cols (version 1.5)

Positive and unit sum constrained least squares: Positive and unit sum constrained least squares

Description

Positive and unit sum constrained least squares.

Usage

pcls(y, x)
mpcls(y, x)

Value

A list including:

be

A numerical matrix with the positively constrained beta coefficients.

mse

A numerical vector with the mean squared error.

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.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris .

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.

See Also

pls, cls, mvpls

Examples

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