Website and Source code

The funStatTest package implements various statistics for two sample comparison testing regarding functional data introduced and used in Smida et al 2022 [1].

This package is developed by:

• Zaineb Smida (ORCID)
• Ghislain Durif (link|ORCID)
• Lionel Cucala (link)

Installation

To install the funStatTest package, you can run:

install.packages("funStatTest")

You can also install the development version of funStatTest with the following command:

remotes::install_git("https://plmlab.math.cnrs.fr/gdurif/funStatTest")

Documentation

See the package vignette and function manuals for more details about the package usage.

Development

The funStatTest was developed using the fusen package [2]. See in the dev sub-directory in the package sources for more information, in particular:

• the file dev/dev_history.Rmd describing the development process
• the file dev/flat_package.Rmd defining the major package functions (from which the vignette is extracted)
• the file dev/flat_internal.Rmd defining package internal functions

The funStatTest website was generated using the pkgdown package [3].

Example

This is a basic example which shows you how to solve a common problem:

library(funStatTest)

Data simulation

We simulate two samples of trajectories diverging by a delta function.

simu_data <- simul_data(
    n_point = 100, n_obs1 = 50, n_obs2 = 75, c_val = 10,
    delta_shape = "quadratic", distrib = "normal"
)
plot_simu(simu_data)

We extract the matrices of trajectories associated to each sample:

MatX <- simu_data$mat_sample1
MatY <- simu_data$mat_sample2

And we compute the different statistics for two sample function data comparison presented in Smida et al 2022 [1]:

res <- comp_stat(MatX, MatY, stat = c("mo", "med", "wmw", "hkr", "cff"))
res
#> $mo
#> [1] 0.9486241
#> 
#> $med
#> [1] 0.9517283
#> 
#> $wmw
#> [1] 0.9074959
#> 
#> $hkr
#>         [,1]
#> T1 31987.663
#> T2  8489.875
#> 
#> $cff
#> [1] 14150.96

We can also compute p-values associated to these statistics:

# small data for the example
simu_data <- simul_data(
    n_point = 20, n_obs1 = 4, n_obs2 = 5, c_val = 10,
    delta_shape = "constant", distrib = "normal"
)
MatX <- simu_data$mat_sample1
MatY <- simu_data$mat_sample2
res <- permut_pval(
    MatX, MatY, n_perm = 200, stat = c("mo", "med", "wmw", "hkr", "cff"),
    verbose = TRUE)
res
#> $mo
#> [1] 0.01492537
#> 
#> $med
#> [1] 0.0199005
#> 
#> $wmw
#> [1] 0.01492537
#> 
#> $hkr
#>          T1          T2 
#> 0.014925373 0.009950249 
#> 
#> $cff
#> [1] 0.009950249

⚠️ computing p-values based on permutations may take some time (for large data or when using a large number of simulations. ⚠️

And we can also run a simulation-based power analysis:

# simulate a few small data for the example
res <- power_exp(
    n_simu = 20, alpha = 0.05, n_perm = 200,
    stat = c("mo", "med", "wmw", "hkr", "cff"),
    n_point = 25, n_obs1 = 4, n_obs2 = 5, c_val = 10, delta_shape = "constant",
    distrib = "normal", max_iter = 10000, verbose = FALSE
)
res$power_res
#> $mo
#> [1] 1
#> 
#> $med
#> [1] 1
#> 
#> $wmw
#> [1] 1
#> 
#> $hkr
#> T1 T2 
#>  1  1 
#> 
#> $cff
#> [1] 1

References