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LinkFunction

LinkFunction
is an option for GeneralizedLinearModelFit which specifies the link function for the generalized linear model.
  • The link function is an invertible function g in the generalized linear model .
Automaticautomatically determined
"name"named link function
ginvertible function
  • The canonical link functions are as follows:
"LogitLink"used for "Binomial"
"ReciprocalLink"used for "Gamma"
"IdentityLink"yused for "Gaussian"
"InverseSquareLink"used for "InverseGaussian"
"LogLink"log(y)used for "Poisson"
  • For "QuasiLikelihood" models, "IdentityLink" is used by default.
  • Other common link functions for binomial data include:
"ProbitLink"
"CauchitLink"
"LogLogLink"-log(-log(y))
"LogComplementLink"log(1-y)
"ComplementaryLogLogLink"log(-log(1-y))
"OddsPowerLink"
  • Other common link functions for count data include:
"NegativeBinomialLink"
  • Other common link functions for positive real-valued data include:
"PowerLink"
  • For "OddsPowerLink", "NegativeBinomialLink" and "PowerLink", the additional parameter Alpha can be given by LinkFunction->{linkname, "LinkParameter"->Alpha}. The parameter Alpha 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 real-valued and invertible on the response domain for the model.
Fit a Poisson model with canonical Log link:
Use a named link:
Use a pure function for a shifted Sqrt link:
In[1]:=
Click for copyable input
Fit a Poisson model with canonical Log link:
In[2]:=
Click for copyable input
Out[2]=
Use a named link:
In[3]:=
Click for copyable input
Out[3]=
Use a pure function for a shifted Sqrt link:
In[4]:=
Click for copyable input
Out[4]=
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