Package 'CompositionalLASSO'

Regression for Compositional Data with Zero Values

Description

A multivariate zero inflated logistic normal regression model is implemented for compositional data with zero values present.

Details

Package:	CompositionalLASSO
Type:	Package
Version:	1.0
Date:	2026-10-22

Maintainers

Michail Tsagris <[email protected]>.

Author(s)

Michail Tsagris [email protected]

References

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

Li Z., Lee K., Karagas M. R., Madan J. C., Hoen A. G., O'Malley A. J. and Li H. (2018). Conditional regression based on a multivariate zero-inflated logistic-normal model for microbiome relative abundance data. Statistics in Biosciences, 10(3): 587–608.

Alenazi A. A. (2022). f-divergence regression models for compositional data. Pakistan Journal of Statistics and Operation Research, 18(4): 867–882.

---

Cross-validation for the LASSO log-ratio regression with compositional response

Description

Cross-validation for the LASSO log-ratio regression with compositional response.

Usage

cv.lasso.compreg(y, x, lambda = NULL, nlambda = 100, nfolds = 10,
folds = NULL, seed = NULL)

Arguments

y	A numerical matrix with compositional data. Zero values are not allowed as the additive log-ratio transformation is applied to the compositional response prior to implementing the LASSO algortihm.
x	A matrix with the predictor variables.
lambda	A user supplied lambda sequence.
nlambda	This information is copied from the package glmnet. The number of $lambda$ values, default is 100.
nfolds	The number of folds for the K-fold cross-validation, set to 10 by default.
folds	If you have the list with the folds supply it here. You can also leave it NULL and it will create folds.
seed	You can specify your own seed number here or leave it NULL.

Details

The K-fold cross-validation is performed in order to select the optimal value for $\lambda$, the penalty parameter in LASSO.

Value

A list including:

kld	The cross-validated Kullback-Leibler divergence for each value of $\lambda$.
lambda.opt	The optimal value of $\lambda$.
be	The regression coefficients for the optimal value of $\lambda$.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

References

Friedman, J., Hastie, T. and Tibshirani, R. (2010) Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, Vol. 33(1), 1-22.

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

See Also

lasso.compreg, lasso.klcompreg, cv.lasso.klcompreg

Examples

y <- as.matrix(iris[, 1:3])
y <- y/rowSums(y)
x <- matrix(rnorm(150 * 50), ncol = 50)
mod <- cv.lasso.compreg(y, x)

---

Cross-validation for the LASSO Kullback-Leibler divergence based regression

Description

Cross-validation for the LASSO Kullback-Leibler divergence based regression.

Usage

cv.lasso.klcompreg(y, x, lambda = NULL, nlambda = 100, type = "grouped",
nfolds = 10, folds = NULL, seed = NULL)

Arguments

y	A numerical matrix with compositional data with or without zeros.
x	A matrix with the predictor variables.
lambda	A user supplied lambda sequence.
nlambda	This information is copied from the package glmnet. The number of $lambda$ values, default is 100.
type	This information is copied from the package glmnet.. If "grouped" then a grouped lasso penalty is used on the multinomial coefficients for a variable. This ensures they are all in our out together. The default in our case is "grouped".
nfolds	The number of folds for the K-fold cross-validation, set to 10 by default.
folds	If you have the list with the folds supply it here. You can also leave it NULL and it will create folds.
seed	You can specify your own seed number here or leave it NULL.

Details

The K-fold cross-validation is performed in order to select the optimal value for $\lambda$, the penalty parameter in LASSO.

Value

A list including:

kld	The cross-validated Kullback-Leibler divergence for each value of $\lambda$.
lambda.opt	The optimal value of $\lambda$.
be	The regression coefficients for the optimal value of $\lambda$.

Author(s)

Michail Tsagris and Abdulaziz Alenazi.

R implementation and documentation: Michail Tsagris [email protected] and Abdulaziz Alenazi [email protected].

References

Alenazi, A. A. (2022). f-divergence regression models for compositional data. Pakistan Journal of Statistics and Operation Research, 18(4): 867–882.

Friedman, J., Hastie, T. and Tibshirani, R. (2010) Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, Vol. 33(1), 1-22.

