After using cross-validation with PCA regression, what weights are then used for the external test set?

Question

Based on this answer, and following the Applied Predictive Modeling text, I am running the following 10-fold cross-validated PCR analysis:

library(AppliedPredictiveModeling) # data
library(caret) # train, cv
library(pls) # pcr function

data(solubility)

# cross-validation setup

set.seed(1)
cv_index <- createFolds(solTrainY, returnTrain = TRUE)
cv_control <- trainControl(method = "cv", index = cv_index)

# run model

set.seed(1)
PCR_Train <- train(solTrainXtrans, y = solTrainY,
                   method = "pcr",
                   tuneGrid = expand.grid(ncomp = 89),
                   trControl = cv_control
)

I have created 10 folds of my data, calculated 89 unsupervised components (independently for each fold), and then performed a regression.

I know I can apply this to my test set to get predicted values using the following code:

predict(PCR_Train, solTestXtrans)

which I would then compare to solTestY.

This is a bit "black-box-y" for me. Specifically, I am wondering what PCA coefficients should be used for my test set. Since I ran PCA for each of the 10 folds, the weights of the 10 sets should be different. I know it is not based on the test data, otherwise something like predict(PCR_Train, solTestXtrans[1, ]) would not return the same value?

Do we just randomly take one of the folds, or does it combine the results somehow?

Answer 1

You are doing the 10-fold CV to find the optimal hyper parameters of your model, so you just fit it again on all your data with the optimal parameters you just found. Your predict function is probably doing it automatically. When in doubt read the documentation e.g: ??caret