Network Comparison Test — nct • Nestimate

Tests whether two networks estimated from independent samples differ at three levels: global strength (M-statistic), network structure (S-statistic, max absolute edge difference), and individual edges (E-statistic per edge). Inference is via permutation of group labels.

Usage

nct(
  data1,
  data2,
  iter = 1000L,
  gamma = 0.5,
  paired = FALSE,
  abs = TRUE,
  weighted = TRUE,
  p_adjust = "none"
)

# S3 method for class 'net_nct'
print(x, ...)

# S3 method for class 'net_nct'
summary(object, ...)

Arguments

data1: A numeric matrix or data.frame of observations from group 1.
data2: A numeric matrix or data.frame of observations from group 2. Same number of columns as data1.
iter: Integer. Number of permutation iterations. Default 1000.
gamma: EBIC tuning parameter for glasso. Default 0.5.
paired: Logical. If TRUE, perform a paired permutation (within-subject swap). Default FALSE.
abs: Logical. If TRUE, compute global strength on absolute edge weights. Default TRUE.
weighted: Logical. If TRUE, use weighted networks for the tests. If FALSE, binarize before computing statistics. Default TRUE.
p_adjust: P-value adjustment method for the per-edge tests (any method in stats::p.adjust.methods). Default "none".
x: For the print() method: an object of class net_nct.
...: In print.net_nct() and summary.net_nct(): Ignored.
object: For the summary() method: an object of class net_nct.

Value

A list of class net_nct with elements:

nw1, nw2: Estimated weighted adjacency matrices.
M: List with observed, perm, p_value for the global strength test. P-values are permutation p-values, (sum(perm >= observed) + 1) / (iter + 1).
S: Same structure for the maximum absolute edge difference.
E: Same structure for the per-edge tests (observed and p_value are one value per upper-triangle edge, perm an iter by edges matrix), plus edge_names, a two-column data frame of the node pairs (NULL when data1 has no column names).
n_iter: Number of permutations.
paired: Whether a paired test was used.
params: List of the settings used: gamma, abs, weighted, p_adjust.

In print.net_nct(): The input object, invisibly.

In summary.net_nct(): A data frame with columns from, to, diff_observed, p_value, significant. Attributes m_stat and s_stat each hold a one-row data frame with observed and p_value.

Details

Follows NetworkComparisonTest::NCT() with defaults abs = TRUE, weighted = TRUE, paired = FALSE. The network estimator is EBIC-selected glasso applied to a Pearson correlation matrix, with Matrix::nearPD symmetrization (matching NCT's NCT_estimator_GGM default). The glasso solver is not the Fortran one NCT wraps, so results agree to independent-solver precision (of the order of 1e-4 on the test statistics) rather than bit-for-bit, even under the same seed.

Methods

summary.net_nct(): Returns a tidy data frame with one row per edge test. The global M (strength) and S (structure) statistics are attached as attributes.

Examples

set.seed(1)
x1 <- matrix(rnorm(100 * 4), 100, 4)
x2 <- matrix(rnorm(100 * 4), 100, 4)
colnames(x1) <- colnames(x2) <- paste0("V", 1:4)
# iter = 20 keeps the example fast; a real analysis uses 1000 or more.
res <- nct(x1, x2, iter = 20)
res
#> Network Comparison Test  [20 permutations | unpaired]
#>   Global strength (M):  observed = 0.0000   p = 1.0000
#>   Network structure (S): observed = 0.0000   p = 1.0000
#>   Edge tests (E):       6 edges, 0 significant at p < 0.05
summary(res)
#>   from to diff_observed p_value significant
#> 1   V1 V2             0       1       FALSE
#> 2   V1 V3             0       1       FALSE
#> 3   V2 V3             0       1       FALSE
#> 4   V1 V4             0       1       FALSE
#> 5   V2 V4             0       1       FALSE
#> 6   V3 V4             0       1       FALSE