Globallm | 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 global testing procedure for testing the significance of the effects of scalar covariates on a functional population.
Globallm(
formula,
B = 1000,
method = "residuals",
dx = NULL,
recycle = TRUE,
stat = "Integral"
)
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. |
stat |
Type of test statistic used for the global test. Possible values are: |
Globallm
returns an object of class
"IWTlm
". The function summary
is used to obtain and print a summary of the results.
This object is a list containing 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). |
Global_pval_F |
Global p-value of the overall test F. |
Global_pval_part |
Global p-value of t-test involving each covariate separately. |
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. |
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 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
Global.result <- Globallm(temperature ~ groups,B=1000)
# Summary of the IWT results
summary(Global.result)
# Plot of the IWT results
layout(1)
plot(Global.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(Global.result,main='NASA data', plot_adjpval = TRUE,xlab='Day',xrange=c(1,365))
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