Log-contrast logistic or Poisson regression with with multiple compositional predictors {Compositional}

Log-contrast logistic or Poisson regression with with multiple compositional predictors

Description

Log-contrast logistic or Poisson regression with with multiple compositional predictors.

Usage

lc.glm2(y, x, z = NULL, model = "logistic", xnew = NULL, znew = NULL)

Arguments

y

A numerical vector containing the response variable values. This is either a binary variable or a vector with counts.

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).

model

This can be either "logistic" or "poisson".

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.

Details

The function performs the log-contrast logistic or Poisson regression model. 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. If you want the regression without the zum-to-zero contraints see ulc.glm2. Extra predictors variables are allowed as well, for instance categorical or continuous.

Value

A list including:

devi

The residual deviance of the logistic or Poisson regression model.

be

The constrained regression coefficients. Their sum (excluding the constant) equals 0.

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 [e-mail].

References

Aitchison J. (1986). The statistical analysis of compositional data. Chapman & Hall.

Lu J., Shi P. and Li H. (2019). Generalized linear models with linear constraints for microbiome compositional data. Biometrics, 75(1): 235–244.

See Also

ulc.glm2, ulc.glm, lc.glm

Examples

y <- rbinom(150, 1, 0.5)
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.glm2(y, x)