Log-contrast regression with multiple compositional predictors {Compositional} R Documentation

## Log-contrast regression with multiple compositional predictors

### Description

Log-contrast regression with multiple compositional predictors.

### Usage

```lc.reg2(y, x, z = NULL, xnew = NULL, znew = NULL)
```

### Arguments

 `y` A numerical vector containing the response variable values. This must be a continuous variable. `x` A list with multiple matrices 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 a list with multiple matrices with 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.

### Details

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.reg2`. Extra predictors variables are allowed as well, for instance categorical or continuous. The difference with `lc.reg` is that instead of one, there are multiple compositions treated as predictor variables.

### Value

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.

### Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

### References

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.

Xiaokang Liu, Xiaomei Cong, Gen Li, Kendra Maas and Kun Chen (2020). Multivariate Log-Contrast Regression with Sub-Compositional Predictors: Testing the Association Between Preterm Infants' Gut Microbiome and Neurobehavioral Outcome. https://arxiv.org/pdf/2006.00487.pdf.

```ulc.reg2, lc.reg, ulc.reg, lcreg.aov, alfa.pcr, alfa.knn.reg ```

### Examples

```y <- iris[, 1]
x <- list()
x1 <- as.matrix(iris[, 2:4])
x1 <- x1 / rowSums(x1)
x[[ 1 ]] <- x1
x[[ 2 ]] <- rdiri(150, runif(4) )
x[[ 3 ]] <- rdiri(150, runif(5) )
mod <- lc.reg2(y, x)
```

[Package Compositional version 5.2 Index]