IWTlm | R Documentation |
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 interval-wise testing procedure (IWT) for testing the significance of the effects of scalar covariates on a functional population.
IWTlm(formula, B = 1000, method = "residuals", dx = NULL, recycle = TRUE)
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 |
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. |
recycle |
flag specifying whether the recycled version of IWT has to be used. |
IWTlm
returns an object of class
"IWTlm
". 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. |
pval_matrix_F |
Matrix of dimensions c(p,p) of the p-values of the interval-wise F-tests. The element (i,j) of matrix pval_matrix_F contains the p-value of the test on interval (j,j+1,...,j+(p-i)). |
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). |
pval_matrix_part |
Array of dimensions c(L+1,p,p) of the p-values of the interval-wise t-tests on covariates. The element (l,i,j) of array pval_matrix_part contains the p-value of the test of covariate l on interval (j,j+1,...,j+(p-i)). |
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. |
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.
See summary.IWTlm
for summaries and plot.IWTlm
for plotting the results.
See ITPlmbspline
for a functional linear model test based on an a-priori selected B-spline basis expansion.
See also IWTaov
to fit and test a functional analysis of variance applying the IWT, and IWT1
, IWT2
for one-population and two-population tests.
# 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 IWT
IWT.result <- IWTlm(temperature ~ groups,B=1000)
# Summary of the IWT results
summary(IWT.result)
# Plot of the IWT results
layout(1)
plot(IWT.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(IWT.result,main='NASA data', plot_adjpval = TRUE,xlab='Day',xrange=c(1,365))
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