# MM-type estimators for linear regression on compositional data

### Description

Uses the `lmrob`

method for robust linear regression models to fit
a linear regression models to compositional data.

### Usage

1 |

### Arguments

`formula` |
The formula for the regression model |

`data` |
The data.frame to use |

### Details

The variables on the right-hand-side of the formula will be transformed with the isometric log-ratio
transformation (`isomLR`

) and then the robust linear regression model is applied to
those transformed variables. The orthonormal basis can be constructed in `p`

different ways,
where `p`

is the number of variables on the RHS of the formula.

To get an interpretable estimate of the regression coefficient for each part of the composition, the data has to be transformed according to each of these orthonormal basis and a regression model has to be fit to every transformed data set.

### Value

A list of type `complmrob`

with fields

- coefficients
the estimated coefficients

- models
the single regression models (one for each orthonormal basis)

- npred
the number of predictor variables

- predictors
the names of the predictor variables

- coefind
the index of the relevent coefficient in the single regression models

- call
how the function was called

- intercept
if an intercept is included

### References

K. Hron, P. Filzmoser & K. Thompson (2012): Linear regression with compositional explanatory variables, Journal of Applied Statistics, DOI:10.1080/02664763.2011.644268

### Examples

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