TWTlm: Threshold-wise testing procedure for testing...

In alessiapini/fdatest: Interval Wise Testing for Functional Data

Threshold-wise testing procedure for testing functional-on-scalar linear models

Description

The function is used to fit and test functional linear models. It can be used to carry out regression, and analysis of variance. It implements the Threshold-wise testing procedure (TWT) for testing the significance of the effects of scalar covariates on a functional population.

Usage

TWTlm(formula, B = 1000, method = "residuals", dx = NULL)

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. Example: y ~ A + B where: y is a matrix of dimension n * p containing the point-wise evaluations of the n functional data on p points or an object of class fd (see fda package) containing the functional data set A, B are n-dimensional vectors containing the values of two covariates. Covariates may be either scalar or factors.
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	step size for the point-wise evaluations of functional data. dx is only used ia an object of class 'fd' is provided as response in the formula.

Value

TWTlm returns an object of class "TWTlm". The function summary is used to obtain and print a summary of the results. An object of class "ITPlm" is a list containing at least the following components:

call	call of the function.
design_matrix	design matrix of the linear model.
unadjusted_pval_F	unadjusted p-value function of the F test.
adjusted_pval_F	adjusted p-value function of the F test.
unadjusted_pval_part	unadjusted p-value functions of the functional t-tests on each covariate, separately (rows) on each domain point (columns).
adjusted_pval_part	adjusted p-values of the functional t-tests on each covariate (rows) on each domain point (columns).
data.eval	evaluation of functional data.
coeff.regr.eval	evaluation of the regression coefficients.
fitted.eval	evaluation of the fitted values.
residuals.eval	evaluation of the residuals.
R2.eval	evaluation of the functional R-suared.

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.

See Also

See summary.TWTlm for summaries and plot.TWTlm for plotting the results. See ITPlmbspline for a functional linear model test based on an a-priori selected B-spline basis expansion. See also TWTaov to fit and test a functional analysis of variance applying the TWT, and TWT1, TWT2 for one-population and two-population tests.

Examples

# Importing the NASA temperatures data set
data(NASAtemp)
# Defining the covariates
temperature <- rbind(NASAtemp$milan,NASAtemp$paris)
groups <- c(rep(0,22),rep(1,22))

# Performing the TWT
TWT.result <- TWTlm(temperature ~ groups,B=1000)
# Summary of the TWT results
summary(TWT.result)

# Plot of the TWT results
layout(1)
plot(TWT.result,main='NASA data', plot_adjpval = TRUE,xlab='Day',xrange=c(1,365))

# All graphics on the same device
layout(matrix(1:6,nrow=3,byrow=FALSE))
plot(TWT.result,main='NASA data', plot_adjpval = TRUE,xlab='Day',xrange=c(1,365))

alessiapini/fdatest documentation built on April 28, 2024, 12:35 a.m.