added delta method for glm links #37
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@spinkney thanks for your contribution! I wanted to just add tests and expand documentation, but the original math gave incorrect results. In the simplest identity case, the derivative is just a bunch a bunch of ones regardless of |
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Nice, I didn't use the identity. Is it still wrong for other links? |
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@spinkney I think there's another multiplication by the original |
| By default (`invlink=identity`), effects are computed on the scale of the | ||
| transformed response. For models with an explicit transformation, that | ||
| transformation is the scale of the effects. For models with a link function, | ||
| the scale of the effects is the _link_ scale, i.e. after application of the | ||
| link function. For example, effects for logitistic regression models are on | ||
| the logit and not the probability scale. |
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why is this the default when the link can (in principle) be obtained from the model itself? to avoid a dependency on GLM?
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Exactly, to avoid the dependency on GLM. As part of the associated docs issue (#38), I think it would be good to have a GLM example. If we decide to take GLM as a dependency, then we should add more specialized methods that take advantage of GLM.mueta rather than using AD for the derivative.
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Apologies for missing the re-review request for this but thanks @kleinschmidt for reviewing, @palday for getting it over the finish line, and of course @spinkney for the contribution. 🙂 |
I added the delta method for SE's after transformation. This pr adds an input into the
effectsfunction for the inverse link. The derivative of the effect is calculated usingForwardDiffand the delta method is used to construct the SEs.I typically do not code in Julia so this may not be very Julian. It only took a few lines of code that I needed for a project I was working on. As such, you may use this pr as a reference to make the code more suitable for your needs and delete this pr.