GET (version 0.1-3)

frank.fglm: F rank functional GLM

Description

Multiple testing in permutation inference for the general linear model (GLM)

Usage

frank.fglm(nsim, formula.full, formula.reduced, curve_sets,
  factors = NULL, ..., GET.args = NULL, mc.cores = 1,
  mc.args = NULL)

Arguments

nsim

The number of random permutations.

formula.full

The formula specifying the general linear model, see formula in lm.

formula.reduced

The formula of the reduced model with nuisance factors only.

curve_sets

A named list of sets of curves giving the dependent variable (Y), and possibly additionally all the factors. The dimensions of the elements should match with each other, i.e. the factor values should be given for each argument value and each function. If factors are given in the argument factors, then can also be just the curve set representing Y. Also fdata objects allowed.

factors

A data frame of factors. An alternative way to specify factors when they are constant for all argument values. The number of rows of the data frame should be equal to the number of curves. Each column should specify the values of a factor.

...

Additional arguments to be passed to lm.

GET.args

A named list of additional arguments to be passed to global_envelope_test.

mc.cores

The number of cores to use, i.e. at most how many child processes will be run simultaneously. Must be at least one, and parallelization requires at least two cores. On a Windows computer mc.cores must be 1 (no parallelization). For details, see mclapply, for which the argument is passed. Parallelization can be used in generating simulations and in calculating the second stage tests.

mc.args

A named list of additional arguments to be passed to mclapply. Only relevant if mc.cores is more than 1.

Value

A global_envelope object, which can be printed and plotted directly.

Details

The function frank.fglm performs a nonparametric test of significance of a covariate in the functional GLM. Similarly as in the graphical functional GLM (graph.fglm), the Freedman-Lane algorithm (Freedman and Lane, 1983) is applied to permute the functions (to obtain the simulations under the null hypothesis of "no effects"); consequently, the test approximately achieves the desired significance level. In contrast to the graphical functional GLM, the F rank functional GLM is based on the F-statistics, that are calculated at each argument value of the functions. The global envelope test is applied to the observed and simulated F-statistics. The test is able to find if the factor of interest is significant and also which argument values of the functional domain are responsible for the potential rejection.

References

Mrkvi<U+010D>ka, T., Myllym<U+00E4>ki, M. and Narisetty, N. N. (2019) New methods for multiple testing in permutation inference for the general linear model. arXiv:1906.09004 [stat.ME]

Freedman, D., & Lane, D. (1983) A nonstochastic interpretation of reported significance levels. Journal of Business & Economic Statistics, 1(4), 292-298. doi:10.2307/1391660

Examples

# NOT RUN {
data(GDPtax)
factors.df <- data.frame(Group = GDPtax$Group, Tax = GDPtax$Profittax)
# }
# NOT RUN {
res.tax_within_group <- frank.fglm(nsim = 999,
                                   formula.full = Y~Group+Tax+Group:Tax,
                                   formula.reduced = Y~Group+Tax,
                                   curve_sets = list(Y=GDPtax$GDP),
                                   factors = factors.df)
# }
# NOT RUN {
plot(res.tax_within_group)
# }