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


  • 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 models, is used by default.
  • Other common link functions for binomial data include:
  • "ProbitLink"
  • Other common link functions for count data include:
  • "NegativeBinomialLink"
  • Other common link functions for positive real-valued data include:
  • "PowerLink"
  • For , , and , the additional parameter can be given by LinkFunction->{linkname, "LinkParameter"->}. The parameter can be any real value for and and any positive value for .
  • With setting LinkFunction->g, g can be any pure function that is real-valued and invertible on the response domain for the model.

ExamplesExamplesopen allclose all

Basic Examples (1)Basic Examples (1)

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Fit a Poisson model with canonical Log link:

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Use a named link:

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Use a pure function for a shifted Sqrt link:

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