Package 'scpropreg'

Simplicially Constrained Regression Models for Proportions

Description

Simplicially Constrained Regression Models for Proportions. The constraint is always that the betas are non-negative and sum to 1.

Details

Package:	scpropreg
Type:	Package
Version:	1.2
Date:	2026-04-15

Maintainers

Michail Tsagris <[email protected]>.

Author(s)

Michail Tsagris [email protected]

References

Iverson Sara J., Field Chris, Bowen W. Don and Blanchard Wade (2004) Quantitative Fatty Acid Signature Analysis: A New Method of Estimating Predator Diets. Ecological Monographs, 74(2): 211-235.

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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, where each columns sums to 1.
Y	The response variable, a numerical matrix, where each column sums to 1.
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:

coefficients	A numerical matrix with the positively constrained beta coefficients.
value	A numerical vector with the mean squared error.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

See Also

kld, mkld

Examples

x <- matrix(runif(30 * 8), ncol = 30)
x <- t( x / rowSums(x) )
y <- runif(30)
y <- y / sum(y)
pcls(y, x)

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QFASA diet estimates for many predators using various distances

Description

QFASA diet estimates for many predators using various distances.

Usage

mkld(Y, x, tol = 1e-8, maxit = 50000, alpha = 0.1)
mait(Y, x, tol = 1e-8, maxit = 50000, alpha = 0.01)
mlsq(Y, x, tol = 1e-8, maxit = 50000, alpha = 0.01)
mlr(Y, x, tol = 1e-8, maxit = 100)

Arguments

Y	The response variable, a matrix with values between 0 and 1 that sum to 1. For some functions, zero values are allowed. Every column corresponds to the food composition of a predator. The column-wise sums are equal to 1.
x	A matrix with independent variables, values between 0 and 1. Each column contains a prey's diet. The column-wise sums are equal to 1.
tol	The tolerance value to terminate the algorithm.
maxit	The maximum iterations allowed.
alpha	The step-size parameter of the fixed points iteration algorithm. This is similar to the $\eta$ parameter in the gradient descent algorithm.

Details

The function estimates the betas that minimize a distance. The fitted values are linear constraints of the observed xs. The constraint is that all beta coefficients are positive and sum to 1. That is $\hat{y}_i= \sum_{j=1}\bm{x}_{ij}\beta_j$ such that $0\leq \beta_j \leq 1$ and $\sum_{j=1}^d\beta_j=1$.

Value

A list including:

coefficients	A numerical matrix with the positively constrained beta coefficients.
value	A numerical vector with the value of the objective function.
iters	The number of iterations required until termination of the algorithm.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

References

Iverson Sara J., Field Chris, Bowen W. Don and Blanchard Wade (2004) Quantitative Fatty Acid Signature Analysis: A New Method of Estimating Predator Diets. Ecological Monographs, 74(2): 211-235.

See Also

kld, mpcls

Examples

x <- matrix(runif(30 * 6), ncol = 30)
x <- t( x / rowSums(x) )
Y <- matrix(runif(30 * 10), ncol = 30)
Y <- t( Y / rowSums(Y) )
mkld(Y, x)

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QFASA diet estimates using various distances

Description

QFASA diet estimates using various distances.

Usage

kld(y, x, tol = 1e-8, maxit = 50000, alpha = 0.1)
ait(y, x, tol = 1e-8, maxit = 50000, alpha = 0.01)
lsq(y, x, tol = 1e-8, maxit = 50000, alpha = 0.01)
jsd(y, x, tol = 1e-8, maxit = 300000, alpha = 0.01)
lr(y, x, tol = 1e-8, maxit = 100)

Arguments

y	The response variable. The predator's food composition. A vector with values between 0 and 1 that sum to 1. For some functions, zero values are allowed.
x	A matrix with independent variables, values between 0 and 1. Each column contains a prey's diet. The column-wise sums are equal to 1.
tol	The tolerance value to terminate the algorithm.
maxit	The maximum iterations allowed.
alpha	The step-size parameter of the fixed points iteration algorithm. This is similar to the $\eta$ parameter in the gradient descent algorithm.

Details

The function estimates the betas that minimize a distance. The fitted values are linear constraints of the observed xs. The constraint is that all beta coefficients are positive and sum to 1. That is $\hat{y}_i= \sum_{j=1}\bm{x}_{ij}\beta_j$ such that $0\leq \beta_j \leq 1$ and $\sum_{j=1}^d\beta_j=1$.

Value

A list including:

coefficients	A numerical matrix with the positively constrained beta coefficients.
value	A numerical vector with the value of the objective function.
iters	The number of iterations required until termination of the algorithm.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

References

Iverson Sara J., Field Chris, Bowen W. Don and Blanchard Wade (2004) Quantitative Fatty Acid Signature Analysis: A New Method of Estimating Predator Diets. Ecological Monographs, 74(2): 211-235.

See Also

mkld, pcls

Examples

x <- matrix(runif(30 * 8), ncol = 30)
x <- t( x / rowSums(x) )
y <- runif(30)
y <- y / sum(y)
kld(y, x)
ait(y, x)
lsq(y, x)
lr(y, x)

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