rofanova: Robust Functional Analysis of Variance
In rofanova: Robust Functional Analysis of Variance

Description Usage Arguments Value References See Also Examples

View source: R/functions.R

Robust Functional Analysis of Variance (RoFANOVA) allows identifying the presence of significant differences, in terms of functional mean, among groups of a functional data by being robust against the presence of outliers (Centofanti et al., 2021).

rofanova(
  X,
  label_1,
  label_2 = NULL,
  B = 100,
  cores = 1,
  family = "bisquare",
  eff = 0.95,
  mu0_g = NULL,
  scale = NULL,
  maxit = 50,
  tol = 1e-04
)

`X`	Either an object of class `fdata` for monodimensional functional data or an object of class `fdata2d` for bi-dimensional functional data.
`label_1`	A vector of containing group label corresponding to the first main effect.
`label_2`	A vector of containing group label corresponding to the second main effect. If it is NULL, the one-way RoFANOVA is performed. Otherwise, the two-way RoFANOVA with interaction is employed. Default is NULL.
`B`	The number of permutations used to approximate the p-value in the permutation test. Default is 1000.
`cores`	If `cores`>1, then parallel computing is used, with `cores` cores. Default is 1.
`family`	The family of loss function for the calculation of the equivariant functional M-estimator. The values allowed are "bisquare" for the bisquare or Tukey's biweight family of loss functions; "huber" for the the Huber's family of loss functions; "optimal" for the optimal family of loss functions; "hampel" for the the Hampel's family of loss functions; "median" for the median loss function. A non-robust functional estimator of the mean based on the standard least squares loss function is used with the value "mean". Default is "bisquare".
`eff`	Asymptotic efficiency of the equivariant functional M-estimator. When `family` is either "mean" or "median", `eff` is ignored.
`mu0_g`	Initial estimate used in re-weighted least-squares algorithm to compute the equivariant functional M-estimator. If NULL the standard non-robust functional mean is used. Default is NULL.
`scale`	Estimate of the standard error of `X`. If NULL, the functional normalized median absolute deviation estimator is used. Default is NULL.
`maxit`	The maximum number of iterations allowed in the re-weighted least-squares algorithm to compute the equivariant functional M-estimator.
`tol`	The tolerance for the stopping condition of the re-weighted least-squares algorithm to compute the equivariant functional M-estimator. The algorithm stops when the relative variation of the weighted norm sum between two consecutive iterations is less than `tol`.

pval_vec Vector of p-value of corresponding to the test of significance of the whole model, the main effects and the interaction. For one-way RoFANOVA, it is the p-value corresponding to the test of the main effect.

Tr_obs The observed value of the test statistic.

Tr_perm The values of the test statistic for each permutation.

mod A list containing the following arguments:

Tr: The observed value of the test statistic.
global_mean: The robust estimate of functional grand mean.
group_mean_1: The robust estimate of the first functional main effect.
group_mean_2: The robust estimate of the second functional main effect. For one-way RoFANOVA, it is NULL.
group_mean_ij: The robust estimate of the group functional mean. For one-way, it RoFANOVA is NULL.
scale: The robust estimate of functional standard deviation.
scale_1: The robust estimate of functional standard deviation corresponding to the first functional main effect.
scale_2: The robust estimate of functional standard deviation corresponding to the second functional main effect. For one-way RoFANOVA, it is NULL.
scale_re: The robust estimate of the functional standard deviation of the error distribution. For one-way RoFANOVA, it is NULL.
X: The variable X.
label_1: The vector of containing group label corresponding to the first main effect.
label_2: The vector of containing group label corresponding to the second main effect. For one-way RoFANOVA, it is NULL.
family: The family of loss function for the calculation of the equivariant functional M-estimator.

Centofanti, F., Colosimo, B.M., Grasso, M.L., Menafoglio, A., Palumbo, B., Vantini, S. (2021). Robust Functional ANOVA with Application to Additive Manufacturing. arXiv preprint arXiv:2112.10643.

fusem funmad

library(rofanova)
data_out<-simulate_data(scenario="one-way")
label_1=data_out$label_1
X_fdata<-data_out$X_fdata
B=10
cores=1
per_list_median<-rofanova(X_fdata,label_1,B = B,family="median",cores=cores)
pvalue_median_vec<-per_list_median$pval_vec
per_list_huber<-rofanova(X_fdata,label_1,B = B,family="huber",cores=cores)
pvalue_huber_vec<-per_list_huber$pval_vec
per_list_bisquare<-rofanova(X_fdata,label_1,B = B,family="bisquare",cores=cores)
pvalue_bisquare_vec<-per_list_bisquare$pval_vec
per_list_hampel<-rofanova(X_fdata,label_1,B = B,family="hampel",cores=cores)
pvalue_hampel_vec<-per_list_hampel$pval_vec
per_list_optimal<-rofanova(X_fdata,label_1,B = B,family="optimal",cores=cores)
pvalue_optimal<-per_list_optimal$pval