qresiduals {statmod}

Randomized Quantile Residuals

Description

Compute randomized quantile residuals for generalized linear models.

Usage

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)

Arguments

glm.obj

Object of class glm. The generalized linear model family is assumed to be binomial for qres.binom, poisson for qres.pois, negative binomial for qres.nbinom, Gamma for qres.gamma, inverse Gaussian for qres.invgauss or tweedie for qres.tweedie.

dispersion

a positive real number. Specifies the value of the dispersion parameter for a Gamma or inverse Gaussian generalized linear model if known. If NULL, the dispersion will be estimated by its Pearson estimator.

Details

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.

Value

Numeric vector of standard normal quantile residuals.

Author(s)

Gordon Smyth

References

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

See Also

residuals.glm

Examples

#  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))
}