nc_test {longevity}

Score test of Northrop and Coleman

Description

This function computes the score test with the piecewise generalized Pareto distribution under the null hypothesis that the generalized Pareto with a single shape parameter is an adequate simplification. The score test statistic is calculated using the observed information matrix; both hessian and score vector are obtained through numerical differentiation.

Usage

nc_test(
  time,
  time2 = NULL,
  event = NULL,
  thresh = 0,
  ltrunc = NULL,
  rtrunc = NULL,
  type = c("right", "left", "interval", "interval2"),
  weights = rep(1, length(time)),
  test = c("score", "lrt"),
  arguments = NULL,
  ...
)

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

a 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".

weights

weights for observations

test

string, either "score" for the score test or "lrt" for the likelihood ratio test.

arguments

a named list specifying default arguments of the function that are common to all elife calls

...

additional parameters, currently ignored

Details

The score test is much faster and perhaps less fragile than the likelihood ratio test: fitting the piece-wise generalized Pareto model is difficult due to the large number of parameters and multimodal likelihood surface.

The reference distribution is chi-square

Value

a data frame with the following variables:

• thresh: threshold for the generalized Pareto distribution

• nexc: number of exceedances

• score: score statistic

• df: degrees of freedom

• pval: the p-value obtained from the asymptotic chi-square approximation.

Examples

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")
test <- nc_test(
  time = x,
  ltrunc = low,
  rtrunc = upp,
  thresh = quantile(x, seq(0, 0.5, by = 0.1)))
print(test)
plot(test)