62 lines
1.7 KiB
R
62 lines
1.7 KiB
R
#' Predicts SDR dimension using \code{\link[mda]{mars}} via a Cross-Validation.
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#'
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#' @param object instance of class \code{cve} (result of \code{cve},
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#' \code{cve.call}).
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#' @param ... ignored.
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#'
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#' @return list with
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#' \itemize{
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#' \item MSE: Mean Square Error,
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#' \item k: predicted dimensions.
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#' }
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#'
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#' @examples
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#' # create B for simulation
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#' B <- rep(1, 5) / sqrt(5)
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#'
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#' set.seed(21)
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#' # creat predictor data x ~ N(0, I_p)
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#' x <- matrix(rnorm(500), 100)
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#'
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#' # simulate response variable
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#' # y = f(B'x) + err
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#' # with f(x1) = x1 and err ~ N(0, 0.25^2)
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#' y <- x %*% B + 0.25 * rnorm(100)
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#'
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#' # Calculate cve for unknown k between min.dim and max.dim.
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#' cve.obj.simple <- cve(y ~ x)
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#'
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#' predict_dim(cve.obj.simple)
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#'
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#' @export
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predict_dim <- function(object, ...) {
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# Get centered training data and dimensions
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X <- scale(object$X, center = TRUE, scale = FALSE)
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n <- nrow(object$X) # umber of training data samples
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Sigma <- (1 / n) * crossprod(X, X)
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eig <- eigen(Sigma)
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Sigma_root <- eig$vectors %*% tcrossprod(diag(sqrt(eig$values)), eig$vectors)
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X <- X %*% solve(Sigma_root)
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pred <- matrix(0, n, length(object$res))
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colnames(pred) <- names(object$res)
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for (dr.k in object$res) {
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# get "name" of current dimension
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k <- as.character(dr.k$k)
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# Project dataset with current SDR basis
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X.proj <- X %*% dr.k$B
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for (i in 1:n) {
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model <- mda::mars(X.proj[-i, ], object$Y[-i])
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pred[i, k] <- predict(model, X.proj[i, , drop = F])
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}
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}
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MSE <- colMeans((pred - object$Y)^2)
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return(list(
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MSE = MSE,
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k = as.integer(names(which.min(MSE)))
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))
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}
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