qqrplot: Q-Q Plots for Quantile Residuals

In topmodels: Infrastructure for Forecasting and Assessment of Probabilistic Models

Q-Q Plots for Quantile Residuals

Description

Visualize goodness of fit of regression models by Quantile-Quantile (Q-Q) plots using quantile residuals. If plot = TRUE, the resulting object of class "qqrplot" is plotted by plot.qqrplot or autoplot.qqrplot before it is returned, depending on whether the package ggplot2 is loaded.

Usage

qqrplot(object, ...)

## Default S3 method:
qqrplot(
  object,
  newdata = NULL,
  plot = TRUE,
  class = NULL,
  detrend = FALSE,
  scale = c("normal", "uniform"),
  nsim = 1L,
  delta = NULL,
  simint = TRUE,
  simint_level = 0.95,
  simint_nrep = 250,
  confint = TRUE,
  ref = TRUE,
  xlab = "Theoretical quantiles",
  ylab = if (!detrend) "Quantile residuals" else "Deviation",
  main = NULL,
  ...
)

Arguments

object	an object from which probability integral transforms can be extracted using the generic function procast.
newdata	an optional data frame in which to look for variables with which to predict. If omitted, the original observations are used.
plot	logical or character. Should the plot or autoplot method be called to draw the computed Q-Q plot? Logical FALSE will suppress plotting, TRUE (default) will choose the type of plot conditional if the package ggplot2 is loaded. Alternatively "base" or "ggplot2" can be specified to explicitly choose the type of plot.
class	should the invisible return value be either a data.frame or a tibble. Either set class expicitly to "data.frame" vs. "tibble", or for NULL it's chosen automatically conditional if the package tibble is loaded.
detrend	logical, defaults to FALSE. Should the qqrplot be detrended, i.e, plotted as a wormplot?
scale	character. On which scale should the quantile residuals be shown: on the probability scale ("uniform") or on the normal scale ("normal").
nsim, delta	arguments passed to qresiduals.
simint	logical. In case of discrete distributions, should the simulation (confidence) interval due to the randomization be visualized?
simint_level	numeric. The confidence level required for calculating the simulation (confidence) interval due to the randomization.
simint_nrep	numeric (positive; default 250). The number of repetitions of simulated quantiles for calculating the simulation (confidence) interval due to the randomization.
confint	logical or character describing the style for plotting confidence intervals. TRUE (default) and "line" will add point-wise confidence intervals of the (randomized) quantile residuals as lines, "polygon" will draw a polygon instead, and FALSE suppresses the drawing.
ref	logical, defaults to TRUE. Should a reference line be plotted?
xlab, ylab, main, ...	graphical parameters passed to plot.qqrplot or autoplot.qqrplot.

Details

Q-Q residuals plots draw quantile residuals (by default on the standard normal scale) against theoretical quantiles from the same distribution. Alternatively, quantile residuals can also be compared on the uniform scale (scale = "uniform") using no transformation. For computation, qqrplot leverages the function qresiduals employing the procast generic.

Additional options are offered for models with discrete responses where randomization of quantiles is needed.

In addition to the plot and autoplot method for qqrplot objects, it is also possible to combine two (or more) Q-Q residuals plots by c/rbind, which creates a set of Q-Q residuals plots that can then be plotted in one go.

Value

An object of class "qqrplot" inheriting from "data.frame" or "tibble" conditional on the argument class with the following variables:

observed	deviations between theoretical and empirical quantiles,
expected	theoretical quantiles,
simint_observed_lwr	lower bound of the simulated confidence interval,
simint_observed_upr	upper bound of the simulated confidence interval,
simint_expected	TODO: (ML) Description missing.

In case of nsim > 1, a set of nsim pairs of observed and expected quantiles are returned (observed_1, expected_1, ... observed_nsim, observed_nsim) is returned.

The "qqrplot" also contains additional attributes xlab, ylab, main, simint_level, scale, and detrended used to create the plot.

References

Dunn KP, Smyth GK (1996). “Randomized Quantile Residuals.” Journal of Computational and Graphical Statistics, 5(3), 236–244. doi: 10.2307/1390802

See Also

plot.qqrplot, wormplot, qresiduals, qqnorm

Examples

## speed and stopping distances of cars
m1_lm <- lm(dist ~ speed, data = cars)

## compute and plot qqrplot
qqrplot(m1_lm)

#-------------------------------------------------------------------------------
## determinants for male satellites to nesting horseshoe crabs
data("CrabSatellites", package = "countreg")

## linear poisson model
m1_pois <- glm(satellites ~ width + color, data = CrabSatellites, family = poisson)
m2_pois <- glm(satellites ~ color, data = CrabSatellites, family = poisson)

## compute and plot qqrplot as base graphic
q1 <- qqrplot(m1_pois, plot = FALSE)
q2 <- qqrplot(m2_pois, plot = FALSE)

## plot combined qqrplot as "ggplot2" graphic
ggplot2::autoplot(c(q1, q2), single_graph = TRUE, col = c(1, 2), fill = c(1, 2))

## Use different `scale`s with confidence intervals
qqrplot(m1_pois, scale = "uniform")
qqrplot(m1_pois, scale = "normal")
qqrplot(m1_pois, detrend = TRUE, scale = "uniform", confint = "line")
qqrplot(m1_pois, detrend = TRUE, scale = "normal", confint = "line")

topmodels documentation built on Sept. 10, 2022, 3 p.m.