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Pretty simple question which should lead to a quick answer. Suppose we are building a parametric model - let's just say OLS linear or logistic regression.

After we do cross validation and examine the test MSEs to determine the model specification that produces the lowest test MSE, how do we determine the parameters of our final model?

  • Let's say we did k-fold CV and thus we would have k training models. Would the coefficients of the final model be the mean or median of the k coefficients?
  • Or, do we just take our entire sample data (combine our test and validation sets) and produce a model with the specifications from above and use those coefficients? Link seems to suggest this method: How to choose a predictive model after k-fold cross-validation?
  • Or another method?

Thanks!

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    $\begingroup$ What question do you have that isn't already answered in the link you provided? Here's another answer. There are plenty of questions about this and we like to avoid duplicates. $\endgroup$ – klumbard Jan 9 at 20:58
  • $\begingroup$ I was hoping to get a more consensus answer as this website has people to take the median: researchgate.net/post/K_fold_cross_validation_model_parameters "You can indeed take the median for the coefficients. However, it is not, in my modest opinion, the main prupose of K-fold cross-validation." $\endgroup$ – confused Jan 10 at 0:35
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Usually, you would use cross-validation on the training data to make decisions. Then, you refit on the full training data to get your final model. The test data remains untouched.

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