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I have done a ridge regression using the 'glmnet' function in R. Then, after finding the optimal lambda parameter, I checked what are the predictors' beta coefficients by extracting glmnet.fit$beta when the lambda is the optimal lambda. All the predictors were scales (mean=0, sd=1) prior to the analysis).

My question is: what do the numbers say?

I assume that the coefficients are not standardized betas. So, are they similar to non-standardized regression coefficients in other regressions? Do they have a certain scale? and if so, what is this scale based on? For example, what is the meaning of a coefficient with a value of.05?

Would appreciate your help and clarification very much.

Thank you

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You interpret the coefficients in the same way as if you do it without regularization. For example, if you run logistic regression and your coefficient for variable x1 is 0.5, then that means the odds ratio is 1.64 and that variable is positively associated with your outcome.

glmnet by default standardizes the variables and that is mentioned in the documentation when (standardize = TRUE). The coefficients you get after that from your model are actually rescaled back to the original scale. A good piece of read about this can be seen here

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