Randomized Quantile Residuals
Compute randomized quantile residuals for generalized linear models.
qresiduals(glm.obj,dispersion=NULL) qresid(glm.obj,dispersion=NULL) qres.binom(glm.obj) qres.pois(glm.obj) qres.nbinom(glm.obj) qres.gamma(glm.obj,dispersion=NULL) qres.invgauss(glm.obj,dispersion=NULL) qres.tweedie(glm.obj,dispersion=NULL) qres.default(glm.obj,dispersion=NULL)
glm.obj |
Object of class |
dispersion |
a positive real number. Specifies the value of the
dispersion parameter for a Gamma or inverse Gaussian generalized linear
model if known. If |
Quantile residuals are based on the idea of inverting the estimated distribution function for each observation to obtain exactly standard normal residuals. In the case of discrete distributions, such as the binomial and Poisson, some randomization is introduced to produce continuous normal residuals. Quantile residuals are the residuals of choice for generalized linear models in large dispersion situations when the deviance and Pearson residuals can be grossly non-normal. Quantile residuals are the only useful residuals for binomial or Poisson data when the response takes on only a small number of distinct values.
Numeric vector of standard normal quantile residuals.
Gordon Smyth
Dunn, K. P., and Smyth, G. K. (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics 5, 1-10. http://www.statsci.org/smyth/pubs/residual.html
Dunn, PK, and Smyth, GK (2018). Generalized linear models with examples in R. Springer, New York, NY. doi: 10.1007/978-1-4419-0118-7
# Poisson example: quantile residuals show no granularity
y <- rpois(20,lambda=4)
x <- 1:20
fit <- glm(y~x, family=poisson)
qr <- qresiduals(fit)
qqnorm(qr)
abline(0,1)
# Gamma example:
# Quantile residuals are nearly normal while usual resids are not
y <- rchisq(20, df=1)
fit <- glm(y~1, family=Gamma)
qr <- qresiduals(fit, dispersion=2)
qqnorm(qr)
abline(0,1)
# Negative binomial example:
if(require("MASS")) {
fit <- glm(Days~Age,family=negative.binomial(2),data=quine)
summary(qresiduals(fit))
fit <- glm.nb(Days~Age,link=log,data = quine)
summary(qresiduals(fit))
}Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.