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 = 1000L, 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.
# 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 = 2L)
# Summary of the IWT results
summary(IWT.result)
# Plot of the IWT results
graphics::layout(1)
plot(
IWT.result,
main = 'NASA data',
plot_adjpval = TRUE,
xlab = 'Day',
xrange = c(1, 365)
)
# All graphics on the same device
graphics::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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