fdatest2: Two population local testing procedures
In alessiapini/fdatest: Interval Wise Testing for Functional Data

fdatest2

R Documentation

Two population local testing procedures

Description

The function implements local testing procedures for testing mean differences between two functional populations. Functional data are tested locally and unadjusted and adjusted p-value functions are provided. The unadjusted p-value function controls the point-wise error rate. The adjusted p-value function can be computed according to the following methods:

Usage

fdatest2(
  data1,
  data2,
  method,
  mu = 0,
  B = 1000L,
  paired = FALSE,
  dx = NULL,
  alternative = "two.sided",
  recycle = TRUE,
  partition = NULL,
  verbose = TRUE
)

Arguments

`data1`	First population's data. Either pointwise evaluations of the functional data set on a uniform grid, or a `fd` object from the package `fda`. If pointwise evaluations are provided, `data2` is a matrix of dimensions `c(n1,J)`, with `J` evaluations on columns and `n1` units on rows.
`data2`	Second population's data. Either pointwise evaluations of the functional data set on a uniform grid, or a `fd` object from the package `fda`. If pointwise evaluations are provided, `data2` is a matrix of dimensions `c(n1,J)`, with `J` evaluations on columns and `n2` units on rows.
`method`	A character string specifying the method chosen to adjust the p-value. Should be one of the following: "`Global`", "`IWT`", "`TWT`", "`PCT`", "`FDR`".
`mu`	Functional mean difference under the null hypothesis. Three possibilities are available for `mu`: a constant (in this case, a constant function is used); a `J`-dimensional vector containing the evaluations on the same grid which `data` are evaluated; a `fd` object from the package `fda` containing one function. Defaults to `mu = 0`.
`B`	The number of iterations of the MC algorithm to evaluate the p-values of the permutation tests. Defaults to `1000L`.
`paired`	Flag indicating whether a paired test has to be performed. Defaults to `FALSE`.
`dx`	Used only if an `fd` object is provided. In this case, `dx` is the size of the discretization step of the gridused to evaluate functional data. If set to `NULL`, a grid of size `100L` is used. Defaults to `NULL`.
`alternative`	A character string specifying the alternative hypothesis. Must be one of `"two.sided"` (default), `"greater"` or `"less"`.
`recycle`	Flag used to decide whether the recycled version of the IWT should be used (see Pini and Vantini, 2017 for details). Defaults to `TRUE`.
`partition`	Used only if `method`="`PCT`". The partition to be used for PCT procedure. Default is `NULL`.
`verbose`	Logical: if `FALSE`, reduces the amount of output. Default is `TRUE`.

Details

global testing (controlling the FWER weakly)
interval-wise testing (controlling the interval-wise error rate)
threshold-wise testing (controlling the FWER asymptotically)
partition closed testing (controlling the FWER on a partition)
functional Benjamini Hochberg (controlling the FDR)

Value

An object of class fdatest2 containing at least the following components:

test: a string vector indicating the type of test performed. In this case equal to "2pop".
mu: evaluation on a grid of the functional mean difference under the null hypothesis (as entered by the user).
unadjusted_pval: evaluation on a grid of the unadjusted p-value function.
adjusted_pval: evaluation on a grid of the adjusted p-value function.
data.eval: evaluation on a grid of the functional data.
ord_labels: vector of labels indicating the group membership of data.eval.

References

Abramowicz, K., Pini, A., Schelin, L., Stamm, A., & Vantini, S. (2022). “Domain selection and familywise error rate for functional data: A unified framework. Biometrics 79(2), 1119-1132.

Pini, A., & Vantini, S. (2017). Interval-wise testing for functional data. Journal of Nonparametric Statistics, 29(2), 407-424

A. Pini and S. Vantini (2017). The Interval Testing Procedure: Inference for Functional Data Controlling the Family Wise Error Rate on Intervals. Biometrics 73(3): 835–845.

Lundtorp Olsen, N., Pini, A., & Vantini, S. (2021). False discovery rate for functional data TEST 30, 784–809.

Examples

# Importing the NASA temperatures data set
data(NASAtemp)

# Performing the TWT for two populations
TWT.result <- fdatest2(
  NASAtemp$paris, NASAtemp$milan, 
  method = "TWT", B = 10L
)

# Plotting the results of the TWT
plot(
  TWT.result, 
  xrange = c(0, 12), 
  main = 'TWT results for testing mean differences'
)

# Selecting the significant components at 5% level
which(TWT.result$adjusted_pval < 0.05)

# Performing the IWT for two populations
IWT.result <- fdatest2(
  NASAtemp$paris, NASAtemp$milan, 
  method = "IWT", B = 10L
)

# Plotting the results of the IWT
plot(
  IWT.result, 
  xrange = c(0, 12), 
  main = 'IWT results for testing mean differences'
)

# Selecting the significant components at 5% level
which(IWT.result$adjusted_pval < 0.05)

alessiapini/fdatest documentation built on Jan. 4, 2025, 5:37 a.m.