Dirichlet regression {Compositional}

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 \phi via the exponential link function \phi = e^{x*b}. 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 [e-mail] and Giorgos Athineou <[e-mail]>.

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)