Dirichlet regression
Dirichlet regression.
diri.reg(y, x, plot = TRUE, xnew = NULL) diri.reg2(y, x, xnew = NULL)
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. |
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 φ via the exponential link function φ = e^{x*b}.
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) in the function "diri.reg2". |
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. |
Michail Tsagris
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>
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.
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)
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