pcls: Positive and unit sum constrained least squares

In cols: Constrained Ordinary Least Squares

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 [e-mail].

See Also

pls, cls, mvpls

Examples

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

cols documentation built on March 24, 2026, 5:07 p.m.