ITP2bspline | R Documentation |
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.
ITP2bspline(
data1,
data2,
mu = 0,
B = 1000,
paired = FALSE,
order = 2,
nknots = dim(data1)[2]
)
ITP2fourier(
data1,
data2,
mu = 0,
B = 1000,
paired = FALSE,
maxfrequency = floor(dim(data1)[2]/2)
)
ITP2pafourier(
data1,
data2,
mu = 0,
B = 1000,
paired = FALSE,
maxfrequency = floor(dim(data1)[2]/2)
)
IWT2(
data1,
data2,
mu = 0,
B = 1000L,
dx = NULL,
recycle = TRUE,
paired = FALSE,
alternative = "two.sided",
verbose = TRUE
)
data1 |
First population's data. Either pointwise evaluations of the
functional data set on a uniform grid, or an |
data2 |
Second population's data. Either pointwise evaluations of the
functional data set on a uniform grid, or an |
mu |
Functional mean difference under the null hypothesis. Three
possibilities are available for
Defaults to |
B |
The number of iterations of the MC algorithm to evaluate the
p-values of the permutation tests. Defaults to |
paired |
Flag indicating whether a paired test has to be performed.
Defaults to |
order |
Order of the B-spline basis expansion. Defaults to |
nknots |
Number of knots of the B-spline basis expansion. Defaults to
|
maxfrequency |
The maximum frequency to be used in the Fourier basis
expansion of data. Defaults to |
dx |
Used only if an |
recycle |
Flag used to decide whether the recycled version of the IWT
should be used (see Pini and Vantini, 2017 for details). Defaults to
|
alternative |
A character string specifying the alternative hypothesis.
Must be one of |
verbose |
Logical: if |
An object of class IWT2
, which 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
interval-wise 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.
A. Pini and S. Vantini (2017). Interval-wise testing for functional data. Journal of Nonparametric Statistics, 29(2), 407-424.
See also plot.fdatest2
and IWTimage
for
plotting the results.
# Performing the IWT for two populations
IWT.result <- IWT2(NASAtemp$paris, NASAtemp$milan, B = 10L)
# 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)
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