Hi Florian,

Ok, I’ll do that!

Thanks for the reply and for the post, again!

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]]>Hi Bernado,

as shown in the picture, a Ridge regression is mathematically the same as a Bayesian regression with a normal prior on the regression slopes. The width of the prior is then the shrinkage penalty, the smaller the prior width, the larger the penalty.

The only difference from the Bayesian perspective is how you set the width of the prior (= shrinkage penalty). I would say that there are 2-3 solutions in practice:

1) set a light shrinkage penalty a priori (this is know as weakly informative priors). If you do this, most people don’t even use the word shrinkage, but effectively, if you do, you have to be less worried about overfitting / parameter selection in a GLMM setting

2) set a stronger shrinkage prior, and get the value from something else (e.g. cross-validation). This is rarely done in my experience

3) set adaptive shrinkage priors, where you make the shrinkage another parameter that is estimated, and set a common prior for the parameters. See for example https://mc-stan.org/rstanarm/reference/priors.html#hierarchical-shrinkage-family

I don’t really have a good review at hand. I would suggest to google for Bayesian shrinkage prior STAN or so to get examples with code.

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]]>Thanks for the post!

I am quite new to shrinkage modeling – most of the studies I’ve done so far on ecology are either based on model selection of have some Bayesian elements – even though very basic, just to allow a little more flexibility over the frequentis approach.

I’ve been collaborating with statisticians who recommend and use methods with shrinkage (Lasso, Ridge), but they are still kind of “mysterious” in practice. Do you have any begginner’s reading suggestion on that?

Once this basics are understood, having a Bayesian version of that seems quite interesting!

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]]>Hi Johannes, thanks for the hints. I added the library(DHARMa), good point. The missing quote seems to be a problem of how wordpress renders the code, when you press “view raw” it’s there.

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]]>in the 2nd line of the code (where you read the data) there is a missing quote and you may want to add `library(DHARMa)` in the beginning.

Thanks for the post

Johannes

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]]>Interesting point. I have made a few simulations about this, and I don’t really see anything unusual happening when varying the intercept, other than the expected result that overall power increases for larger intercepts.

I did not understand what you mean with 250 observations cancel each other out?

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]]>Hi, thanks for the kind word. About the paper … yes, it’s on my list of urgent things to do … unfortunately it’s not the only item there. But I hope to be able to put out something more formal soon.

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