Skip to contents

Create a link_fns S3 object

Source: R/s3-link_fns-class.R
as.link_fns.Rd

The link function class allows forwards and backwards transformation. Link functions can be defined by name or using a statistical distribution in which case the forward link is a logit of the cumulative probability and the reverse is the quantile of the expit.

Usage

# S3 method for class 'character'
as.link_fns(x, ...)

# S3 method for class 'dist_fns'
as.link_fns(x, ...)

# S3 method for class 'family'
as.link_fns(x, ...)

# S3 method for class 'numeric'
as.link_fns(x, ..., na.rm = TRUE)

as.link_fns(x, ...)

Arguments

x

a range of values that for the support

...

ignored

na.rm

remove NAs when estimating mean and sd for data driven link functions

Value

a link_fns S3 object

Details

A link_fns S3 object encapsulates a monotonic transformation function \(h\), its inverse \(h^{-1}\), and their derivatives \(h'\) and \((h^{-1})'\). It also defines the support (domain) \([a, b]\) of the original space and the range \([h(a), h(b)]\) of the transformed space.

The function dispatches based on the input x:

  • character: Selects standard links (e.g., "log", "logit", "probit", "identity"). For example, "log" defines \(h(x) = \log(x)\) with support \((0, \infty)\).

  • dist_fns: Defines the link as the logit of the CDF and the quantile of the expit: \(h(x) = \text{logit}(F(x))\), \(h^{-1}(z) = F^{-1}(\text{expit}(z))\), where \(F\) and \(F^{-1}\) are the CDF and quantile functions from the dist_fns object. The support is determined by the quantile function's range (e.g., \([Q(0), Q(1)]\)).

  • family (from stats): Uses the link function and its inverse from the GLM family object.

  • numeric: If length 2, interprets as a support range \([a, b]\) and creates a logit-like transformation mapping this range to \((-\infty, \infty)\): \(h(x) = \text{logit}(\frac{x-a}{b-a})\). If all values are finite and length > 2, creates a standardization link: \(h(x) = \frac{x-\mu}{\sigma}\), where \(\mu\) and \(\sigma\) are the mean and standard deviation of the input vector.

Methods (by class)

  • as.link_fns(character): Link function from name

  • as.link_fns(dist_fns): Link function from name

  • as.link_fns(family): Link function from name

  • as.link_fns(numeric): Link function from support vector

Unit tests



links = c("ident", "log", "logit", "probit", "cloglog", "neginv", "inv2")
test = seq(0.1,0.9,0.1) # within support of all links
for (l in links) {
  lfn = as.link_fns(l)
  t = lfn$trans(test)
  i = lfn$inv(t)
  testthat::expect_equal(i,test)
}