Package 'codalm'

Transformation-free Linear Regression for Compositional Outcomes and Predictors

Description

Implements the expectation-maximization (EM) algorithm as described in Fiksel et al. (2022) for transformation-free linear regression for compositional outcomes and predictors.

Usage

codalm(y, x, accelerate = TRUE)

Arguments

y	A matrix of compositional outcomes. Each row is an observation, and must sum to 1. If any rows do not sum to 1, they will be renormalized
x	A matrix of compositional predictors. Each row is an observation, and must sum to 1. If any rows do not sum to 1, they will be renormalized
accelerate	A logical variable, indicating whether or not to use the Squarem algorithm for acceleration of the EM algorithm. Default is TRUE.

Value

A $D_s$ x $D_r$ compositional coefficient matrix, where $D_s$ and $D_r$ are the dimensions of the compositional predictor and outcome, respectively

References

https://doi.org/10.1111/biom.13465

Examples

require(ggtern)
data("WhiteCells", package = 'ggtern')
image <- subset(WhiteCells, Experiment == "ImageAnalysis")
image_mat <- as.matrix(image[,c("G", "L", "M")])
microscopic <- subset(WhiteCells, Experiment == "MicroscopicInspection")
microscopic_mat <- as.matrix(microscopic[,c("G", "L", "M")])
x <- image_mat  / rowSums(image_mat)
y <- microscopic_mat / rowSums(microscopic_mat)
codalm(y, x)

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Bootstrap Confidence Intervals Linear Regression for Compositional Outcomes and Predictors

Description

Implements percentile based bootstrapping to estimate the confidence intervals for the regression coefficients when doing linear regression for compositional outcomes and predictors

Usage

codalm_ci(
  y,
  x,
  accelerate = TRUE,
  nboot = 500,
  conf = 0.95,
  parallel = FALSE,
  ncpus = NULL,
  strategy = NULL,
  init.seed = 123
)

Arguments

y	A matrix of compositional outcomes. Each row is an observation, and must sum to 1. If any rows do not sum to 1, they will be renormalized
x	A matrix of compositional predictors. Each row is an observation, and must sum to 1. If any rows do not sum to 1, they will be renormalized
accelerate	A logical variable, indicating whether or not to use the Squarem algorithm for acceleration of the EM algorithm. Default is TRUE
nboot	The number of bootstrap repetitions to use. Default is 500
conf	A scalar between 0 and 1 containing the confidence level of the required intervals. Default is .95.
parallel	A logical variable, indicating whether or not to use a parallel operation for computing the permutation statistics
ncpus	Optional argument. When provided, is an integer giving the number of clusters to be used in parallelization. Defaults to the number of cores, minus 1.
strategy	Optional argument. When provided, this will be the evaluation function (or name of it) to use for parallel computation (if parallel = TRUE). Otherwise, if parallel = TRUE, then this will default to multisession. See plan.
init.seed	The initial seed for the permutations. Default is 123.

Value

A list, with ci_L and ci_U, giving the lower and upper bounds of each element of the B matrix

Examples

require(ggtern)
data("WhiteCells", package = 'ggtern')
image <- subset(WhiteCells, Experiment == "ImageAnalysis")
image_mat <- as.matrix(image[,c("G", "L", "M")])
microscopic <- subset(WhiteCells, Experiment == "MicroscopicInspection")
microscopic_mat <- as.matrix(microscopic[,c("G", "L", "M")])
x <- image_mat  / rowSums(image_mat)
y <- microscopic_mat / rowSums(microscopic_mat)
codalm_ci(y, x, nboot = 50, conf = .95)

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Permutation Test for Linear Independence Between Compositional Outcomes and Predictors

Description

Implements the loss function based permutation test as described in Fiksel et al. (2022) for a test of linear independence between compositional outcomes and predictors.

Usage

codalm_indep_test(
  y,
  x,
  nperms = 500,
  accelerate = TRUE,
  parallel = FALSE,
  ncpus = NULL,
  strategy = NULL,
  init.seed = 123
)

Arguments

y	A matrix of compositional outcomes. Each row is an observation, and must sum to 1. If any rows do not sum to 1, they will be renormalized
x	A matrix of compositional predictors. Each row is an observation, and must sum to 1. If any rows do not sum to 1, they will be renormalized
nperms	The number of permutations. Default is 500.
accelerate	A logical variable, indicating whether or not to use the Squarem algorithm for acceleration of the EM algorithm. Default is TRUE.
parallel	A logical variable, indicating whether or not to use a parallel operation for computing the permutation statistics
ncpus	Optional argument. When provided, is an integer giving the number of clusters to be used in parallelization. Defaults to the number of cores, minus 1.
strategy	Optional argument. When provided, this will be the evaluation function (or name of it) to use for parallel computation (if parallel = TRUE). Otherwise, if parallel = TRUE, then this will default to multisession. See plan.
init.seed	The initial seed for the permutations. Default is 123.

Value

The p-value for the independence test

Examples

require(gtools)
x <- rdirichlet(100, c(1, 1, 1))
y <- rdirichlet(100, c(1, 1, 1))
codalm_indep_test(y, x)


require(ggtern)
data("WhiteCells", package = 'ggtern')
image <- subset(WhiteCells, Experiment == "ImageAnalysis")
image_mat <- as.matrix(image[,c("G", "L", "M")])
microscopic <- subset(WhiteCells, Experiment == "MicroscopicInspection")
microscopic_mat <- as.matrix(microscopic[,c("G", "L", "M")])
x  <- image_mat  / rowSums(image_mat)
y <- microscopic_mat / rowSums(microscopic_mat)
codalm_indep_test(y, x)

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