jlmerclusterperm

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Julia GLM.jl and MixedModels.jl based implementation of the cluster-based permutation test for time series data, powered by JuliaConnectoR.

Installation and usage

Install the released version of jlmerclusterperm from CRAN:

install.packages("jlmerclusterperm")

Or install the development version from GitHub with:

# install.packages("remotes")
remotes::install_github("yjunechoe/jlmerclusterperm")

Using jlmerclusterperm requires a prior installation of the Julia programming language, which can be downloaded from either the official website or using the command line utility juliaup. Julia version >=1.8 is required and 1.9 or higher is preferred for the substantial speed improvements.

Before using functions from jlmerclusterperm, an initial setup is required via calling jlmerclusterperm_setup(). The very first call on a system will install necessary dependencies (this only happens once and takes around 10-15 minutes).

Subsequent calls to jlmerclusterperm_setup() incur a small overhead of around 30 seconds, plus slight delays for first-time function calls. You pay up front for start-up and warm-up costs and get blazingly-fast functions from the package.

# Both lines must be run at the start of each new session
library(jlmerclusterperm)
jlmerclusterperm_setup()

See the Get Started page on the package website for background and tutorials.

Quick tour of package functionalities

Wholesale CPA with clusterpermute()

A time series data:

chickweights <- ChickWeight
chickweights$Time <- as.integer(factor(chickweights$Time))
matplot(
  tapply(chickweights$weight, chickweights[c("Time", "Diet")], mean),
  type = "b", lwd = 3, ylab = "Weight", xlab = "Time"
)

Preparing a specification object with make_jlmer_spec():

chickweights_spec <- make_jlmer_spec(
  formula = weight ~ 1 + Diet,
  data = chickweights,
  subject = "Chick", time = "Time"
)
chickweights_spec
#> ── jlmer specification ───────────────────────────────────────── <jlmer_spec> ──
#> Formula: weight ~ 1 + Diet2 + Diet3 + Diet4
#> Predictors:
#>   Diet: Diet2, Diet3, Diet4
#> Groupings:
#>   Subject: Chick
#>   Trial:
#>   Time: Time
#> Data:
#>   weight Diet2 Diet3 Diet4 Chick Time
#> 1     42     0     0     0     1    1
#> 2     51     0     0     0     1    2
#> 3     59     0     0     0     1    3
#>  [ reached 'max' / getOption("max.print") -- omitted 575 rows ]
#> ────────────────────────────────────────────────────────────────────────────────

Cluster-based permutation test with clusterpermute():

set_rng_state(123L)
clusterpermute(
  chickweights_spec,
  threshold = 2.5,
  nsim = 100
)
#> $null_cluster_dists
#> ── Null cluster-mass distribution (t > 2.5) ──────────── <null_cluster_dists> ──
#> Diet2 (n = 100)
#>   Mean (SD): -0.039 (1.89)
#>   Coverage intervals: 95% [-2.862, 0.000]
#> Diet3 (n = 100)
#>   Mean (SD): -0.129 (2.02)
#>   Coverage intervals: 95% [0.000, 0.000]
#> Diet4 (n = 100)
#>   Mean (SD): 0.296 (3.21)
#>   Coverage intervals: 95% [0.000, 5.797]
#> ────────────────────────────────────────────────────────────────────────────────
#> 
#> $empirical_clusters
#> ── Empirical clusters (t > 2.5) ──────────────────────── <empirical_clusters> ──
#> Diet2
#>   [3, 4]: 6.121 (p=0.0495)
#> Diet3
#>   [3, 12]: 35.769 (p=0.0099)
#> Diet4
#>   [2, 8]: 32.442 (p=0.0099)
#> ────────────────────────────────────────────────────────────────────────────────

