IWTaov | R Documentation |
The function implements the Interval Wise Testing procedure for testing mean differences between several functional populations in a one-way or multi-way functional analysis of variance framework. 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.
IWTaov(formula, B = 1000L, method = "residuals", dx = NULL, recycle = TRUE)
formula |
An object of class " |
B |
The number of iterations of the MC algorithm to evaluate the
p-values of the permutation tests. The defualt is |
method |
Permutation method used to calculate the p-value of permutation
tests. Choose " |
dx |
Used only if a |
recycle |
Flag used to decide whether the recycled version of the IWT
should be used (see Pini and Vantini, 2017 for details). Default is
|
IWTaov
returns an object of class
"IWTaov
". The function summary
is used to obtain and print a
summary of the results. An object of class "IWTaov
" is a list
containing at least the following components:
call
: The matched call.
design_matrix
: The design matrix of the functional-on-scalar linear
model.
unadjusted_pval_F
: Evaluation on a grid of the unadjusted p-value
function of the functional F-test.
pval_matrix_F
: Matrix of dimensions c(p,p)
of the p-values of
the intervalwise F-tests. The element (i,j)
of matrix pval.matrix
contains the p-value of the test of interval indexed by
(j,j+1,...,j+(p-i))
.
adjusted_pval_F
: Evaluation on a grid of the adjusted p-value function
of the functional F-test.
unadjusted_pval_factors
: Evaluation on a grid of the unadjusted p-value
function of the functional F-tests on each factor of the analysis of
variance (rows).
pval_matrix_factors
: Array of dimensions c(L+1,p,p)
of the p-values
of the multivariate F-tests on factors. The element (l,i,j)
of array
pval.matrix
contains the p-value of the joint NPC test on factor l
of
the components (j,j+1,...,j+(p-i))
.
adjusted_pval_factors
: Adjusted p-values of the functional F-tests on
each factor of the analysis of variance (rows) and each basis coefficient
(columns).
data.eval
: Evaluation on a fine uniform grid of the functional data
obtained through the basis expansion.
coeff.regr.eval
: Evaluation on a fine uniform grid of the functional
regression coefficients.
fitted.eval
: Evaluation on a fine uniform grid of the fitted values of
the functional regression.
residuals.eval
: Evaluation on a fine uniform grid of the residuals of
the functional regression.
R2.eval
: Evaluation on a fine uniform grid of the functional R-squared
of the regression.
heatmap.matrix.F
: Heatmap matrix of p-values of functional F-test (used
only for plots).
heatmap.matrix.factors
: Heatmap matrix of p-values of functional
F-tests on each factor of the analysis of variance (used only for plots).
Pini, A., & Vantini, S. (2017). Interval-wise testing for functional data. Journal of Nonparametric Statistics, 29(2), 407-424.
Pini, A., Vantini, S., Colosimo, B. M., & Grasso, M. (2018). Domain‐selective functional analysis of variance for supervised statistical profile monitoring of signal data. Journal of the Royal Statistical Society: Series C (Applied Statistics) 67(1), 55-81.
Abramowicz, K., Hager, C. K., Pini, A., Schelin, L., Sjostedt de Luna, S., & Vantini, S. (2018). Nonparametric inference for functional‐on‐scalar linear models applied to knee kinematic hop data after injury of the anterior cruciate ligament. Scandinavian Journal of Statistics 45(4), 1036-1061.
D. Freedman and D. Lane (1983). A Nonstochastic Interpretation of Reported Significance Levels. Journal of Business & Economic Statistics 1.4, 292-298.
B. F. J. Manly (2006). Randomization, Bootstrap and Monte Carlo Methods in Biology. Vol. 70. CRC Press.
See summary.IWTaov
for summaries and
plot.IWTaov
for plotting the results. See
ITPaovbspline
for a functional analysis of variance test
based on B-spline basis expansion. See also IWTlm
to fit and
test a functional-on-scalar linear model applying the IWT, and
IWT1
, IWT2
for one-population and
two-population tests.
temperature <- rbind(NASAtemp$milan, NASAtemp$paris)
groups <- c(rep(0, 22), rep(1, 22))
# Performing the IWT
IWT.result <- IWTaov(temperature ~ groups, B = 10L)
# Summary of the ITP results
summary(IWT.result)
# Plot of the IWT results
graphics::layout(1)
plot(IWT.result)
# All graphics on the same device
graphics::layout(matrix(1:4, nrow = 2, byrow = FALSE))
plot(
IWT.result,
main = 'NASA data',
plot.adjpval = TRUE,
xlab = 'Day',
xrange = c(1, 365)
)
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