Package 'cols'

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:	1.3
Date:	2024-11-19

Maintainers

Michail Tsagris <[email protected]>.

Author(s)

Michail Tsagris [email protected]

References

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

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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 $R^T \beta = c$. 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 [email protected].

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)

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Constrained least squares

Description

Lower and upper bound constrained least squares

Usage

int.cls(y, x, lb, ub)

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.
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).

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 [email protected].

See Also

pls

Examples

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

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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. 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 [email protected].

See Also

pls, cls, mvpls

Examples

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

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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. 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 [email protected].

See Also

cls, pcls, mvpls

Examples

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

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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.

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 [email protected].

See Also

cls

Examples

y <- as.matrix( iris[, 1:2] )
x <- as.matrix( iris[, 3:4] )
mvpls(y, x)

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