# comp.reg: Multivariate regression with compositional data In Compositional: Compositional Data Analysis

## Description

Multivariate regression with compositional data.

## Usage

 `1` ```comp.reg(y, x, type = "classical", xnew = NULL, yb = NULL) ```

## Arguments

 `y` A matrix with compsitional data. Zero values are not allowed. `x` The predictor variable(s), they have to be continuous. `type` The type of regression to be used, "classical" for standard multivariate regression, or "spatial" for spatial median regression, which is also robust. `xnew` This is by default set to NULL. If you have new data whose compositional data values you want to predict, put them here. `yb` If you have already transformed the data using the additive log-ratio transformation, plut it here. Othewrise leave it NULL. This is intended to be used in the function `alfareg.tune` in order to speed up the process.

## Details

The additive log-ratio transformation is applied and then the chosen multivariate regression is implemented. The alr is easier to explain than the ilr and that is why the latter is avoided here.

## Value

A list including:

 `runtime` The time required by the regression. `be` The beta coefficients. `seb` The standard error of the beta coefficients. `est` The fitted values of xnew if xnew is NULL.

## Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <[email protected]> and Giorgos Athineou <[email protected]>

## References

Mardia K.V., Kent J.T., and Bibby J.M. (1979). Multivariate analysis. Academic press.

Aitchison J. (1986). The statistical analysis of compositional data. Chapman \& Hall.

```multivreg, spatmed.reg, js.compreg, diri.reg ```
 ```1 2 3 4 5 6``` ```library(MASS) y <- as.matrix(iris[, 1:3]) y <- y / rowSums(y) x <- as.vector(iris[, 4]) mod1 <- comp.reg(y, x) mod2 <- comp.reg(y, x, type = "spatial") ```