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#' @title GMDH MIA auxiliar functions
#'
#' @description Performs auxiliar tasks to predict.mia
#'
#' @keywords internal
#'
fun.N_3 <- function(x, y) {
nombres <- colnames(x)
resultado <- vector(mode = "list", length = 2)
names(resultado) <- c("coef", "CV")
tol <- sqrt(.Machine$double.eps)
x <- cbind(1, x[, 1], x[, 2],
I(x[, 1]^2), I(x[, 2]^2),
x[, 1] * x[, 2])
Xsvd <- svd(x)
D <- diag(1 / Xsvd$d)
D[D <= tol] <- 0
XtX_inv <- Xsvd$v %*% D %*% D %*% t(Xsvd$v)
C <- XtX_inv %*% crossprod(x, y)
rownames(C) <- c("Ind", nombres, paste0(nombres, "^2", sep = ""), "interac")
RSS <- sum((x %*% C - y)^2)
n <- nrow(x)
sigma2 <- RSS / n
rank <- ncol(x)
k <- rank + 1
logL <- -(n / 2) * (log(RSS / n)) - (n / 2) * (log(2 * pi)) - (n / 2)
covmat <- sigma2 * XtX_inv
lambdas <- eigen(covmat, only.values = TRUE)$values
lambda_m <- mean(lambdas)
complexity <- (1 / 2) / (lambda_m * lambda_m) * sum((lambdas - lambda_m)^2)
CV <- -2 * logL + complexity
CV <- round(CV, digits = 6)
resultado$coef <- C
resultado$CV <- CV
class(resultado) <- "neurona"
return(resultado)
}
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