Calculating working residuals of a Gamma GLM model

Question

I am trying to calculate the working residuals of a Gamma GLM model. I'm doing this manually because I want to calculate the partial residuals step-by-step. My model and its coefficients and predictions are described below:

library(datasets)
data(mtcars)

model <- glm(mpg ~ cyl + disp + hp, data=mtcars, family=Gamma)
coefs <- coef(model)
pred <- coefs[1] + coefs[2]*mtcars$cyl + coefs[3]*mtcars$disp + coefs[4]*mtcars$hp

I tried to calculate the working residuals by applying the formula (value - fitted.value)/fitted.value , which works fine for a Poisson glm. However, it didn't work for Gamma since the values differ from those I generate using the function resid():

(mtcars$mpg - (-pred^(-1)))/-pred^(-1))
resid(model, type="working")

Does anybody know how to estimate such working residuals to then calculate the partial residuals?

Your prediction code won't predict the actual value of the response, but will be on the scale of the linear predictors. You would need to call `Gamma()$linkinv()` on your prediction to get predicted responses, which may help. — Marius, Nov 29 '18 at 22:46

Zheyuan Li · Accepted Answer · 2018-11-29T22:57:33.827

The working residuals are just model$residuals. See ?glm

## setup
library(datasets)
data(mtcars)
model <- glm(mpg ~ cyl + disp + hp, data = mtcars, family = Gamma)

## family info
oo <- Gamma(link = "inverse")

## compute linear predictor manually (assuming no model offset)
coefs <- coef(model)
eta <- coefs[1] + coefs[2] * mtcars$cyl + coefs[3] * mtcars$disp +
       coefs[4] * mtcars$hp

## compute working residuals
resi_working <- (mtcars$mpg - oo$linkinv(eta)) / oo$mu.eta(eta)

## validation
range(resi_working - model$residuals)
#[1] 0 0

Calculating working residuals of a Gamma GLM model

1 Answers1