S3 Methods for Plotting PIT Histograms

Generic plotting functions for probability integral transform (PIT) histograms of the class "pithist" computed by link{pithist}.

# S3 method for pithist
plot(
  x,
  single_graph = FALSE,
  style = NULL,
  freq = NULL,
  expected = TRUE,
  confint = NULL,
  confint_level = 0.95,
  confint_type = c("exact", "approximation"),
  simint = NULL,
  xlim = c(NA, NA),
  ylim = c(0, NA),
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  axes = TRUE,
  box = TRUE,
  col = "black",
  border = "black",
  lwd = NULL,
  lty = 1,
  alpha_min = 0.2,
  expected_col = NULL,
  expected_lty = NULL,
  expected_lwd = 1.75,
  confint_col = NULL,
  confint_lty = 2,
  confint_lwd = 1.75,
  confint_alpha = NULL,
  simint_col = "black",
  simint_lty = 1,
  simint_lwd = 1.75,
  ...
)

# S3 method for pithist
lines(
  x,
  freq = NULL,
  expected = FALSE,
  confint = FALSE,
  confint_level = 0.95,
  confint_type = c("exact", "approximation"),
  simint = FALSE,
  col = "black",
  lwd = 2,
  lty = 1,
  expected_col = "black",
  expected_lty = 2,
  expected_lwd = 1.75,
  confint_col = "black",
  confint_lty = 1,
  confint_lwd = 1.75,
  confint_alpha = 1,
  simint_col = "black",
  simint_lty = 1,
  simint_lwd = 1.75,
  ...
)

# S3 method for pithist
autoplot(
  object,
  single_graph = FALSE,
  style = NULL,
  freq = NULL,
  expected = NULL,
  confint = NULL,
  confint_level = 0.95,
  confint_type = c("exact", "approximation"),
  simint = NULL,
  xlim = c(NA, NA),
  ylim = c(0, NA),
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  legend = FALSE,
  theme = NULL,
  colour = NULL,
  fill = NULL,
  size = NULL,
  linetype = NULL,
  alpha = NULL,
  expected_colour = NULL,
  expected_size = 0.75,
  expected_linetype = NULL,
  expected_alpha = NA,
  confint_colour = NULL,
  confint_fill = NULL,
  confint_size = 0.75,
  confint_linetype = NULL,
  confint_alpha = NULL,
  simint_colour = "black",
  simint_size = 0.5,
  simint_linetype = 1,
  simint_alpha = NA,
  ...
)

Arguments

single_graph: logical. Should all computed extended reliability diagrams be plotted in a single graph? If yes, style must be set to "line".
style: NULL or character specifying the style of pithist. For style = "bar" a traditional PIT hisogram is drawn, for style = "line" solely the upper border line is plotted. single_graph = TRUE always results in a combined line-style PIT histogram.
freq: NULL or logical. TRUE will enforce the PIT to be represented by frequencies (counts) while FALSE will enforce densities.
expected: logical. Should the expected values be plotted as reference?
confint: NULL or logical. Should confident intervals be drawn? Either logical or as
confint_level: numeric in [0, 1]. The confidence level to be shown.
confint_type: character. Which type of confidence interval should be plotted: `"exact"` or `"approximation"`. According to Agresti and Coull (1998), for interval estimation of binomial proportions an approximation can be better than exact.
simint: NULL or logical. In case of discrete distributions, should the simulation (confidence) interval due to the randomization be visualized? character string defining one of `"polygon"`, `"line"` or `"none"`. If freq = NULL it is taken from the object.
xlim, ylim, xlab, ylab, main, axes, box: graphical parameters.
col, border, lwd, lty, alpha_min: graphical parameters for the main part of the base plot.
simint_col, simint_lty, simint_lwd, confint_col, confint_lty, confint_lwd, confint_alpha, expected_col, expected_lty, expected_lwd: Further graphical parameters for the `confint` and `simint` line/polygon in the base plot.
...: further graphical parameters passed to the plotting function.
object, x: an object of class pithist.
legend: logical. Should a legend be added in the ggplot2 style graphic?
theme: Which `ggplot2` theme should be used. If not set, theme_bw is employed.
colour, fill, size, linetype, alpha: graphical parameters for the histogram style part in the autoplot.
simint_colour, simint_size, simint_linetype, simint_alpha, confint_colour, confint_fill, confint_size, confint_linetype, expected_colour, expected_size, expected_linetype, expected_alpha: Further graphical parameters for the `confint` and `simint` line/polygon using autoplot.

