plotPredIntNparDesign: Plots for a Sampling Design Based on a Nonparametric Prediction Interval

Description

Create plots involving sample size ($n$), number of future observations ($m$), minimum number of future observations the interval should contain ($k$), and confidence level ($1-\alpha$) for a nonparametric prediction interval.

Usage

plotPredIntNparDesign(x.var = "n", y.var = "conf.level", range.x.var = NULL,  n = max(25, lpl.rank + n.plus.one.minus.upl.rank + 1),  k = 1, m = ifelse(x.var == "k", ceiling(max.x), 1), conf.level = 0.95,  pi.type = "two.sided", lpl.rank = ifelse(pi.type == "upper", 0, 1),  n.plus.one.minus.upl.rank = ifelse(pi.type == "lower", 0, 1), n.max = 5000,  maxiter = 1000, plot.it = TRUE, add = FALSE, n.points = 100,  plot.col = "black", plot.lwd = 3 * par("cex"), plot.lty = 1,  digits = .Options$digits, cex.main = par("cex"), ..., main = NULL,  xlab = NULL, ylab = NULL, type = "l")

Arguments

x.var

character string indicating what variable to use for the x-axis. Possible values are "n" (sample size; the default), "conf.level" (the confidence level), "k" (minimum number of future observations the interval should contain), and "m" (number of future observations).

y.var

character string indicating what variable to use for the y-axis. Possible values are "conf.level" (confidence level; the default), and "n" (sample size).

range.x.var

numeric vector of length 2 indicating the range of the x-variable to use for the plot. The default value depends on the value of x.var. When x.var="n" the default value is c(2,50). When x.var="conf.level", the default value is c(0.5, 0.99). When x.var="k" or x.var="m", the default value is c(1, 20).

numeric scalar indicating the sample size. The default value is max(25, lpl.rank + n.plus.one.minus.upl.rank + 1). Missing (NA), undefined (NaN), and infinite (Inf, -Inf) values are not allowed. This argument is ignored if either x.var="n" or y.var="n".

positive integer specifying the minimum number of future observations out of m that should be contained in the prediction interval. The default value is k=1.

positive integer specifying the number of future observations. The default value is ifelse(x.var == "k", ceiling(max.x), 1). That is, if x.var="k" then the default value is the smallest integer greater than or equal to the maximum value that $k$ will take on in the plot; otherwise the default value is m=1.

conf.level

numeric scalar between 0 and 1 indicating the confidence level associated with the prediction interval. The default value is conf.level=0.95.

pi.type

character string indicating what kind of prediction interval to compute. The possible values are "two-sided" (the default), "lower", and "upper".

lpl.rank

non-negative integer indicating the rank of the order statistic to use for the lower bound of the prediction interval. If pi.type="two-sided" or pi.type="lower", the default value is lpl.rank=1 (implying the minimum value is used as the lower bound of the prediction interval). If pi.type="upper", this argument is set equal to 0.

n.plus.one.minus.upl.rank

non-negative integer related to the rank of the order statistic to use for the upper bound of the prediction interval. A value of n.plus.one.minus.upl.rank=1 (the default) means use the first largest value, and in general a value of n.plus.one.minus.upl.rank=$i$ means use the $i$'th largest value. If pi.type="lower", this argument is set equal to 0.

n.max

for the case when y.var="n", a positive integer greater than 2 indicating the maximum possible sample size. The default value is n.max=5000.

maxiter

positive integer indicating the maximum number of iterations to use in the uniroot search algorithm for sample size when y.var="n". The default value is maxiter=1000.

plot.it

a logical scalar indicating whether to create a plot or add to the existing plot (see add) on the current graphics device. If plot.it=FALSE, no plot is produced, but a list of (x,y) values is returned (see VALUE). The default value is plot.it=TRUE.

add

a logical scalar indicating whether to add the design plot to the existing plot (add=TRUE), or to create a plot from scratch (add=FALSE). The default value is add=FALSE. This argument is ignored if plot.it=FALSE.

n.points

a numeric scalar specifying how many (x,y) pairs to use to produce the plot. There are n.points x-values evenly spaced between range.x.var[1] and range.x.var[2]. The default value is n.points=100.

plot.col

a numeric scalar or character string determining the color of the plotted line or points. The default value is plot.col="black". See the entry for col in the help file for par for more information.

plot.lwd

a numeric scalar determining the width of the plotted line. The default value is 3*par("cex"). See the entry for lwd in the help file for par for more information.

plot.lty

a numeric scalar determining the line type of the plotted line. The default value is plot.lty=1. See the entry for lty in the help file for par for more information.

digits

a scalar indicating how many significant digits to print out on the plot. The default value is the current setting of options("digits").

cex.main, main, xlab, ylab, type, ...

additional graphical parameters (see par).

Value

plotPredIntNparDesign invisibly returns a list with components x.var and y.var, giving coordinates of the points that have been or would have been plotted.

Details

See the help file for predIntNpar, predIntNparConfLevel, and predIntNparN for information on how to compute a nonparametric prediction interval, how the confidence level is computed when other quantities are fixed, and how the sample size is computed when other quantities are fixed.

References

See the help file for predIntNpar.

Examples

Run this code

  # Look at the relationship between confidence level and sample size for a 
  # two-sided nonparametric prediction interval for the next m=1 future observation.

  dev.new()
  plotPredIntNparDesign()

  #==========

  # Plot confidence level vs. sample size for various values of number of 
  # future observations (m):

  dev.new()
  plotPredIntNparDesign(k = 1, m = 1, ylim = c(0, 1), main = "") 

  plotPredIntNparDesign(k = 2, m = 2, add = TRUE, plot.col = "red") 

  plotPredIntNparDesign(k = 3, m = 3, add = TRUE, plot.col = "blue") 

  legend("bottomright", c("m=1", "m=2", "m=3"), lty = 1, lwd = 3 * par("cex"), 
    col = c("black", "red", "blue"), bty = "n") 

  title(main = paste("Confidence Level vs. Sample Size for Nonparametric PI", 
    "with Various Values of m", sep="\n"))

  #==========

  # Example 18-3 of USEPA (2009, p.18-19) shows how to construct 
  # a one-sided upper nonparametric prediction interval for the next 
  # 4 future observations of trichloroethylene (TCE) at a downgradient well.  
  # The data for this example are stored in EPA.09.Ex.18.3.TCE.df.  
  # There are 6 monthly observations of TCE (ppb) at 3 background wells, 
  # and 4 monthly observations of TCE at a compliance well.
  #
  # Modify this example by creating a plot to look at confidence level versus 
  # sample size (i.e., number of observations at the background wells) for 
  # predicting the next m = 4 future observations when constructing a one-sided 
  # upper prediction interval based on the maximum value.

  dev.new()
  plotPredIntNparDesign(k = 4, m = 4, pi.type = "upper")

  #==========

  # Clean up
  #---------
  graphics.off()

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