Compositional (version 3.7)

Divergence based regression for compositional data: Divergence based regression for compositional data

Description

Regression for compositional data based on the Kullback-Leibler the Jensen-Shannon divergence and the symmetric Kullback-Leibler divergence.

Usage

kl.compreg(y, x, B = 1, ncores = 1, xnew = NULL, tol = 1e-07, maxiters = 50)
js.compreg(y, x, B = 1, ncores = 1, xnew = NULL)
symkl.compreg(y, x, B = 1, ncores = 1, xnew = NULL)

Arguments

y

A matrix with the compositional data (dependent variable). Zero values are allowed.

x

The predictor variable(s), they can be either continnuous or categorical or both.

B

If B is greater than 1 bootstrap estimates of the standard error are returned. If B=1, no standard errors are returned.

ncores

If ncores is 2 or more parallel computing is performed. This is to be used for the case of bootstrap. If B=1, this is not taken into consideration.

xnew

If you have new data use it, otherwise leave it NULL.

tol

The tolerance value to terminate the Newton-Raphson procedure.

maxiters

The maximum number of Newton-Raphson iterations.

Value

A list including:

runtime

The time required by the regression.

iters

The number of iterations required by the Newton-Raphson in the kl.compreg function.

loglik

The log-likelihood. This is actually a quasi multinomial regression. This is bascially minus the half deviance, or \(- sum_{i=1}^ny_i\log{y_i/\hat{y}_i}\).

be

The beta coefficients.

seb

The standard error of the beta coefficients, if bootstrap is chosen, i.e. if B > 1.

est

The fitted values of xnew if xnew is not NULL.

Details

In the kl.compreg the Kullback-Leibler divergence is adopted as the objective function. The js.compreg uses the Jensen-Shannon divergence and the symkl.compreg uses the symmetric Kullback-Leibler divergence. There is no actual log-likelihood for neither regression.

References

Murteira, Jose MR, and Joaquim JS Ramalho 2016. Regression analysis of multivariate fractional data. Econometric Reviews 35(4): 515-552.

Tsagris, Michail (2015). A novel, divergence based, regression for compositional data. Proceedings of the 28th Panhellenic Statistics Conference, 15-18/4/2015, Athens, Greece. https://arxiv.org/pdf/1511.07600.pdf

Endres, D. M. and Schindelin, J. E. (2003). A new metric for probability distributions. Information Theory, IEEE Transactions on 49, 1858-1860.

Osterreicher, F. and Vajda, I. (2003). A new class of metric divergences on probability spaces and its applicability in statistics. Annals of the Institute of Statistical Mathematics 55, 639-653.

See Also

diri.reg, js.compreg, ols.compreg, comp.reg

Examples

# NOT RUN {
library(MASS)
x <- as.vector(fgl[, 1])
y <- as.matrix(fgl[, 2:9])
y <- y / rowSums(y)
mod1<- kl.compreg(y, x, B = 1, ncores = 1)
mod2 <- js.compreg(y, x, B = 1, ncores = 1)
# }