IWTaov: Interval Wise Testing procedure for testing functional...
In alessiapini/fdatest: Interval Wise Testing for Functional Data

IWTaov

R Documentation

Interval Wise Testing procedure for testing functional analysis of variance

Description

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.

Usage

IWTaov(formula, B = 1000, method = "residuals", dx = NULL, recycle = TRUE)

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. The defualt is `B=1000`.
`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.
`dx`	Used only if a `fd` object is provided. In this case, `dx` is the size of the discretization step of the grid used to evaluate functional data. If set to `NULL`, a grid of size 100 is used. Default is `NULL`.
`recycle`	Flag used to decide whether the recycled version of the IWT should be used (see Pini and Vantini, 2017 for details). Default is `TRUE`.

Value

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).

References

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.

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 IWT
IWT.result <- IWTaov(temperature ~ groups,B=1000)

# Summary of the ITP results
summary(IWT.result)

# Plot of the IWT results
layout(1)
plot(IWT.result)

# All graphics on the same device
layout(matrix(1:4,nrow=2,byrow=FALSE))
plot(IWT.result,main='NASA data', plot_adjpval = TRUE,xlab='Day',xrange=c(1,365))

alessiapini/fdatest documentation built on April 23, 2024, 2:31 a.m.