R中不同相关矩阵的交叉验证PCA

Question

我想根据 MSE、AIC 和 Adjusted R squared 评估基于 R 中不同相关系数（例如 Pearson、Kendall）的各种主成分模型。我创建了以下函数，但是我找不到方法“ force”函数根据给定的相关矩阵执行主成分回归。因此，我最终得到了完全相同的结果。有人可以帮助我吗？

library(caret)
    
set.seed(123)
df <- data.frame(Y = rnorm(100), X1 = rnorm(100), X2 = rnorm(100), X3 = rnorm(100), X4 = rnorm(100), X5 = rnorm(100))

X <- df[,-1]
Y <- df[,1]

# compute Pearson's and Spearman's correlation matrices
cor1 <- cor(X, method = "pearson")
cor2 <- cor(X, method = "kendall")

# define function to compute PCA with cross-validation and return MSE, AIC, and adjusted R-squared
pca_cv_mse_aic_r2 <- function(X, Y, cor_mat, ncomp, nfolds) {
  
  # create empty vectors to store results
  mse <- rep(0, ncomp)
  aic <- rep(0, ncomp)
  adj_r2 <- rep(0, ncomp)
  
  # loop over the number of components
  for (i in 1:ncomp) {
    
    # perform PCA with cross-validation
    pca <- caret::train(X, Y, method = "pcr", preProc = c("center", "scale"),
                        tuneLength = nfolds, trControl = trainControl(method = "cv", number = nfolds),
                        tuneGrid = data.frame(ncomp = i))
    
    # compute MSE, AIC, and adjusted R-squared
    pred <- predict(pca, newdata = X)
    mse[i] <- mean((pred - Y)^2)
    aic[i] <- AIC(lm(Y ~ pred + 1))
    adj_r2[i] <- summary(lm(Y ~ pred))$adj.r.squared
  }
  
  # return a list of results
  return(list(mse = mse, aic = aic, adj_r2 = adj_r2))
}

# compute the MSE, AIC, and adjusted R-squared of PCA models with different correlation matrices and numbers of components
results1 <- pca_cv_mse_aic_r2(X, Y, cor1, 5, 10)
results2 <- pca_cv_mse_aic_r2(X, Y, cor2, 5, 10)