Constrained least squares {cols} | R Documentation |
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, |
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 mtsagris@uoc.gr.
References
Hansen, B. E. (2022). Econometrics, Princeton University Press.
See Also
Examples
x <- as.matrix( iris[1:50, 1:4] )
y <- rnorm(50)
R <- c(1, 1, 1, 1)
cls(y, x, R, 1)