Out-of-fold vs training error in caret - r

Question

Using cross validation in model tuning, I get different error rates from caret::train's results object and calculating the error myself on its pred object. I'd like to understand why they differ, and ideally how to use out-of-fold error rates for model selection, plotting model performance, etc.
The pred object contains out-of-fold predictions. The docs are pretty clear that trainControl(..., savePredictions = "final") saves out-of-fold predictions for the best hyperparameter values: "an indicator of how much of the hold-out predictions for each resample should be saved... "final" saves the predictions for the optimal tuning parameters." (Keeping "all" predictions and then filtering to the best tuning values doesn't resolve the issue.)
The train docs say that the results object is "a data frame the training error rate..." I'm not sure what that means, but the values for the best row are consistently different from the metrics calculated on pred. Why do they differ and how can I make them line up?
d <- data.frame(y = rnorm(50))
d$x1 <- rnorm(50, d$y)
d$x2 <- rnorm(50, d$y)
train_control <- caret::trainControl(method = "cv",
number = 4,
search = "random",
savePredictions = "final")
m <- caret::train(x = d[, -1],
y = d$y,
method = "ranger",
trControl = train_control,
tuneLength = 3)
#> Loading required package: lattice
#> Loading required package: ggplot2
m
#> Random Forest
#>
#> 50 samples
#> 2 predictor
#>
#> No pre-processing
#> Resampling: Cross-Validated (4 fold)
#> Summary of sample sizes: 38, 36, 38, 38
#> Resampling results across tuning parameters:
#>
#> min.node.size mtry splitrule RMSE Rsquared MAE
#> 1 2 maxstat 0.5981673 0.6724245 0.4993722
#> 3 1 extratrees 0.5861116 0.7010012 0.4938035
#> 4 2 maxstat 0.6017491 0.6661093 0.4999057
#>
#> RMSE was used to select the optimal model using the smallest value.
#> The final values used for the model were mtry = 1, splitrule =
#> extratrees and min.node.size = 3.
MLmetrics::RMSE(m$pred$pred, m$pred$obs)
#> [1] 0.609202
MLmetrics::R2_Score(m$pred$pred, m$pred$obs)
#> [1] 0.642394
Created on 2018-04-09 by the reprex package (v0.2.0).

Answer 1

The RMSE for cross validation is not calculated the way you show, but rather for each fold and then averaged. Full example:
set.seed(1)
d <- data.frame(y = rnorm(50))
d$x1 <- rnorm(50, d$y)
d$x2 <- rnorm(50, d$y)
train_control <- caret::trainControl(method = "cv",
number = 4,
search = "random",
savePredictions = "final")
set.seed(1)
m <- caret::train(x = d[, -1],
y = d$y,
method = "ranger",
trControl = train_control,
tuneLength = 3)
#output
Random Forest
50 samples
2 predictor
No pre-processing
Resampling: Cross-Validated (4 fold)
Summary of sample sizes: 37, 38, 37, 38
Resampling results across tuning parameters:
min.node.size mtry splitrule RMSE Rsquared MAE
8 1 extratrees 0.6106390 0.4360609 0.4926629
12 2 extratrees 0.6156636 0.4294237 0.4954481
19 2 variance 0.6472539 0.3889372 0.5217369
RMSE was used to select the optimal model using the smallest value.
The final values used for the model were mtry = 1, splitrule = extratrees and min.node.size = 8.
RMSE for best model is 0.6106390
Now calculate the RMSE for each fold and average:
m$pred %>%
group_by(Resample) %>%
mutate(rmse = caret::RMSE(pred, obs)) %>%
summarise(mean = mean(rmse)) %>%
pull(mean) %>%
mean
#output
0.610639
m$pred %>%
group_by(Resample) %>%
mutate(rmse = MLmetrics::RMSE(pred, obs)) %>%
summarise(mean = mean(rmse)) %>%
pull(mean) %>%
mean
#output
0.610639

Answer 2

I get different results. This is apparently a random process.
MLmetrics::RMSE(m$pred$pred, m$pred$obs)
[1] 0.5824464
> MLmetrics::R2_Score(m$pred$pred, m$pred$obs)
[1] 0.5271595
If you want a random (more accurately a pseudo-random process to be reproducible, then use set.seed immediately prior to the call.