% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/simplexreg_links.R
\name{dispersion_links}
\alias{dispersion_links}
\alias{dispersion_link}
\alias{dispersion_link_inv}
\alias{dispersion_link_deriv1}
\alias{dispersion_link_inv_deriv1}
\title{Dispersion Link Functions and Their Derivatives}
\usage{
dispersion_link(sigma2, type = c("log", "sqrt", "identity"))

dispersion_link_inv(eta, type = c("log", "sqrt", "identity"))

dispersion_link_deriv1(sigma2, type = c("log", "sqrt", "identity"))

dispersion_link_inv_deriv1(eta, type = c("log", "sqrt", "identity"))
}
\arguments{
\item{sigma2}{Dispersion parameter (numeric vector, \eqn{\sigma^2 > 0}).}

\item{type}{Type of link: \code{"log"}, \code{"sqrt"} or \code{"identity"}.}

\item{eta}{Linear predictor of dispersion (numeric vector).}
}
\value{
Numeric vector with transformed values.
}
\description{
Provides the link function, its inverse, and derivative for the dispersion
submodel in the simplex regression.
Supported link types are: \code{"log"}, \code{"sqrt"} and \code{"identity"}.
}
\details{
Available link functions:
\itemize{
  \item Log (\code{"log"}): \eqn{h(\sigma^2) = \log(\sigma^2)} (ensures positivity);
  \item Sqrt (\code{"sqrt"}): \eqn{h(\sigma^2) = \sqrt{\sigma^2}};
  \item Identity (\code{"identity"}): \eqn{h(\sigma^2) = \sigma^2} (no transformation).
}
}
\examples{
dispersion_link(1.5, type = "log")
dispersion_link(c(0.5, 1, 2), type = "sqrt")
dispersion_link_inv(0, type = "log")
dispersion_link_deriv1(1, type = "log")
dispersion_link_inv_deriv1(0, type = "log")

}
\seealso{
\code{\link{simplexreg}}, \code{\link{fixed_mean_links}},
\code{\link{parametric_mean_links}}.
}
