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)
```

### 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 φ via the exponential link function φ = e^{x*b}.

### 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) 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.

### 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.

```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)
```

[Package Compositional version 5.2 Index]