Local Two-Sample Test for Network-Valued Data

Usage

test2_local(
  x,
  y,
  partition,
  representation = "adjacency",
  distance = "frobenius",
  stats = c("flipr:t_ip", "flipr:f_ip"),
  B = 1000L,
  alpha = 0.05,
  test = "exact",
  k = 5L,
  seed = NULL,
  verbose = FALSE
)

Arguments

x: Either an object of class nvd listing networks in sample 1 or a distance matrix of size \(n_1 + n_2\).
y: Either an object of class nvd listing networks in sample 2 or an integer value specifying the size of sample 1 or an integer vector specifying the indices of the observations belonging to sample 1.
partition: Either a list or an integer vector specifying vertex memberships into partition elements.
representation: A string specifying the desired type of representation, among: "adjacency", "laplacian" and "modularity". Defaults to "adjacency".
distance: A string specifying the chosen distance for calculating the test statistic, among: "hamming", "frobenius", "spectral" and "root-euclidean". Defaults to "frobenius".
stats: A character vector specifying the chosen test statistic(s), among: "original_edge_count", "generalized_edge_count", "weighted_edge_count", "student_euclidean", "welch_euclidean" or any statistics based on inter-point distances available in the flipr package: "flipr:student_ip", "flipr:fisher_ip", "flipr:bg_ip", "flipr:energy_ip", "flipr:cq_ip". Defaults to c("flipr:student_ip", "flipr:fisher_ip").
B: The number of permutation or the tolerance. If this number is lower than 1, it is intended as a tolerance. Otherwise, it is intended as the number of required permutations. Defaults to 1000L.
alpha: Significance level for hypothesis testing. If set to 1, the function outputs properly adjusted p-values. If lower than 1, then only p-values lower than alpha are properly adjusted. Defaults to 0.05.
test: A character string specifying the formula to be used to compute the permutation p-value. Choices are "estimate", "upper_bound" and "exact". Defaults to "exact" which provides exact tests.
k: An integer specifying the density of the minimum spanning tree used for the edge count statistics. Defaults to 5L.
seed: An integer for specifying the seed of the random generator for result reproducibility. Defaults to NULL.
verbose: Boolean specifying whether information on intermediate tests should be printed in the process (default: FALSE).

Value

A length-2 list reporting the adjusted p-values of each element of the partition for the intra- and inter-tests.

Examples

n <- 5L
p1 <- matrix(
  data = c(0.1, 0.4, 0.1, 0.4,
           0.4, 0.4, 0.1, 0.4,
           0.1, 0.1, 0.4, 0.4,
           0.4, 0.4, 0.4, 0.4),
  nrow = 4,
  ncol = 4,
  byrow = TRUE
)
p2 <- matrix(
  data = c(0.1, 0.4, 0.4, 0.4,
           0.4, 0.4, 0.4, 0.4,
           0.4, 0.4, 0.1, 0.1,
           0.4, 0.4, 0.1, 0.4),
  nrow = 4,
  ncol = 4,
  byrow = TRUE
)
sim <- sample2_sbm(n, 68, p1, c(17, 17, 17, 17), p2, seed = 1234)
m <- as.integer(c(rep(1, 17), rep(2, 17), rep(3, 17), rep(4, 17)))
test2_local(sim$x, sim$y, m,
            seed = 1234,
            alpha = 0.05,
            B = 19)
#> $intra
#> # A tibble: 4 × 3
#>   E     pvalue truncated
#>   <chr>  <dbl> <lgl>    
#> 1 P1    0.548  TRUE     
#> 2 P2    0.548  TRUE     
#> 3 P3    0.0480 FALSE    
#> 4 P4    0.548  TRUE     
#> 
#> $inter
#> # A tibble: 6 × 4
#>   E1    E2    pvalue truncated
#>   <chr> <chr>  <dbl> <lgl>    
#> 1 P1    P2    0.548  TRUE     
#> 2 P1    P3    0.0480 FALSE    
#> 3 P1    P4    0.548  TRUE     
#> 4 P2    P3    0.0480 FALSE    
#> 5 P2    P4    0.548  TRUE     
#> 6 P3    P4    0.0480 FALSE    
#>