How to use codalm

We will start by loading the codalm R package, in addition to the future and future.apply packages, which we will use for bootstrapping.

library(codalm)
require('future')
#> Loading required package: future
require('future.apply')
#> Loading required package: future.apply

We will be analyzing how the percentages of mothers and fathers with low, medium, and high education levels relate to each other, across 31 countries in Europe. The format that we need is for both compositions to be in matrices, with one row per observation. We will also normalize the rows of these matrices to ensure that they sum to 1, although the codalm function would also take care of this for us.

data("educFM")
father <- as.matrix(educFM[,2:4])
father <- father / rowSums(father)
mother <- as.matrix(educFM[,5:7] )
mother <- mother/rowSums(mother)

To estimate the coefficient matrix B, we can use the codalm function.

B_est <- codalm(y = father, x = mother)
B_est
#>              [,1]       [,2]       [,3]
#> [1,] 9.113082e-01 0.05115443 0.03753734
#> [2,] 1.427924e-08 0.90541094 0.09458905
#> [3,] 1.860624e-07 0.14154036 0.85845945

To see the interpretation of this matrix, please see Fiksel et al. (2021). If all the rows of B_est are exactly the same, it is recommended to set accelerate = FALSE as a sensitivity check.

We can also use the bootstrap to estimate 95% confidence intervals. We will only use 50 bootstrap iterations as an example (nboot = 50), but is recommended to do more.

B_ci <- codalm_ci(y = father, x = mother, nboot = 50,
                   conf = .95)
B_ci$ci_L
#>              [,1]         [,2]       [,3]
#> [1,] 8.398315e-01 1.689452e-02 0.01890371
#> [2,] 5.512479e-23 8.310054e-01 0.04690478
#> [3,] 1.533253e-13 1.876738e-09 0.64493422
B_ci$ci_U
#>            [,1]      [,2]      [,3]
#> [1,] 0.95443317 0.1174445 0.0696308
#> [2,] 0.04001022 0.9522237 0.1655356
#> [3,] 0.16044680 0.3550658 1.0000000

These matrices given the lower and upper bounds for the confidence interval for each element of the coefficient matrix.

You can also take advantage of parallelization, if you have multiple cores available.

ncores <- 2
B_ci_parallel <- codalm_ci(y = father, x = mother, nboot = 50,
                   conf = .95, parallel = TRUE, ncpus = ncores, strategy = 'multisession')
identical(B_ci$ci_L, B_ci_parallel$ci_L)
#> [1] TRUE
identical(B_ci$ci_U, B_ci_parallel$ci_U)
#> [1] TRUE

Finally, we will do a permutation test for linear independence. Again, we will only do 50 permutations as an example, but in practice this number should be higher. For demonstration purposes, we will generate the compositional outcome independently of the compositional predictor

set.seed(123)
x <- gtools::rdirichlet(100, rep(1, 3))
y <- gtools::rdirichlet(100, rep(1, 3))
indep_test_pval <- codalm_indep_test(y = y, x = x,
                                     nperms = 100, init.seed = 123)
indep_test_pval
#> [1] 0.2871287

This function can also be parallelized. Unlike the bootstrapping, there is no need to differentiate between whether the user is using a Windows or Unix system.

indep_test_pval_parallel <- codalm_indep_test(y = y, x = x,
                                              nperms = 100, init.seed = 123,
                                              parallel = TRUE, ncpus = ncores,
                                              strategy = 'multisession')
indep_test_pval_parallel
#> [1] 0.2871287