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: - 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)

Usage

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

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. The default is `mu=0`.
`B`	The number of iterations of the MC algorithm to evaluate the p-values of the permutation tests. The defualt is `B=1000`.
`paired`	Flag indicating whether a paired test has to be performed. Default is `FALSE`.
`dx`	Used only if a `fd` object is provided. In this case, `dx` is the size of the discretization step of the grid used to evaluate functional data. If set to `NULL`, a grid of size 100 is used. Default is `NULL`.
`alternative`	A character string specifying the alternative hypothesis, must be one of "`two.sided`" (default), "`greater`" or "`less`".
`recycle`	Used only if `method`="`IWT`". Flag used to decide whether the recycled version of the IWT should be used. Default is `TRUE`.
`partition`	Used only if `method`="`PCT`". The partition to be used for PCT procedure. Default is `NULL`.

Value

fdatest2 returns an object of class "fdatest2" containing at least the following components:

`test`	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,"TWT")

# 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,"IWT")

# 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 April 28, 2024, 12:35 a.m.