LinkFunction
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LinkFunction
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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:
-
Automatic automatically determined "name" named link function g invertible 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 real‐valued 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 real‐valued and invertible on the response domain for the model.
Examples
Basic Examples (1)Summary of the most common use cases
In[1]:=1

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https://wolfram.com/xid/0e7qdyfm-dqgov5
Fit a Poisson model with canonical Log link:
In[2]:=2

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https://wolfram.com/xid/0e7qdyfm-4nk7e
Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0e7qdyfm-c07mea
Out[3]=3

Use a pure function for a shifted Sqrt link:
In[4]:=4

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https://wolfram.com/xid/0e7qdyfm-cdftkh
Out[4]=4

Wolfram Research (2008), LinkFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/LinkFunction.html.
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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.
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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.
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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
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Wolfram Language. (2008). LinkFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LinkFunction.html
BibTeX
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@misc{reference.wolfram_2025_linkfunction, author="Wolfram Research", title="{LinkFunction}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/LinkFunction.html}", note=[Accessed: 17-May-2025
]}
BibLaTeX
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@online{reference.wolfram_2025_linkfunction, organization={Wolfram Research}, title={LinkFunction}, year={2008}, url={https://reference.wolfram.com/language/ref/LinkFunction.html}, note=[Accessed: 17-May-2025
]}