Transformation-free Linear Regression for Compositional Outcomes and Predictors

Source: R/codalm_em.R

Implements the expectation-maximization (EM) algorithm as described in Fiksel et al. (2020) for transformation-free linear regression for compositional outcomes and predictors.

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://arxiv.org/abs/2004.07881

Examples

require(ggtern)
#> Loading required package: ggtern
#> Loading required package: ggplot2
#> Registered S3 methods overwritten by 'ggtern':
#>   method           from   
#>   grid.draw.ggplot ggplot2
#>   plot.ggplot      ggplot2
#>   print.ggplot     ggplot2
#> --
#> Remember to cite, run citation(package = 'ggtern') for further info.
#> --
#> 
#> Attaching package: ‘ggtern’
#> The following objects are masked from ‘package:ggplot2’:
#> 
#>     aes, annotate, ggplot, ggplot_build, ggplot_gtable, ggplotGrob,
#>     ggsave, layer_data, theme_bw, theme_classic, theme_dark,
#>     theme_gray, theme_light, theme_linedraw, theme_minimal, theme_void
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)
#>              [,1]       [,2]         [,3]
#> [1,] 9.742582e-01 0.02292755 2.814241e-03
#> [2,] 3.267605e-09 1.00000000 3.620972e-10
#> [3,] 9.484137e-18 0.04198815 9.580118e-01