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

See Also

lasso.klcompreg, lasso.compreg, cv.lasso.compreg

Examples

y <- as.matrix(iris[, 1:3])
y <- y/rowSums(y)
x <- matrix(rnorm(150 * 50), ncol = 50)
mod <- cv.lasso.klcompreg(y, x)

---

Cross-validation for the LASSO log-ratio regression with compositional response

Description

Cross-validation for the LASSO log-ratio regression with compositional response.

Usage

cv.lasso.mziln(y, x, lambda = NULL, nlambda = 100, nfolds = 10,
folds = NULL, seed = NULL)

Arguments

y	A numerical matrix with compositional data. Zero values are not allowed as the additive log-ratio transformation is applied to the compositional response prior to implementing the LASSO algortihm.
x	A matrix with the predictor variables.
lambda	A user supplied lambda sequence.
nlambda	This information is copied from the package glmnet. The number of $lambda$ values, default is 100.
nfolds	The number of folds for the K-fold cross-validation, set to 10 by default.
folds	If you have the list with the folds supply it here. You can also leave it NULL and it will create folds.
seed	You can specify your own seed number here or leave it NULL.

Details

The K-fold cross-validation is performed in order to select the optimal value for $\lambda$, the penalty parameter in LASSO.

Value

A list including:

kld	The cross-validated Kullback-Leibler divergence for each value of $\lambda$.
lambda.opt	The optimal value of $\lambda$.
be	The regression coefficients for the optimal value of $\lambda$.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

References

Li Z., Lee K., Karagas M. R., Madan J. C., Hoen A. G., O'Malley A. J. and Li H. (2018). Conditional regression based on a multivariate zero-inflated logistic-normal model for microbiome relative abundance data. Statistics in Biosciences, 10(3): 587–608.

Friedman, J., Hastie, T. and Tibshirani, R. (2010) Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, Vol. 33(1), 1-22.

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

See Also

lasso.compreg, lasso.klcompreg, lasso.mziln

Examples

y <- as.matrix(iris[, 1:3])
y <- y / rowSums(y)
y[sample(150, 10), 3] <- 0
y <- y / rowSums(y)
x <- matrix(rnorm(150 * 50), ncol = 50)
mod <- cv.lasso.mziln(y, x)

---

LASSO log-ratio regression

Description

LASSO log-ratio regression.

Usage

lasso.compreg(y, x, lambda = NULL, nlambda = 100, xnew = NULL)

Arguments

y	A numerical matrix with compositional data. Zero values are not allowed as the additive log-ratio transformation is applied to the compositional response prior to implementing the LASSO algortihm.
x	A numerical matrix containing the predictor variables.
lambda	This information is copied from the package glmnet. A user supplied lambda sequence. Typical usage is to have the program compute its own lambda sequence based on nlambda and lambda.min.ratio. Supplying a value of lambda overrides this. WARNING: use with care. Avoid supplying a single value for lambda (for predictions after CV use predict() instead). Supply instead a decreasing sequence of lambda values. glmnet relies on its warms starts for speed, and its often faster to fit a whole path than compute a single fit.
nlambda	This information is copied from the package glmnet. The number of $lambda$ values, default is 100.
xnew	If you have new data use it, otherwise leave it NULL.

Details

The function uses the glmnet package to perform LASSO penalised regression. For more details see the function in that package.

Value

A list including:

be	A list with the estimated regression coefficients for each value of $\lambda$.
info	A matrix with two columns, the values of lambda used and their corresponding Kullback-Leibler divergence between the observed and the fitted values.
est	If you supply a matrix in the "xnew" argument this will return an array of many matrices with the fitted values, where each matrix corresponds to each value of $\lambda$.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

References

Friedman, J., Hastie, T. and Tibshirani, R. (2010) Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, Vol. 33(1), 1-22.

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

See Also

cv.lasso.compreg, lasso.klcompreg, cv.lasso.klcompreg, lasso.mziln

Examples

y <- as.matrix(iris[, 1:3])
y <- y/rowSums(y)
x <- matrix(rnorm(150 * 50), ncol = 50)
mod <- lasso.compreg(y, x)

---

LASSO Kullback-Leibler divergence based regression

Description

LASSO Kullback-Leibler divergence based regression.

