MM-type estimators for linear regression on compositional data

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Description

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

Usage

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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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data <- data.frame(lifeExp = state.x77[, "Life Exp"], USArrests[ , -3])
mUSArr <- complmrob(lifeExp ~ ., data = data)
summary(mUSArr)