LinkFunction

LinkFunction

is an option for GeneralizedLinearModelFit that specifies the link function for the generalized linear model.

Details

  • The link function is an invertible function in the generalized linear model .
  • Possible settings for LinkFunction include:
  • Automaticautomatically determined
    "name"named link function
    ginvertible function
  • The default value Automatic uses the canonical link for the ExponentialFamily associated with the model.
  • The canonical link functions are as follows:
  • "LogitLink"used for "Binomial"
    "ReciprocalLink"used for "Gamma"
    "IdentityLink"used for "Gaussian"
    "InverseSquareLink"used for "InverseGaussian"
    "LogLink"used for "Poisson"
  • For "QuasiLikelihood" models, "IdentityLink" is used by default.
  • Other common link functions for binomial data include:
  • "ProbitLink"
    "CauchitLink"
    "LogLogLink"
    "LogComplementLink"
    "ComplementaryLogLogLink"
    "OddsPowerLink"
  • Other common link functions for count data include:
  • "NegativeBinomialLink"
  • Other common link functions for positive realvalued data include:
  • "PowerLink"
  • For "OddsPowerLink", "NegativeBinomialLink", and "PowerLink", the additional parameter α can be given by LinkFunction->{linkname,"LinkParameter"->α}. The parameter α can be any real value for "OddsPowerLink" and "PowerLink" and any positive value for "NegativeBinomialLink".
  • With setting LinkFunction->g, g can be any pure function that is realvalued and invertible on the response domain for the model.

Examples

Basic Examples  (1)

Fit a Poisson model with canonical Log link:

Use a named link:

Use a pure function for a shifted Sqrt link:

Wolfram Research (2008), LinkFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/LinkFunction.html.

Text

Wolfram Research (2008), LinkFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/LinkFunction.html.

CMS

Wolfram Language. 2008. "LinkFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LinkFunction.html.

APA

Wolfram Language. (2008). LinkFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LinkFunction.html

BibTeX

@misc{reference.wolfram_2022_linkfunction, author="Wolfram Research", title="{LinkFunction}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/LinkFunction.html}", note=[Accessed: 05-July-2022 ]}

BibLaTeX

@online{reference.wolfram_2022_linkfunction, organization={Wolfram Research}, title={LinkFunction}, year={2008}, url={https://reference.wolfram.com/language/ref/LinkFunction.html}, note=[Accessed: 05-July-2022 ]}