Usage

lasso.klcompreg(y, x, lambda = NULL, nlambda = 100, type = "grouped", xnew = NULL)

Arguments

y	A numerical matrix with compositional data. Zero values are allowed.
x	A numerical matrix containing the predictor variables.
lambda	This information is copied from the package glmnet. A user supplied lambda sequence. Typical usage is to have the program compute its own lambda sequence based on nlambda and lambda.min.ratio. Supplying a value of lambda overrides this. WARNING: use with care. Avoid supplying a single value for lambda (for predictions after CV use predict() instead). Supply instead a decreasing sequence of lambda values. glmnet relies on its warms starts for speed, and its often faster to fit a whole path than compute a single fit.
nlambda	This information is copied from the package glmnet. The number of $lambda$ values, default is 100.
type	This information is copied from the package glmnet.. If "grouped" then a grouped lasso penalty is used on the multinomial coefficients for a variable. This ensures they are all in our out together. The default in our case is "grouped".
xnew	If you have new data use it, otherwise leave it NULL.

Details

The function uses the glmnet package to perform LASSO penalised regression. For more details see the function in that package.

Value

A list including:

be	A list with the estimated regression coefficients for each value of $\lambda$.
info	A matrix with two columns, the values of lambda used and their corresponding Kullback-Leibler divergence between the observed and the fitted values.
est	If you supply a matrix in the "xnew" argument this will return an array of many matrices with the fitted values, where each matrix corresponds to each value of $\lambda$.

Author(s)

Michail Tsagris and Abdulaziz Alenazi.

R implementation and documentation: Michail Tsagris [email protected] and Abdulaziz Alenazi [email protected].

References

Alenazi A. A. (2022). f-divergence regression models for compositional data. Pakistan Journal of Statistics and Operation Research, 18(4): 867–882.

Friedman J., Hastie T. and Tibshirani R. (2010) Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, Vol. 33(1), 1–22.

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

See Also

cv.lasso.klcompreg, lasso.compreg, lasso.mziln

Examples

y <- as.matrix(iris[, 1:3])
y <- y/rowSums(y)
x <- matrix(rnorm(150 * 50), ncol = 50)
mod <- lasso.klcompreg(y, x)

---

LASSO using the multivariate zero inflated logistic normal regression

Description

LASSO using the multivariate zero inflated logistic normal regression.

Usage

lasso.mziln(y, x, lambda = NULL, nlambda = 100, xnew = NULL)

Arguments

y	A numerical matrix with compositional data with zero values.
x	A numerical matrix containing the predictor variables.
lambda	This information is copied from the package glmnet. A user supplied lambda sequence. Typical usage is to have the program compute its own lambda sequence based on nlambda and lambda.min.ratio. Supplying a value of lambda overrides this. WARNING: use with care. Avoid supplying a single value for lambda (for predictions after CV use predict() instead). Supply instead a decreasing sequence of lambda values. glmnet relies on its warms starts for speed, and its often faster to fit a whole path than compute a single fit.
nlambda	This information is copied from the package glmnet. The number of $lambda$ values, default is 100.
xnew	If you have new data use it, otherwise leave it NULL.

Details

The function uses the glmnet package to perform LASSO penalised regression.

Value

A list including:

be	A list with the estimated regression coefficients for each value of $\lambda$.
info	A matrix with two columns, the values of lambda used and their corresponding Kullback-Leibler divergence between the observed and the fitted values.
est	If you supply a matrix in the "xnew" argument this will return an array of many matrices with the fitted values, where each matrix corresponds to each value of $\lambda$.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [email protected].

References

Li Z., Lee K., Karagas M. R., Madan J. C., Hoen A. G., O'Malley A. J. and Li H. (2018). Conditional regression based on a multivariate zero-inflated logistic-normal model for microbiome relative abundance data. Statistics in Biosciences, 10(3): 587–608.

Friedman, J., Hastie, T. and Tibshirani, R. (2010) Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, Vol. 33(1), 1-22.

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

See Also

cv.lasso.mziln, cv.lasso.compreg, cv.lasso.klcompreg

Examples

y <- as.matrix(iris[, 1:3])
y <- y / rowSums(y)
y[sample(150, 10), 3] <- 0
y <- y / rowSums(y)
x <- matrix(rnorm(150 * 50), ncol = 50)
mod <- lasso.mziln(y, x)

---