PCT2: Two population Partition Closed Testing procedure

In alessiapini/fdatest: Interval Wise Testing for Functional Data

Two population Partition Closed Testing procedure

Description

The function implements the Partition Closed 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 family-wise error rate asymptotically.

Usage

PCT2(
  data1,
  data2,
  partition,
  mu = 0,
  B = 1000L,
  paired = FALSE,
  dx = NULL,
  alternative = "two.sided"
)

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.
partition	Vector of length J containing the labels assigning each point of the domain to an element of the partition.
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".

Value

An object of class fdatest2 containing 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.

See Also

See also plot.fdatest2 for plotting the results.

Examples

# Importing the NASA temperatures data set
data(NASAtemp)

# Performing the PCT for two populations
# Choosing as partition the 4 seasons of the year
partition <- c(
  rep(1, 31 + 28 + 21), 
  rep(2, 10 + 30 + 31 + 21), 
  rep(3, 9 + 31 + 31 + 23), 
  rep(4, 7 + 31 + 30 + 21), 
  rep(1, 10)
)
partition <- factor(partition)

PCT.result <- PCT2(NASAtemp$paris, NASAtemp$milan, partition = partition)

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

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

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