caret train() predicts very different then predict.glm()

Question

I am trying to estimate a logistic regression, using the 10-fold cross-validation.

#import libraries
library(car); library(caret); library(e1071); library(verif         


        

Answer 1

You are trying to get an idea of the in-sample fit using a confusion matrix. Your first approach using the glm() function is fine.

The problem with the second approach using train() lies in the returned object. You are trying to extract the in-sample fitted values from it by fit$pred$pred. However, fit$pred does not contain the fitted values that are aligned to chile.v or chile$vote. It contains the observations and fitted values of the different (10) folds:

> head(fit$pred)
  pred obs rowIndex parameter Resample
1    N   N        2      none   Fold01
2    Y   Y       20      none   Fold01
3    Y   Y       28      none   Fold01
4    N   N       38      none   Fold01
5    N   N       55      none   Fold01
6    N   N       66      none   Fold01
> tail(fit$pred)
     pred obs rowIndex parameter Resample
1698    Y   Y     1592      none   Fold10
1699    Y   N     1594      none   Fold10
1700    N   N     1621      none   Fold10
1701    N   N     1656      none   Fold10
1702    N   N     1671      none   Fold10
1703    Y   Y     1689      none   Fold10 

So, due to the randomness of the folds, and because you are predicting 0 or 1, you get an accuracy of roughly 50%.

The in-sample fitted values you are looking for are in fit$finalModel$fitted.values. Using those:

fitpred <- fit$finalModel$fitted.values
fitpredt <- function(t) ifelse(fitpred > t , 1,0)
> confusionMatrix(fitpredt(0.3),chile.v)
Confusion Matrix and Statistics

          Reference
Prediction   0   1
         0 773  44
         1  94 792

               Accuracy : 0.919          
                 95% CI : (0.905, 0.9315)
    No Information Rate : 0.5091         
    P-Value [Acc > NIR] : < 2.2e-16      

                  Kappa : 0.8381         
 Mcnemar's Test P-Value : 3.031e-05      

            Sensitivity : 0.8916         
            Specificity : 0.9474         
         Pos Pred Value : 0.9461         
         Neg Pred Value : 0.8939         
             Prevalence : 0.5091         
         Detection Rate : 0.4539         
   Detection Prevalence : 0.4797         
      Balanced Accuracy : 0.9195         

       'Positive' Class : 0               

Now the accuracy is around the expected value. Setting the threshold to 0.5 yields about the same accuracy as the estimate from the 10-fold cross validation:

> confusionMatrix(fitpredt(0.5),chile.v)
Confusion Matrix and Statistics

          Reference
Prediction   0   1
         0 809  64
         1  58 772

               Accuracy : 0.9284          
                 95% CI : (0.9151, 0.9402)
[rest of the output omitted]            

> fit
Generalized Linear Model 

1703 samples
   7 predictors
   2 classes: 'N', 'Y' 

No pre-processing
Resampling: Cross-Validated (10 fold) 

Summary of sample sizes: 1533, 1532, 1532, 1533, 1532, 1533, ... 

Resampling results

  Accuracy  Kappa  Accuracy SD  Kappa SD
  0.927     0.854  0.0134       0.0267  

Additionally, regarding your expectation "that the cross validated results should not perform much worse than the first model," please check summary(res.chileIII) and summary(fit). The fitted models and coefficients are exactly the same so they will give the same results.

P.S. I know my answer to this question is late--i.e. this is quite an old question. Is it OK to answer these questions anyway? I am new here and did not find anything about "late answers" in the help.