| Type: | Package |
| Title: | Constrained Ordinary Least Squares |
| Version: | 1.5 |
| Date: | 2024-12-20 |
| Author: | Michail Tsagris [aut, cre] |
| Maintainer: | Michail Tsagris <mtsagris@uoc.gr> |
| Depends: | R (≥ 4.0) |
| Imports: | quadprog, Rfast, Rfast2 |
| Description: | Constrained ordinary least squares is performed. One constraint is that all beta coefficients (including the constant) cannot be negative. They can be either 0 or strictly positive. Another constraint is that the sum of the beta coefficients equals a constant. References: Hansen, B. E. (2022). Econometrics, Princeton University Press. <ISBN:9780691235899>. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| NeedsCompilation: | no |
| Packaged: | 2024-12-20 15:31:15 UTC; mtsag |
| Repository: | CRAN |
| Date/Publication: | 2024-12-20 16:10:02 UTC |
Constrained Ordinary Least Squares
Description
Constrained ordinary least squares is performed. One constraint is that all beta coefficients (including the constant) cannot be negative. They can be either 0 or strictly positive. Another constraint is that the sum of the beta coefficients equals a constant. References: Hansen, B.E. (2022). Econometrics, Princeton University Press.
Details
| Package: | cols |
| Type: | Package |
| Version: | 1.5 |
| Date: | 2024-12-20 |
Maintainers
Michail Tsagris <mtsagris@uoc.gr>.
Author(s)
Michail Tsagris mtsagris@uoc.gr
References
Hansen, B. E. (2022). Econometrics, Princeton University Press.
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)
Constrained least squares
Description
Lower and upper bound constrained least squares
Usage
int.cls(y, x, lb, ub)
int.mcls(y, x, lb, ub)
Arguments
y |
The response variable. For the int.cls() a numerical vector with observations, but for the int.mcls() a numerical matrix . |
x |
A matrix with independent variables, the design matrix. |
lb |
A vector or a single value with the lower bound(s) in the coefficients. |
ub |
A vector or a single value with the upper bound(s) in the coefficients. |
Details
This function performs least squares under the constraint that the beta coefficients lie within interval(s), i.e. min \sum_{i=1}^n(y_i-\bm{x}_i^\top\bm{\beta})^2 such that lb_j\leq \beta_j \leq ub_j.
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.
See Also
Examples
x <- as.matrix( iris[1:50, 1:4] )
y <- rnorm(50)
int.cls(y, x, -0.2, 0.2)
Positive and unit sum constrained least squares
Description
Positive and unit sum constrained least squares.
Usage
pcls(y, x)
mpcls(y, x)
Arguments
y |
The response variable. For the pcls() a numerical vector with observations, but for the mpcls() a numerical matrix. |
x |
A matrix with independent variables, the design matrix. |
Details
The constraint is that all beta coefficients are positive and sum to 1. that is
min \sum_{i=1}^n(y_i-\bm{x}_i\top\bm{\beta})^2 such that 0\leq \beta_j \leq 1 and \sum_{j=1}^d\beta_j=1. The pcls() function performs a single regression model, whereas the mpcls() 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 positively 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.
See Also
Examples
x <- as.matrix( iris[1:50, 1:4] )
y <- rnorm(50)
pcls(y, x)
Positively constrained least squares
Description
Positively constrained least squares.
Usage
pls(y, x)
mpls(y, x)
Arguments
y |
The response variable. For the pls() a numerical vector with observations, but for the mpls() a numerical matrix . |
x |
A matrix with independent variables, the design matrix. |
Details
The constraint is that all beta coefficients (including the constant) are non negative, i.e.
min \sum_{i=1}^n(y_i-\bm{x}_i^\top\bm{\beta})^2 such that \beta_j \geq 0. The pls() function performs a single regression model, whereas the mpls() 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 positively constrained beta coefficients. |
mse |
A numerical vector with the mean squared error(s). |
Author(s)
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
See Also
Examples
x <- as.matrix( iris[1:50, 1:4] )
y <- rnorm(50)
pls(y, x)
Positively constrained least squares with a multivariate response
Description
Positively constrained least squares with a multivariate response.
Usage
mvpls(y, x)
Arguments
y |
The response variables, a numerical matrix with observations. |
x |
A matrix with independent variables, the design matrix. |
Details
The constraint is that all beta coefficients (including the constant) are positive, i.e.
min \sum_{i=1}^n(\bm{y}_i-\bm{x}_i\bm{\beta})^\top(\bm{y}_i-\bm{x}_i\bm{\beta}) such that \beta_{jk}\geq 0.
Value
A list including:
be |
The positively constrained beta coefficients. |
mse |
The mean squared error. |
Author(s)
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
See Also
Examples
y <- as.matrix( iris[, 1:2] )
x <- as.matrix( iris[, 3:4] )
mvpls(y, x)