Details

PIT histograms graphically evaluate the probability integral transform (PIT), i.e., the value that the predictive CDF attains at the observation, with a uniform distribution. For a well calibrated model fit, the observation will be drawn from the predictive distribution and the PIT will have a standard uniform distribution.

PIT histograms can be rendered as ggplot2 or base R graphics by using the generics autoplot or plot. For a single base R graphically panel, lines adds an additional PIT histogram.

References

Agresti A, Coull AB (1998). “Approximate is Better than ``Exact'' for Interval Estimation of Binomial Proportions.” The American Statistician, 52(2), 119--126. doi:10.1080/00031305.1998.10480550

Czado C, Gneiting T, Held L (2009). “Predictive Model Assessment for Count Data.” Biometrics, 65(4), 1254--1261. doi:10.2307/2981683

Dawid AP (1984). “Present Position and Potential Developments: Some Personal Views: Statistical Theory: The Prequential Approach”, Journal of the Royal Statistical Society: Series A (General), 147(2), 278--292. doi:10.2307/2981683

Diebold FX, Gunther TA, Tay AS (1998). “Evaluating Density Forecasts with Applications to Financial Risk Management”. International Economic Review, 39(4), 863--883. doi:10.2307/2527342

Gneiting T, Balabdaoui F, Raftery AE (2007). “Probabilistic Forecasts, Calibration and Sharpness”. Journal of the Royal Statistical Society: Series B (Methodological). 69(2), 243--268. doi:10.1111/j.1467-9868.2007.00587.x

Examples


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

## compute and plot pithist
pithist(m1_lm)


## customize colors and style
pithist(m1_lm, expected_col = "blue", lty = 2, pch = 20, style = "line")


## add separate model
if (require("crch", quietly = TRUE)) {
  m1_crch <- crch(dist ~ speed | speed, data = cars)
  #lines(pithist(m1_crch, plot = FALSE), col = 2, lty = 2, confint_col = 2) #FIXME
}

#-------------------------------------------------------------------------------
if (require("crch")) {

  ## precipitation observations and forecasts for Innsbruck
  data("RainIbk", package = "crch")
  RainIbk <- sqrt(RainIbk)
  RainIbk$ensmean <- apply(RainIbk[, grep("^rainfc", names(RainIbk))], 1, mean)
  RainIbk$enssd <- apply(RainIbk[, grep("^rainfc", names(RainIbk))], 1, sd)
  RainIbk <- subset(RainIbk, enssd > 0)

  ## linear model w/ constant variance estimation
  m2_lm <- lm(rain ~ ensmean, data = RainIbk)

  ## logistic censored model
  m2_crch <- crch(rain ~ ensmean | log(enssd), data = RainIbk, left = 0, dist = "logistic")

  ## compute pithists
  pit2_lm <- pithist(m2_lm, plot = FALSE)
  pit2_crch <- pithist(m2_crch, plot = FALSE)

  ## plot in single graph with style "line"
  plot(c(pit2_lm, pit2_crch),
    col = c(1, 2), confint_col = c(1, 2), expected_col = 3,
    style = "line", single_graph = TRUE
  )
}


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

## linear poisson model
m3_pois <- glm(satellites ~ width + color, data = CrabSatellites, family = poisson)

## compute and plot pithist as "ggplot2" graphic
pithist(m3_pois, plot = "ggplot2")

Arguments

Details

References

See also

Examples