Including random effects:

chickweights_re_spec <- make_jlmer_spec(
  formula = weight ~ 1 + Diet + (1 | Chick),
  data = chickweights,
  subject = "Chick", time = "Time"
)
set_rng_state(123L)
clusterpermute(
  chickweights_re_spec,
  threshold = 2.5,
  nsim = 100
)$empirical_clusters
#> ── Empirical clusters (t > 2.5) ──────────────────────── <empirical_clusters> ──
#> Diet2
#>   [3, 4]: 6.387 (p=0.0594)
#> Diet3
#>   [2, 12]: 39.919 (p=0.0099)
#> Diet4
#>   [2, 8]: 33.853 (p=0.0099)
#> ────────────────────────────────────────────────────────────────────────────────

Piecemeal approach to CPA

Computing time-wise statistics of the observed data:

empirical_statistics <- compute_timewise_statistics(chickweights_spec)
matplot(t(empirical_statistics), type = "b", pch = 1, lwd = 3, ylab = "t-statistic")
abline(h = 2.5, lty = 3)

Identifying empirical clusters:

empirical_clusters <- extract_empirical_clusters(empirical_statistics, threshold = 2.5)
empirical_clusters
#> ── Empirical clusters (t > 2.5) ──────────────────────── <empirical_clusters> ──
#> Diet2
#>   [3, 4]: 6.121
#> Diet3
#>   [3, 12]: 35.769
#> Diet4
#>   [2, 8]: 32.442
#> ────────────────────────────────────────────────────────────────────────────────

Simulating the null distribution:

set_rng_state(123L)
null_statistics <- permute_timewise_statistics(chickweights_spec, nsim = 100)
null_cluster_dists <- extract_null_cluster_dists(null_statistics, threshold = 2.5)
null_cluster_dists
#> ── Null cluster-mass distribution (t > 2.5) ──────────── <null_cluster_dists> ──
#> Diet2 (n = 100)
#>   Mean (SD): -0.039 (1.89)
#>   Coverage intervals: 95% [-2.862, 0.000]
#> Diet3 (n = 100)
#>   Mean (SD): -0.129 (2.02)
#>   Coverage intervals: 95% [0.000, 0.000]
#> Diet4 (n = 100)
#>   Mean (SD): 0.296 (3.21)
#>   Coverage intervals: 95% [0.000, 5.797]
#> ────────────────────────────────────────────────────────────────────────────────

Significance testing the cluster-mass statistic:

calculate_clusters_pvalues(empirical_clusters, null_cluster_dists, add1 = TRUE)
#> ── Empirical clusters (t > 2.5) ──────────────────────── <empirical_clusters> ──
#> Diet2
#>   [3, 4]: 6.121 (p=0.0495)
#> Diet3
#>   [3, 12]: 35.769 (p=0.0099)
#> Diet4
#>   [2, 8]: 32.442 (p=0.0099)
#> ────────────────────────────────────────────────────────────────────────────────

Iterating over a range of threshold values:

walk_threshold_steps(empirical_statistics, null_statistics, steps = c(2, 2.5, 3))
#>    threshold predictor id start end length sum_statistic     pvalue
#> 1        2.0     Diet2  1     3   5      3      8.496376 0.07920792
#> 2        2.0     Diet3  1     2  12     11     38.216035 0.00990099
#> 3        2.0     Diet4  1     2  12     11     41.651468 0.00990099
#> 4        2.5     Diet2  1     3   4      2      6.121141 0.04950495
#> 5        2.5     Diet3  1     3  12     10     35.768957 0.00990099
#> 6        2.5     Diet4  1     2   8      7     32.442352 0.00990099
#> 31       3.0     Diet3  1     3   5      3     12.719231 0.00990099
#> 21       3.0     Diet3  2     9  12      4     14.037622 0.00990099
#> 41       3.0     Diet4  1     2   7      6     29.659402 0.00990099

Acknowledgments

Citations

If you use jlmerclusterperm for cluster-based permutation test with mixed-effects models in your research, please cite one (or more) of the following as you see fit.

To cite jlmerclusterperm:

To cite the cluster-based permutation test:

To cite the Julia programming language:

To cite the GLM.jl and MixedModels.jl Julia libraries, consult their Zenodo pages: