Square root–Log Link Mixtures

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.

Author

Thomas W. Yee

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.

Examples

mu  <- seq(0.01, 3, length = 10)
sloglink(mu)
#>  [1] -4.577258276 -1.002076937 -0.376030510  0.006651554  0.308344050
#>  [6]  0.571901705  0.812442769  1.036354822  1.246856665  1.445904973
max(abs(sloglink(sloglink(mu), inv = TRUE) - mu))  # 0?
#> [1] 8.348877e-14