Globalaov | R Documentation |
The function implements the Global 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 globally 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 weakly. Since this is a global test, the adjusted p-value function is constant.
Globalaov(
formula,
B = 1000,
dx = NULL,
recycle = TRUE,
method = "residuals",
stat = "Integral"
)
formula |
An object of class " |
B |
The number of iterations of the MC algorithm to evaluate the
p-values of the permutation tests. 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
|
method |
Permutation method used to calculate the p-value of permutation
tests. Choose " |
stat |
Type of test statistic used for the global test. Possible values
are: |
An object of class IWTaov
. The function summary
is used to
obtain and print a summary of the results. This object is a list containing
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.
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).
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).
Global_pval_F
: Global p-value of the overall test F.
Global_pval_factors
: Global p-value of test F involving each factor
separately.
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.
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.
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.
# Importing the NASA temperatures data set
data(NASAtemp)
temperature <- rbind(NASAtemp$milan, NASAtemp$paris)
groups <- c(rep(0, 22), rep(1, 22))
# Performing the test
Global.result <- Globalaov(temperature ~ groups, B = 1000)
# Summary of the test results
summary(Global.result)
# Plot of the results
layout(1)
plot(Global.result)
# All graphics on the same device
layout(matrix(1:4, nrow = 2, byrow = FALSE))
plot(
Global.result,
main = 'NASA data',
plot.adjpval = TRUE,
xlab = 'Day',
xrange = c(1, 365)
)
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