Algorithm for forward stepwise regression












1












$begingroup$


I am trying to implement the algorithm for forward stepwise selection following the book "Introduction to Statistical learning":



The steps listed in the book are:



Algorithm 6.2 Forward stepwise selection

1. Let M0 denote the null model, which contains no predictors.

2. For k = 0, . . . , p − 1:

(a) Consider all p − k models that augment the predictors in Mk

with one additional predictor.

(b) Choose the best among these p − k models, and call it Mk+1.

Here best is defined as having smallest RSS or highest R2.

3. Select a single best model from among M0, . . . ,Mp using crossvalidated

prediction error, Cp (AIC), BIC, or adjusted R2.


My question is I am not quite clear on whether or not cross validation should be used in step2. If so, why? or else why not?






regression cross-validation







share|cite|improve this question









$endgroup$

















    1












    $begingroup$


    I am trying to implement the algorithm for forward stepwise selection following the book "Introduction to Statistical learning":



    The steps listed in the book are:



    Algorithm 6.2 Forward stepwise selection
    
1. Let M0 denote the null model, which contains no predictors.
    
2. For k = 0, . . . , p − 1:
    
(a) Consider all p − k models that augment the predictors in Mk
    
with one additional predictor.
    
(b) Choose the best among these p − k models, and call it Mk+1.
    
Here best is defined as having smallest RSS or highest R2.
    
3. Select a single best model from among M0, . . . ,Mp using crossvalidated
    
prediction error, Cp (AIC), BIC, or adjusted R2.


    My question is I am not quite clear on whether or not cross validation should be used in step2. If so, why? or else why not?






    regression cross-validation







    share|cite|improve this question









    $endgroup$















      1












      1








      1





      $begingroup$


      I am trying to implement the algorithm for forward stepwise selection following the book "Introduction to Statistical learning":



      The steps listed in the book are:



      Algorithm 6.2 Forward stepwise selection
      
1. Let M0 denote the null model, which contains no predictors.
      
2. For k = 0, . . . , p − 1:
      
(a) Consider all p − k models that augment the predictors in Mk
      
with one additional predictor.
      
(b) Choose the best among these p − k models, and call it Mk+1.
      
Here best is defined as having smallest RSS or highest R2.
      
3. Select a single best model from among M0, . . . ,Mp using crossvalidated
      
prediction error, Cp (AIC), BIC, or adjusted R2.


      My question is I am not quite clear on whether or not cross validation should be used in step2. If so, why? or else why not?






      regression cross-validation







      share|cite|improve this question









      $endgroup$




      I am trying to implement the algorithm for forward stepwise selection following the book "Introduction to Statistical learning":



      The steps listed in the book are:



      Algorithm 6.2 Forward stepwise selection
      
1. Let M0 denote the null model, which contains no predictors.
      
2. For k = 0, . . . , p − 1:
      
(a) Consider all p − k models that augment the predictors in Mk
      
with one additional predictor.
      
(b) Choose the best among these p − k models, and call it Mk+1.
      
Here best is defined as having smallest RSS or highest R2.
      
3. Select a single best model from among M0, . . . ,Mp using crossvalidated
      
prediction error, Cp (AIC), BIC, or adjusted R2.


      My question is I am not quite clear on whether or not cross validation should be used in step2. If so, why? or else why not?






      regression cross-validation




      regression cross-validation






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 3 hours ago









      southwindsouthwind

      63




      63






















          1 Answer
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          $begingroup$


          best is defined as having smallest RSS or highest R2.




          Cross-validation is not mentioned here, so per the text, you would simply choose the model based on in-sample RSS or $R^2$.



          Overfitting is (hopefully) controlled by the cross-validation in step 3.



          Of course, nothing keeps you from modifying the algorithm given in the book. Just note that you will then do a lot of cross-validation, since you would cross-validate $p-k$ models in each of $p$ iterations of step 2.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            If I perform cross-validation in step 2, do I still need step 3 since I can just select the model with the smallest error from step 2?
            $endgroup$
            – southwind
            2 hours ago











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          $begingroup$


          best is defined as having smallest RSS or highest R2.




          Cross-validation is not mentioned here, so per the text, you would simply choose the model based on in-sample RSS or $R^2$.



          Overfitting is (hopefully) controlled by the cross-validation in step 3.



          Of course, nothing keeps you from modifying the algorithm given in the book. Just note that you will then do a lot of cross-validation, since you would cross-validate $p-k$ models in each of $p$ iterations of step 2.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            If I perform cross-validation in step 2, do I still need step 3 since I can just select the model with the smallest error from step 2?
            $endgroup$
            – southwind
            2 hours ago
















          2












          $begingroup$


          best is defined as having smallest RSS or highest R2.




          Cross-validation is not mentioned here, so per the text, you would simply choose the model based on in-sample RSS or $R^2$.



          Overfitting is (hopefully) controlled by the cross-validation in step 3.



          Of course, nothing keeps you from modifying the algorithm given in the book. Just note that you will then do a lot of cross-validation, since you would cross-validate $p-k$ models in each of $p$ iterations of step 2.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            If I perform cross-validation in step 2, do I still need step 3 since I can just select the model with the smallest error from step 2?
            $endgroup$
            – southwind
            2 hours ago














          2












          2








          2





          $begingroup$


          best is defined as having smallest RSS or highest R2.




          Cross-validation is not mentioned here, so per the text, you would simply choose the model based on in-sample RSS or $R^2$.



          Overfitting is (hopefully) controlled by the cross-validation in step 3.



          Of course, nothing keeps you from modifying the algorithm given in the book. Just note that you will then do a lot of cross-validation, since you would cross-validate $p-k$ models in each of $p$ iterations of step 2.






          share|cite|improve this answer









          $endgroup$




          best is defined as having smallest RSS or highest R2.




          Cross-validation is not mentioned here, so per the text, you would simply choose the model based on in-sample RSS or $R^2$.



          Overfitting is (hopefully) controlled by the cross-validation in step 3.



          Of course, nothing keeps you from modifying the algorithm given in the book. Just note that you will then do a lot of cross-validation, since you would cross-validate $p-k$ models in each of $p$ iterations of step 2.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 2 hours ago









          Stephan KolassaStephan Kolassa

          44.1k692161




          44.1k692161












          • $begingroup$
            If I perform cross-validation in step 2, do I still need step 3 since I can just select the model with the smallest error from step 2?
            $endgroup$
            – southwind
            2 hours ago


















          • $begingroup$
            If I perform cross-validation in step 2, do I still need step 3 since I can just select the model with the smallest error from step 2?
            $endgroup$
            – southwind
            2 hours ago
















          $begingroup$
          If I perform cross-validation in step 2, do I still need step 3 since I can just select the model with the smallest error from step 2?
          $endgroup$
          – southwind
          2 hours ago




          $begingroup$
          If I perform cross-validation in step 2, do I still need step 3 since I can just select the model with the smallest error from step 2?
          $endgroup$
          – southwind
          2 hours ago


















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