outcome; a linear relationship between each continuous predictor and the logit (log-odds) of the outcome; no influential outliers; and no multicollinearity among predictors. (Logistic regression does not assume normality or homoscedasticity of residuals like linear regression.)
Compute the logit of the fitted probabilities (log(p/(1-p))) and plot each continuous predictor against it with a loess smoother. A roughly straight loess curve means the predictor is linear in the logit; a clear bend means you should transform it (log, polynomial, or spline).
Use plot(model, which = 4) for Cook’s distance to flag the largest values, then check the standardized residuals (rstandard(model)) — a point is a likely influential outlier only if its absolute standardized residual exceeds 3. Large Cook’s distance alone isn’t enough.
No. Unlike linear regression, logistic regression does not assume normally distributed residuals or constant variance. Its assumptions are a binary outcome, linearity of the logit, no influential points, and no multicollinearity.
Compare each VIF to the rule-of-thumb threshold of 5. For question 2, recall that the linearity assumption is about the logit, and a curved relationship breaks it.
All VIFs are below 2, so there is no multicollinearity to worry about. For question 2: a U-shaped loess curve means the predictor is not linear in the logit — the linearity assumption is violated. A fix is to add a quadratic term (poly(x, 2)) or a spline, which lets the model bend with the relationship; then re-plot to confirm the curve straightens.
You can now diagnose a logistic regression in R: confirm the binary outcome, check logit-linearity for each continuous predictor, screen for influential points with Cook’s distance and standardized residuals, and test multicollinearity with VIF — applying the right fix for any violation. A checked logistic model is one whose odds ratios you can report with confidence.
@online{2026,
author = {},
title = {Logistic {Regression} {Assumptions} and {Diagnostics} in {R}},
date = {2026-06-23},
url = {https://www.datanovia.com/learn/biostatistics/regression/logistic-regression-assumptions-and-diagnostics-in-r},
langid = {en}
}