R/MSE_loc.R

In CorReg: Linear Regression Based on Linear Structure Between Variables

#' Simple MSE function
#' 
#' @description
#' This function computes the MSE (Mean Squared Error) of prediction associated to a vector of coefficients \code{A} used to predict a response variable \code{Y} by linear regression on \code{X}, with an intercept or not.
#' 
#' @param Y the response variable (vector)
#' @param X the dataset (matrix of covariates)
#' @param A the vector of coefficients
#' @param intercept (boolean) to add a column of 1 to \code{X} if \code{A} contains an intercept and \code{X} doesn't.
#' @return the Mean Squared Error observed on \code{X} when using \code{A} coefficients to predict \code{Y}.
#'
#' @examples
#' # dataset generation
#' base = mixture_generator(n = 15, p = 5, valid = 100, scale = TRUE)
#' X_appr = base$X_appr # learning sample
#' Y_appr = base$Y_appr # response variable
#' X_test = base$X_test # validation sample
#' Y_test = base$Y_test # response variable (validation sample)
#' A = lm(Y_appr ~ X_appr)$coefficients
#' MSE_loc(Y = Y_appr, X = X_appr, A = A) # MSE on the learning dataset
#' MSE_loc(Y = Y_test, X = X_test, A = A) # MSE on the validation sample
#' 
#' @export
MSE_loc <- function(Y = Y, X = X, A = A, intercept = TRUE) {
  if (intercept) {
    X = as.matrix(cbind(1, X))
  }
  return(mean((Y - X %*% A)^2))
}