sloglink: Square root-Log Link Mixtures

In VGAM: Vector Generalized Linear and Additive Models

Square root–Log Link Mixtures

Description

Computes some square root–log mixture link transformations, including their inverse and the first few derivatives.

Usage

  sloglink(theta, bvalue = NULL, taumix.log = 1, tol = 1e-13,
    nmax = 99, inverse = FALSE, deriv = 0, short = TRUE,
    tag = FALSE, c10 = c(2, -2))
lcsloglink(theta, bvalue = NULL, pmix.log = 0.01, tol = 1e-13,
    nmax = 99, inverse = FALSE, deriv = 0, short = TRUE,
    tag = FALSE, c10 = c(2, -2))

Arguments

theta	Numeric or character. See below for further details.
bvalue	See Links.
taumix.log	Numeric, of length 1. Mixing parameter directed at loglink. Then 1 - exp(-taumix.log * theta) is used to weight sqrtlink. Thus a 0 value will result in loglink, and a very large numeric such as 1e4 should be roughly equivalent to sqrtlink over almost all of the parameter space.
pmix.log	Numeric, of length 1. Mixing probability assigned to loglink. Then 1 - pmix.log is used to weight sqrtlink. Thus a 0 value will result in sqrtlink and 1 is equivalent to loglink.
tol, nmax	Arguments fed into a function implementing a vectorized bisection method.
inverse, deriv, short, tag	Details at Links.
c10	See sqrtlink and loglink.

Details

For general information see alogitlink.

Value

The following holds for the linear combination (LC) variant. For deriv = 0, (1 - pmix.log) * sqrtlink(mu, c10 = c10) + pmix.log * loglink(mu) when inverse = FALSE, and if inverse = TRUE then a nonlinear equation is solved for mu, given eta passed in as theta. For deriv = 1, then the function returns d eta / d theta as a function of theta if inverse = FALSE, else if inverse = TRUE then it returns the reciprocal.

Warning

The default values for taumix.log and pmix.log may change in the future. The name and order of the arguments may change too.

Author(s)

Thomas W. Yee

See Also

alogitlink, sqrtlink, loglink, Links, poissonff, hdeff.

Examples

mu  <- seq(0.01, 3, length = 10)
sloglink(mu)
max(abs(sloglink(sloglink(mu), inv = TRUE) - mu))  # 0?

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.