glmxdiag (version 1.0.0)

Qresiduals: Graphical normality testing for quantile residuals

Description

Derives quantile residuals of the input model and creates two plots: the first compares density of a standard normal distribution to the residuals' empirical density while the other one is a QQplot.

Usage

Qresiduals(model, plot.it = TRUE)

Arguments

model

a model supported by glmxdiag.

plot.it

logical, whether to plot the results or not.

Value

Called for side effects but invisibly returns the calculated quantile residuals.

Details

Quantile residuals are defined on a continuous cumulative distribution function; for binomial, beta-binomial, poisson and negative binomial regression models the Randomized quantile residuals are used.

Residuals have an important role inside the global diagnostic of a regression model. Any departure from the standard normal distribution can be considered as a warning that one or more aspects of the model are misspecified. Quantile residuals are particullary useful with models that do not have a continuous response variable, such as a binomial or poisson models; see examples.

References

Peter K. Dunn and Gordon K. Smyth (1996). Randomized Quantile Residuals. Journal of Computational and Graphical Statistics.

Examples

# NOT RUN {
# Simulate the data

set.seed(10)
n <- 100
x1 <- rt(n, df = 4)
x2 <- rnorm(n, sd = 2)
b <- c(1, .5, .5)
eta <- b[1] + b[2] * x1 + b[3] * x2
prob <- exp(eta)/(1 + exp(eta))
y <- rbinom(n, size = 1, prob = prob)

# The model is correctly specified
mod <- glm(y ~ x1 + x2, family = binomial)

res.p <- residuals(mod, type = 'pearson')
res.d <- residuals(mod, type = 'deviance')
qres <- Qresiduals(mod, plot.it = FALSE)

shapiro.test(res.p) # not normal
shapiro.test(res.d) # not normal
shapiro.test(qres) # normal

y.hat <- fitted(mod)

plot(y.hat, res.p) # uninformative 
plot(y.hat, res.d) # uninformative 
plot(y.hat, qres)

Qresiduals(mod)

# }