topmodels

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 `proresiduals`.
`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 proresiduals 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

Examples

library("topmodels")


## 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")