Randomized Quantile Residuals

qres Randomized quantile residuals

DESCRIPTION

Computes randomized quantile residuals for binomial, Poisson, negative binomial, gamma and inverse Gaussian generalized linear models.

USAGE

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)

REQUIRED ARGUMENT

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.

OPTIONAL ARGUMENT

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 (gamma) or by restricted maximum likelihood (inverse Gaussian).

VALUE

Numeric vector of standard normal quantile residuals.

BACKGROUND

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.

REFERENCE

Dunn, K. P., and Smyth, G. K. (1996). Randomized quantile residuals. J. Comput. Graph. Statist., 5, 1-10.

EXAMPLES

This is a binary regression (binomial) example. Compare the data analysis of the kyphosis data set in the S-Plus manual entry on logistic regression.

> kyph.glm <- glm(Kyphosis ~ Age+Number+Start, family=binomial, data=kyphosis)
> r <- qres.binom(kyph.glm)
> plot(fitted(kyph.glm),r)

The plot of residuals against fitted values shows reasonable random scatter.

> plot(kyphosis$Age,r)
> plot(kyphosis$Number,r)
> plot(kyphosis$Start,r)

# Gamma example with chisquare responses on 1 df glm.obj <- glm(y~x,family=Gamma(link="log")) qr <- qres.gamma(glm.obj,dispersion=2) qqnorm(qr) abline(0,1)

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