cls: Constrained least squares

In cols: Constrained Ordinary Least Squares

Constrained least squares

Description

Constrained least squares.

Usage

cls(y, x, R, ca)
mvcls(y, x, R, ca)

Arguments

y	The response variable. For the cls() a numerical vector with observations, but for the mvcls() a numerical matrix .
x	A matrix with independent variables, the design matrix.
R	The R vector that contains the values that will multiply the beta coefficients. See details and examples.
ca	The value of the constraint, R^T \beta = c. See details and examples.

Details

This is described in Chapter 8.2 of Hansen (2019). The idea is to inimise the sum of squares of the residuals under the constraint R^\top \bm{\beta} = c. As mentioned above, be careful with the input you give in the x matrix and the R vector. The cls() function performs a single regression model, whereas the mcls() function performs a regression for each column of y. Each regression is independent of the others.

Value

A list including:

be	A numerical matrix with the constrained beta coefficients.
mse	A numerical vector with the mean squared error.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

Hansen, B. E. (2022). Econometrics, Princeton University Press.

See Also

pls, int.cls

Examples

x <- as.matrix( iris[1:50, 1:4] )
y <- rnorm(50)
R <- c(1, 1, 1, 1)
cls(y, x, R, 1)

cols documentation built on April 3, 2025, 10:33 p.m.