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,
method = "residuals",
dx = NULL,
recycle = TRUE,
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. The defualt is |
method |
Permutation method used to calculate the p-value of permutation tests. Choose " |
dx |
Used only if a |
stat |
Type of test statistic used for the global test. Possible values are: |
Globalaov
returns 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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