ps_newtonRaphson {glmglrt}

Newton-Raphson algorithm when parameters may not be estimable outside of their parameter space

Description

This is used by confint_contrast.default to find the lower and upper boundaries of the confidence interval so that they have a P-value equal to 1-level. This makes it possible to compute contrast on log-binomial models when solutions are close to the boundaries of the parameter space and Newton-Raphson may compute some intermediate values outside of the valid parameter space, leading to P-values equal to NA.

Usage

ps_newtonRaphson(
  rootfun,
  x,
  xabstol = 1e-05,
  derivdelta = xabstol,
  yabstol = 1e-05,
  niter = 100,
  extraiter = 0
)

Arguments

rootfun

a function taking a single numeric value. The algorithm searches for a root (zero) of this function.

x

a single numeric value; starting value, not too far from the root of rootfun.

xabstol

a single numeric value; when two consecutive iterations of the algorithm lead to x solutions with a difference larger than xabstol, the algorithm has not yet converged and continues to run. Set to Inf, if you want to only want to rely on yabstol.

derivdelta

a single numeric value; the numeric delta used for numeric derivation of rootfun (assessed at x-derivdelta and x+derivdelta)

yabstol

a single numeric value; when the algorithm leads to a y=rootfun(x) larger (in absolute value) than yabstol, the algorithm has not yet converged and continues to run. Set to Inf, if you want to only want to rely on xabstol.

niter

a single integer value; the maximum number of iterations before considering that the algorithm failed to converge.

extraiter

a single integer value; the number of extra iterations performed once convergence has been found. This is useful to make sure that convergence is good on platforms having high floating point precision allowing to use, at the same time, a weak convergence tolerance to make sure it converges on platforms having low floating point precision.

Details

It assumes that rootfun is NA above the upper boundary of the parameter space and below the lower boundary of the parameter space. The parameter space must not have "holes" (i.e. valid, then invalid, then valid again). Invalid values are described by NA. The actual interval of valid values are automatically found by the algorithm, so you do not have to explicitly specify the minimum and maximum values of the parameter space.

Value

a list object with the following fields:

root

the x value so that rootfun(x) is as close as possible to 0

f.root

rootfun(root)

yabstol

the parameter of the same name

iter

the number of iterations of the Newton-Raphson algorithm performed before reaching convergence

estim.prec

the latest move (on the x variable) done before convergence

prevx

the previous x value, in the algorithm, just before x=root was reached

prevy

rootfun(prevx)

prevder

numeric derivative of rootfun at prevx