Globalaov: Global testing procedure for testing functional analysis of...
In alessiapini/fdatest: Interval Wise Testing for Functional Data

Globalaov

R Documentation

Global testing procedure for testing functional analysis of variance

Description

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.

Usage

Globalaov(
  formula,
  B = 1000,
  dx = NULL,
  recycle = TRUE,
  method = "residuals",
  stat = "Integral"
)

Arguments

`formula`	An object of class "`formula`" (or one that can be coerced to that class): a symbolic description of the model to be fitted. The output variable of the formula can be either a matrix of dimension `c(n,J)` collecting the pointwise evaluations of `n` functional data on the same grid of `J` points, or a `fd` object from the package `fda`.
`B`	The number of iterations of the MC algorithm to evaluate the p-values of the permutation tests. Defaults to `1000L`.
`dx`	Used only if an `fd` object is provided. In this case, `dx` is the size of the discretization step of the gridused to evaluate functional data. If set to `NULL`, a grid of size `100L` is used. Defaults to `NULL`.
`recycle`	Flag used to decide whether the recycled version of the IWT should be used (see Pini and Vantini, 2017 for details). Defaults to `TRUE`.
`method`	Permutation method used to calculate the p-value of permutation tests. Choose "`residuals`" for the permutations of residuals under the reduced model, according to the Freedman and Lane scheme, and "`responses`" for the permutation of the responses, according to the Manly scheme.
`stat`	Type of test statistic used for the global test. Possible values are: `'Integral'` (default) for the integral over the domain of the F-test statistic; `'Max'` for max over the domain of the F-test statistic.

Value

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.

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.
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.

Examples

# 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)
)

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