Dirichlet regression {Compositional} | R Documentation |
Dirichlet regression
Description
Dirichlet regression.
Usage
diri.reg(y, x, plot = FALSE, xnew = NULL)
diri.reg2(y, x, xnew = NULL)
diri.reg3(y, x, xnew = NULL)
Arguments
y |
A matrix with the compositional data (dependent variable). Zero values are not allowed. |
x |
The predictor variable(s), they can be either continuous or categorical or both. |
plot |
A boolean variable specifying whether to plot the leverage values of the observations or not. This is taken into account only when xnew = NULL. |
xnew |
If you have new data use it, otherwise leave it NULL. |
Details
A Dirichlet distribution is assumed for the regression. This involves numerical optimization.
The function "diri.reg2()" allows for the covariates to be linked with the precision parameter
via the exponential link function
. The function "diri.reg3()"
links the covariates to the alpha parameters of the Dirichlet distribution, i.e. it uses the
classical parametrization of the distribution. This means, that there is a set of regression
parameters for each component.
Value
A list including:
runtime |
The time required by the regression. |
loglik |
The value of the log-likelihood. |
phi |
The precision parameter. If covariates are linked with it (function "diri.reg2()"), this will be a vector. |
phipar |
The coefficients of the phi parameter if it is linked to the covariates. |
std.phi |
The standard errors of the coefficients of the phi parameter is it linked to the covariates. |
log.phi |
The logarithm of the precision parameter. |
std.logphi |
The standard error of the logarithm of the precision parameter. |
be |
The beta coefficients. |
seb |
The standard error of the beta coefficients. |
sigma |
Th covariance matrix of the regression parameters (for the mean vector and the phi parameter)". |
lev |
The leverage values. |
est |
For the "diri.reg" this contains the fitted or the predicted values (if xnew is not NULL). For the "diri.reg2" if xnew is NULL, this is also NULL. |
Author(s)
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>.
References
Maier, Marco J. (2014) DirichletReg: Dirichlet Regression for Compositional Data in R. Research Report Series/Department of Statistics and Mathematics, 125. WU Vienna University of Economics and Business, Vienna. http://epub.wu.ac.at/4077/1/Report125.pdf
Gueorguieva, Ralitza, Robert Rosenheck, and Daniel Zelterman (2008). Dirichlet component regression and its applications to psychiatric data. Computational statistics & data analysis 52(12): 5344-5355.
Ng Kai Wang, Guo-Liang Tian and Man-Lai Tang (2011). Dirichlet and related distributions: Theory, methods and applications. John Wiley & Sons.
Aitchison J. (1986). The statistical analysis of compositional data. Chapman & Hall.
See Also
js.compreg, kl.compreg, ols.compreg, comp.reg, alfa.reg, diri.nr, dda
Examples
x <- as.vector(iris[, 4])
y <- as.matrix(iris[, 1:3])
y <- y / rowSums(y)
mod1 <- diri.reg(y, x)
mod2 <- diri.reg2(y, x)
mod3 <- comp.reg(y, x)