Log-contrast regression with compositional predictor variables
Log-contrast regression with compositional predictor variables.
lc.reg(y, x, xnew = NULL)
y |
A numerical vector containing the response variable values. This must be a continuous variable. |
x |
A matrix with the predictor variables, the compositional data. No zero values are allowed. |
xnew |
A matrix containing the new compositional data whose response is to be predicted. If you have no new data, leave this NULL as is by default. |
The function performs the log-contrast regression model as described in Aitchison (2003), pg. 84-85. The logarithm of the compositional predictor variables is used (hence no zero values are allowed). The response variable is linked to the log-transformed data with the constraint that the sum of the regression coefficients equals 0. Hence, we apply constrained least squares, which has a closed form solution. The constrained least squares is described in Chapter 8.2 of Hansen (2019). The idea is to inimise the sum of squares of the residuals under the constraint R^T β = c, where c=0 in our case.
A list including:
be |
The constrained regression coefficients. Their sum equals 0. |
covbe |
If covariance matrix of the constrained regression coefficients. |
va |
The estimated regression variance. |
residuals |
The vector of residuals. |
est |
If the argument "xnew" was given these are the predicted or estimated values, otherwise it is NULL. |
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
Aitchison J. (1986). The statistical analysis of compositional data. Chapman \& Hall.
Hansen, B. E. (2019). Econometrics. https://www.ssc.wisc.edu/~bhansen/econometrics/Econometrics.pdf
y <- iris[, 4] x <- as.matrix(iris[, 1:3]) x <- x / rowSums(x) mod <- lc.reg(y, x)
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