ITPaovbspline: Interval Testing Procedure for testing unctional analysis of...
In alessiapini/fdatest: Interval Wise Testing for Functional Data

ITPaovbspline

R Documentation

Interval Testing Procedure for testing unctional analysis of variance with B-spline basis

Description

The function implements the Interval Testing Procedure for testing for significant differences between several functional population evaluated on a uniform grid, in a functional analysis of variance setting. Data are represented by means of the B-spline basis and the significance of each basis coefficient is tested with an interval-wise control of the Family Wise Error Rate. The default parameters of the basis expansion lead to the piece-wise interpolating function.

Usage

ITPaovbspline(
  formula,
  order = 2,
  nknots = dim(model.response(model.frame(formula)))[2],
  B = 1000,
  method = "residuals"
)

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.
`order`	Order of the B-spline basis expansion. The default is `order=2`.
`nknots`	Number of knots of the B-spline basis expansion. The default is `nknots=dim(data1)[2]`.
`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.

Value

ITPaovbspline returns an object of class "ITPaov". The function summary is used to obtain and print a summary of the results. An object of class "ITPaov" 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.
`basis`	String vector indicating the basis used for the first phase of the algorithm. In this case equal to `"B-spline"`.
`coeff`	Matrix of dimensions `c(n,p)` of the `p` coefficients of the B-spline basis expansion. Rows are associated to units and columns to the basis index.
`coeff.regr`	Matrix of dimensions `c(L+1,p)` of the `p` coefficients of the B-spline basis expansion of the intercept (first row) and the `L` effects of the covariates specified in `formula`. Columns are associated to the basis index.
`pval.F`	Unadjusted p-values of the functional F-test for each basis coefficient.
`pval.matrix.F`	Matrix of dimensions `c(p,p)` of the p-values of the multivariate F-tests. The element `(i,j)` of matrix `pval.matrix` contains the p-value of the joint NPC test of the components `(j,j+1,...,j+(p-i))`.
`adjusted.pval.F`	Adjusted p-values of the functional F-test for each basis coefficient.
`pval.factors`	Unadjusted p-values of the functional F-tests on each factor of the analysis of variance, separately (rows) and each basis coefficient (columns).
`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

A. Pini and S. Vantini (2017). The Interval Testing Procedure: Inference for Functional Data Controlling the Family Wise Error Rate on Intervals. Biometrics 73(3): 835–845.

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 ITP
ITP.result <- ITPaovbspline(temperature ~ groups,B=1000,nknots=20,order=3)

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

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

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

alessiapini/fdatest documentation built on April 17, 2024, 8:39 p.m.