binned_residuals() for checking linearity of the logit

[rbcavanaugh]

I'm using performance::binned_residuals(model, term = "x") to check the linearity of the logit assumption for a continuous predictor.

In a simulation where the assumption is met, the default residuals = "deviance" produces a clear trend in average residuals across the predictor's range. This looks like a potential problem plot is meant to detect, but it's a false positive here since the model is correctly specified. Switching to residuals = "response" removes the drift. Do you all have a recommendation between the deviance vs. response residual type for checking linearity here? I think Gelman used response as far as I could tell. thanks!

library(performance)

set.seed(1)
n <- 5000
x <- runif(n, 0, 10)

logit_true <- -2 + 0.4 * x 
y <- rbinom(n, 1, plogis(logit_true))

df <- data.frame(x = x, y = y)
model <- glm(y ~ x, data = df, family = binomial)

# Default: deviance residuals
plot(binned_residuals(model, term = "x")) 

# Response residuals
plot(binned_residuals(model, term = "x", residuals = "response"))

^{Created on 2026-08-25 with reprex v2.1.1}

[strengejacke]

In the Gelman/Hill book, and in the documentation, it says:

The residuals values from logistic regression (observed values minus expected values).

However, the example from arm::binnedplot() uses resid(), which defaults to deviance residuals.

But observed minus expected would indeed be "response". We should probably change the default, especially since you have a nice simulation example that shows this.

library(performance)

set.seed(1)
n <- 5000
x <- runif(n, 0, 10)

logit_true <- -2 + 0.4 * x 
y <- rbinom(n, 1, plogis(logit_true))

df <- data.frame(x = x, y = y)
model <- glm(y ~ x, data = df, family = binomial)
arm::binnedplot(predict(model), resid(model), sqrt(n))

^{Created on 2026-08-26 with reprex v2.1.1}

[rbcavanaugh]

Got it - that's helpful thanks. I was going a little crazy trying to understand why the deviance residuals showed this sort of bias when the response residuals and simulated residuals from DHARMa did not. I'll use the observed - expected.

[strengejacke]

The default has changed now:
#943

Will be on cran soon, I guess