Divergence based regression for compositional data: Divergence based regression for compositional data
Description
Regression for compositional data based on the Kullback-Leibler and the Jensen-Shannon 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)
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. This involves numerical optimization. There is no actual log-likelihood. As for the js.compreg another divergence is used.
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
# 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)
# }