Timeline for What useful properties does the canonical link function have?

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Nov 18, 2021 at 12:23	comment	added	Scortchi♦		... the variance function is given by $\frac{\operatorname{d} \mu}{\operatorname{d} \theta} = \frac{\operatorname{d} \mu}{\operatorname{d} \nu}\cdot\frac{\operatorname{d} \nu}{\operatorname{d} \theta}$. The link is canonical when $\nu=\theta$: so in this case the latter derivative is 1 & the variance function given by $\frac{\operatorname{d} \mu}{\operatorname{d} \nu}$.)
Nov 18, 2021 at 11:34	comment	added	Scortchi♦		The first paragraph's not wrong but could be confusing - as if you were saying "If you want to get the right mean-variance relationship for your model, be sure to use the canonical link". (Letting $\theta$ be the canonical parameter in an exponential dispersion family, as explained in kjetil's answer, ...
Oct 14, 2021 at 15:42	history	edited	AdamO	CC BY-SA 4.0	added 62 characters in body
Dec 31, 2020 at 19:42	comment	added	IceCreamToucan		Should this say $\mu = \exp( \nu) /(1+\exp(\nu))$?
May 23, 2019 at 19:10	history	edited	AdamO	CC BY-SA 4.0	added 373 characters in body
May 23, 2019 at 19:05	history	answered	AdamO	CC BY-SA 4.0