Positive and unit sum constrained least squares {cols} | R Documentation |
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)