IWT2: Two population Interval Wise Testing procedure
In alessiapini/fdatest: Interval Wise Testing for Functional Data

Description Usage Arguments Value References See Also Examples

The function implements the Interval Wise Testing procedure 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 controls the interval-wise error rate.

1 2	IWT2(data1, data2, mu = 0, B = 1000, paired = FALSE, dx = NULL, recycle = TRUE, alternative = "two.sided")

`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.
`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`.
`recycle`	Flag used to decide whether the recycled version of the IWT should be used (see Pini and Vantini, 2017 for details). Default is `TRUE`.
`alternative`	A character string specifying the alternative hypothesis, must be one of "`two.sided`" (default), "`greater`" or "`less`".

IWT2 returns an object of class "IWT2". An object of class "IWT2" is a list 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.
`pval_matrix`	Matrix of dimensions `c(p,p)` of the p-values of the intervalwise tests. The element `(i,j)` of matrix `pval.matrix` contains the p-value of the test contains the p-value of the test of interval indexed by `(j,j+1,...,j+(p-i))`.
`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

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.

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

See also plot.IWT2 and IWTimage for plotting the results.

# Importing the NASA temperatures data set
data(NASAtemp)

# Performing the IWT for two populations
IWT.result <- IWT2(NASAtemp$paris,NASAtemp$milan)

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

# Plotting the p-value heatmap
IWTimage(IWT.result,abscissa.range=c(0,12))

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