Binned-residual plot for a generalised linear model — binned_residual

For a fitted glm (especially binary or count models), a plot of raw residuals against fitted values is hard to read because the residuals take only a few values. Following Gelman and Hill (2007), this plot instead splits the data into equal-count bins of fitted values and plots, for each bin, the mean residual against the mean fitted value. Under a well-specified model the binned residuals scatter around zero, and about 95% of them should fall within the grey \(\pm 2\) standard-error band, computed per bin as \(2\,\hat{\sigma}_{\text{bin}}/\sqrt{n_{\text{bin}}}\) from the residuals in that bin. Systematic departures (a trend, or many points outside the band) indicate a misspecified mean structure.

Usage

binned_residual_plot(
  model,
  bins = NULL,
  type = c("response", "pearson"),
  point_colour = depictr_brand(),
  band_colour = depictr_accent(),
  title = NULL
)

Arguments

model: A fitted glm object (an lm is also accepted and treated as a Gaussian GLM).
bins: Number of bins. The default follows Gelman and Hill's rule of thumb of roughly \(\sqrt{n}\) bins (bounded to a sensible range).
type: Residual type used for the bin means: "response" (observed minus fitted on the response scale, the Gelman-Hill default) or "pearson".
point_colour, band_colour: Colours for the bin points and the \(\pm 2\) SE band. Default to the depictr brand and accent colours.
title: Plot title.

Value

A ggplot2::ggplot object. The per-bin summary (mean fitted, mean residual, SE bound and an outside flag) is attached as attr(plot, "bins").

References

Gelman A, Hill J (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, Cambridge, UK. ISBN 978-0-521-68689-1. doi:10.1017/CBO9780511790942 .

Examples

gfit <- glm(adverse_event ~ biomarker + age + arm,
            data = clinical_trial, family = binomial)
binned_residual_plot(gfit)