tstab: Threshold stability plots

Description

The generalized Pareto and exponential distribution are threshold stable. This property, which is used for extrapolation purposes, can also be used to diagnose goodness-of-fit: we expect the parameters \(\xi\) and \(\tilde{\sigma} = \sigma + \xi u\) to be constant over a range of thresholds. The threshold stability plot consists in plotting maximum likelihood estimates with pointwise confidence interval. This function handles interval truncation and right-censoring.

Usage

tstab(
  time,
  time2 = NULL,
  event = NULL,
  thresh = 0,
  ltrunc = NULL,
  rtrunc = NULL,
  type = c("right", "left", "interval", "interval2"),
  family = c("gp", "exp"),
  method = c("wald", "profile"),
  level = 0.95,
  plot = TRUE,
  plot.type = c("base", "ggplot"),
  which.plot = c("scale", "shape"),
  weights = NULL,
  arguments = NULL,
  ...
)

Value

an invisible list with pointwise estimates and confidence intervals for the scale and shape parameters

Arguments

time: excess time of the event of follow-up time, depending on the value of event
time2: ending excess time of the interval for interval censored data only.
event: status indicator, normally 0=alive, 1=dead. Other choices are TRUE/FALSE (TRUE for death). For interval censored data, the status indicator is 0=right censored, 1=event at time, 2=left censored, 3=interval censored. Although unusual, the event indicator can be omitted, in which case all subjects are assumed to have experienced an event.
thresh: vector of thresholds
ltrunc: lower truncation limit, default to NULL
rtrunc: upper truncation limit, default to NULL
type: character string specifying the type of censoring. Possible values are "right", "left", "interval", "interval2".
family: string; distribution, either generalized Pareto (gp) or exponential (exp)
method: string; the type of pointwise confidence interval, either Wald (wald) or profile likelihood (profile)
level: probability level for the pointwise confidence intervals
plot: logical; should a plot be returned alongside with the estimates? Default to TRUE
plot.type: string; either base for base R plots or ggplot for ggplot2 plots
which.plot: string; which parameters to plot;
weights: weights for observations
arguments: a named list specifying default arguments of the function that are common to all elife calls
...: additional arguments for optimization, currently ignored.

Details

The shape estimates are constrained

Examples

Run this code

set.seed(1234)
n <- 100L
x <- samp_elife(n = n,
                scale = 2,
                shape = -0.2,
                lower = low <- runif(n),
                upper = upp <- runif(n, min = 3, max = 20),
                type2 = "ltrt",
                family = "gp")
tstab_plot <- tstab(time = x,
                    ltrunc = low,
                   rtrunc = upp,
                   thresh = quantile(x, seq(0, 0.5, length.out = 4)))
plot(tstab_plot, plot.type = "ggplot")