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?
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