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Link Functions

This section lists the link function types supported by the TraitSimulation module.

LinkFunction

LinkFunction is an abstract type. It’s the super type of each specific link function type listed below. All sub types of LinkFunction have constructors of the form [name of the link](), and contain link_inv::Function as their member variables. For example the constructor for identity link function type is IdentityLink(), and its link_inv member variable is the function f(x) = x.

LinkFunctionType

LinkFunctionType is a type alias for a single link function or a vector of link functions.

CauchitLink

Implements the Cauchit link $g(\mu) = \text{arctan}(\mu)/\pi+1/2$, which has inverse $g^{-1}(\eta) = \text{tan}[(\eta-1/2)\pi]$.

CloglogLink

Implements the complementary log log link, $g(\mu) = \log(-\log(1-\mu))$ which has invserse $g^{-1}(\eta) = 1 - \exp(-\exp(\eta))$.

IdentityLink

Implements the identity link $g(\mu) = \mu$, which has inverse $g^{-1}(\eta) = \eta$

InverseLink

Implements the inverse link $g(\mu) = 1/\mu$, which has inverse $g^{-1}(\eta) = 1/\eta$

LogitLink

Implements the logit link $g(\mu) = \log(\mu / (1-\mu))$, which has inverse $g^{-1}(\eta) = 1 / (1+\exp(-\eta))$.

ProbitLink

Implements the probit link $g(\mu) = \Phi^{-1}(\mu)$, which has inverse $g^{-1}(\eta) = \Phi(\eta)$

SqrtLink

Implements the square root link $g(\mu) = \sqrt{\mu}$, which has inverse $g^{-1}(\eta) = \eta^2$.

LogLink

Implements the log link $g(\mu) = \log(\mu)$, which has inverse $g^{-1}(\eta) = \exp(\eta)$.