rchemo (version 0.1-3)

orthog: Orthogonalization of a matrix to another matrix

Description

Function orthog orthogonalizes a matrix \(Y\) to a matrix \(X\). The row observations can be weighted.

The function uses function lm.

Usage

orthog(X, Y, weights = NULL)

Value

Y

The \(Y\) matrix orthogonalized to \(X\).

b

The regression coefficients used for orthogonalization.

Arguments

X

A \(n x p\) matrix or data frame.

Y

A \(n x q\) matrix or data frame to orthogonalize to \(X\).

weights

A vector of length \(n\) defining a priori weights to apply to the observations. Internally, weights are "normalized" to sum to 1. Default to NULL (weights are set to \(1 / n\)).

Examples

n <- 8 ; p <- 3
set.seed(1)
X <- matrix(rnorm(n * p, mean = 10), ncol = p, byrow = TRUE)
Y <- matrix(rnorm(n * 2, mean = 10), ncol = 2, byrow = TRUE)
colnames(Y) <- c("y1", "y2")
set.seed(NULL)
X
Y

res <- orthog(X, Y)
res$Y
crossprod(res$Y, X)
res$b

# Same as:
fm <- lm(Y ~ X)
Y - fm$fitted.values
fm$coef

#### WITH WEIGHTS

w <- 1:n
fm <- lm(Y ~ X, weights = w)
Y - fm$fitted.values
fm$coef

res <- orthog(X, Y, weights = w)
res$Y
t(res$Y) 
res$b