#' Linear regression
#'
#' Runs an OLS regression not unlike \code{\link{lm}}
#'
#' @param y response vector (1 x n)
#' @param X covariate matrix (p x n) with no intercept
#'
#' @return A list with 4 elements: coefficients, vcov, sigma, df
#'
#' @examples
#' data(mtcars)
#' X <- as.matrix(mtcars[, c("cyl", "disp", "hp")])
#' y <- mtcars[, "mpg"]
#' linmodEst(y, X)
#'
#' @export
#'
linmodEst <- function(x, y) {
## compute QR-decomposition of x
qx <- qr(x)
## compute (x’x)^(-1) x’y
coef <- solve.qr(qx, y)
## degrees of freedom and standard deviation of residuals
df <- nrow(x) - ncol(x)
sigma2 <- sum((y - x %*% coef) ^ 2) / df
## compute sigma^2 * (x’x)^-1
vcov <- sigma2 * chol2inv(qx$qr)
colnames(vcov) <- rownames(vcov) <- colnames(x)
list(
coefficients = coef,
vcov = vcov,
sigma = sqrt(sigma2),
df = df
)
}
linmod <- function(x, ...)
UseMethod("linmod")
linmod.default <- function(x, y, ...) {
x <- as.matrix(x)
y <- as.numeric(y)
est <- linmodEst(x, y)
est$fitted.values <- as.vector(x %*% est$coefficients)
est$residuals <- y - est$fitted.values
est$call <- match.call()
class(est) <- "linmod"
est
}
print.linmod <- function(x, ...) {
cat("Call:\n")
print(x$call)
cat("\nCoefficients:\n")
print(x$coefficients)
}
summary.linmod <- function(object, ...) {
se <- sqrt(diag(object$vcov))
tval <- coef(object) / se
TAB <- cbind(
Estimate = coef(object),
StdErr = se,
t.value = tval,
p.value = 2 * pt(-abs(tval), df = object$df)
)
res <- list(call = object$call,
coefficients = TAB)
class(res) <- "summary.linmod"
res
}
print.summary.linmod <- function(x, ...) {
cat("Call:\n")
print(x$call)
cat("\n")
printCoefmat(x$coefficients, P.value = TRUE, has.Pvalue = TRUE)
}
linmod.formula <- function(formula, data = list(), ...) {
mf <- model.frame(formula = formula, data = data)
x <- model.matrix(attr(mf, "terms"), data = mf)
y <- model.response(mf)
est <- linmod.default(x, y, ...)
est$call <- match.call()
est$formula <- formula
est
}
predict.linmod <- function(object, newdata = NULL, ...) {
if (is.null(newdata))
y <- fitted(object)
else{
if (!is.null(object$formula)) {
## model has been fitted using formula interface
x <- model.matrix(object$formula, newdata)
}
else{
x <- newdata
}
y <- as.vector(x %*% coef(object))
}
y
}
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