$k$-fold cross-validation on a logistic regression: So which is the fitted model? [duplicate]

Question

I am planning to use a $10$-fold strategy in order to validate the results of a logistic regression analysis.

I am a bit confused about the procedure I must follow.

More precisely: Let us suppose that my cross-validation returns acceptable values (for the average AUC, average misclassification rates, etc.) and reveals that everything is OK. Which is the predictive model or formula I should return in such a case?

First of all, I have already read (here, for instance: With k-fold cross-validation, do you average all $k$ models to build the final model?) and understood that a $k$-fold cross-validation procedure aims at assessing the performance of a predictive analysis on a given data set (in terms of its ability to accurately predict on new data). I mean, it is not a technique for building predictive models, but a way to measure whether a given fitted model can be overfitting or not (roughly speaking).

OK, so, as far as I understand, I must do this:

1. Randomly divide the sample into $k$ equally sized subsamples (using stratification if necessary).

2. For $i=1$ to $k$:

   • Perform a logistic regression analysis using all the cases not in subsample $i$ as the training set.
   • Use subsample $i$ as the validation set. Calculate performance parameters.
3. Calculate average performance parameters.

Let us imagine that step 3 allows us to conclude that logistic regression performs well on our data.

Now, I have obtained $k$ predictive models. Is this right?

So, which one of them is the final model I should use? Or, should I build (and return to the final user) a definitive logistic regression predictive model using all cases in the sample?

Sorry if this is too simple or too wrong. I would really appreciate if you can answer my questions.

EDIT:

Actually, my question is about cross-validation, but I wanted to specify that I am dealing with logistic regression, just in case it helps.

Answer 1

Cross Validation is typically used to search hyper parameter space to find an optimal value.

In your case you are using cross validation to get a better estimate of the error. If the variance of error between different folds is low then you are doing ok on the technique. The test error is average cross validation error.

I will typically give the final model by training it again on the entire data set.