Log-contrast regression with compositional predictor variables {Compositional} | R Documentation |
Log-contrast regression with compositional predictor variables.
lc.reg(y, x, z = NULL, xnew = NULL, znew = 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. |
z |
A matrix, data.frame, factor or a vector with some other covariate(s). |
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. |
znew |
A matrix, data.frame, factor or a vector with the values of some other covariate(s). 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
minimise the sum of squares of the residuals under the constraint R^T β = c, where c=0
in our case. If you want the regression without the zum-to-zero contraints see ulc.reg
.
Extra predictors variables are allowed as well, for instance categorical or continuous.
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 arguments "xnew" and znew were 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
ulc.reg, lcreg.aov, lc.reg2, alfa.pcr, alfa.knn.reg
y <- iris[, 1] x <- as.matrix(iris[, 2:4]) x <- x / rowSums(x) mod1 <- lc.reg(y, x) mod2 <- lc.reg(y, x, z = iris[, 5])