Network Comparison Test

Permutation test for whether two groups' Gaussian graphical models differ, on three invariants (van Borkulo et al. 2022): network structure (M, the largest absolute edge difference), global strength (S, the difference in summed absolute edge weights; with abs = FALSE, summed signed weights, i.e. global expected influence) and individual edges (E). Networks are EBIC graphical lassos (clean-room pure R). Equivalent in purpose to NetworkComparisonTest::NCT(), and equal to it in its permutation draws: under the same seed both permute the same rows, so the two differ only by the glasso solver's convergence tolerance.

Usage

net_compare(
  data1,
  data2 = NULL,
  iter = 1000L,
  gamma = 0.5,
  paired = FALSE,
  abs = TRUE,
  weighted = TRUE,
  p_adjust = "none",
  na_method = c("pairwise", "listwise")
)

Arguments

data1, data2

Numeric data frames/matrices with the same variables. When data1 is a psychnet_group, data2 names the two levels to compare (defaulting to its two levels when there are exactly two).

iter

Number of permutations. Default 1000.

gamma

EBIC hyperparameter. Default 0.5.

paired

Logical; within-row swapping for paired designs (row i of data1 and of data2 are the same unit). Default FALSE.

abs

Logical; compare absolute edge weights. Default TRUE.

weighted

Logical; if FALSE, binarize networks first. Default TRUE.

p_adjust

Multiple-comparison adjustment for per-edge p-values (any stats::p.adjust method). Default "none".

na_method

"pairwise" (default) or "listwise" handling of missing values; see Details.

Value

An object of class psychnet_nct, a list with $nw1, $nw2 (the two estimated weighted adjacency matrices); the three tests, each with observed, perm and p_value: $structure (statistic M, the largest absolute edge difference), $strength (statistic S, the absolute difference in global strength; also by_group, each network's global strength) and $E (per-edge absolute differences; also edge_names, a from/to data frame aligned to the per-edge vector); plus n_iter, n (rows used per group), groups (display names: the argument names, or the group levels), paired and params. The letters follow van Borkulo et al. (2022) and NetworkComparisonTest; $M and $S (which before psychnets 0.6.0 held the two global tests the other way round) raise a psychnet_renamed error. Printing the object shows every result; as tables, summary() gives the M and S tests and as.data.frame() one row per edge (see summary.psychnet_nct()).

Errors of class psychnet_bad_input for malformed arguments or groups whose columns differ (in name or order); of class psychnet_degenerate_sample when (pairwise) a variable pair shares fewer than two observed rows in a group or a permuted split. Warnings of class psychnet_constant_variable (a constant variable in an observed group) and psychnet_estimator_mismatch (a group object built with an estimator or settings other than EBIC glasso).

Details

The two groups must hold the same variables in the same order (non-numeric columns such as an id or a group label are dropped first).

Missing data follow na_method. "pairwise" (default) keeps every row, permutes rows as usual, and estimates each (sub)sample from its pairwise-complete correlation matrix (projected to the nearest positive definite correlation matrix), with the median pairwise co-observation count as the sample size – the same treatment as ebic_glasso(). "listwise" drops incomplete rows first (in a paired design, a pair is dropped when either member is incomplete). Complete data are unaffected by the choice.

A variable without variation in a group, or in a permuted split (a rare binary item can be constant in a split), enters that network as an isolated node – the convention of every psychnets estimator for a constant column. The statistic is then defined on every split, so the permutation test stays exact. A constant variable in an observed group raises a psychnet_constant_variable warning.

References

van Borkulo, C. D., van Bork, R., Boschloo, L., Kossakowski, J. J., Tio, P., Schoevers, R. A., Borsboom, D., & Waldorp, L. J. (2022). Comparing network structures on three aspects: A permutation test. Psychological Methods. doi:10.1037/met0000476

Examples

set.seed(1)
a <- matrix(stats::rnorm(100 * 4), 100, 4)
b <- matrix(stats::rnorm(100 * 4), 100, 4)
colnames(a) <- colnames(b) <- paste0("V", 1:4)
fit <- net_compare(a, b, iter = 10)  # iter >= 1000 for real use
fit
#> Network Comparison Test: a vs b
#> 10 permutations, independent groups, n = 100 and 100
#> 
#>   Test                  Statistic       p
#>   M  network structure      0.000   1.000 
#>   S  global strength        0.000   1.000 
#>        a 0.000 vs b 0.000
#>   E  edges differing       0 of 6
#> 
#>   Edges, largest difference first
#>   Edge          a       b  |diff|       p
#>   V1 - V2   0.000   0.000   0.000   1.000 
#>   V1 - V3   0.000   0.000   0.000   1.000 
#>   V1 - V4   0.000   0.000   0.000   1.000 
#>   V2 - V3   0.000   0.000   0.000   1.000 
#>   V2 - V4   0.000   0.000   0.000   1.000 
#>   V3 - V4   0.000   0.000   0.000   1.000 
#> 
#>   * p < 0.05
summary(fit)
#>                test statistic observed p_value significant
#> 1 network structure         M        0       1       FALSE
#> 2   global strength         S        0       1       FALSE
as.data.frame(fit)
#>   from to weight_1 weight_2 difference p_value significant
#> 1   V1 V2        0        0          0       1       FALSE
#> 2   V1 V3        0        0          0       1       FALSE
#> 3   V2 V3        0        0          0       1       FALSE
#> 4   V1 V4        0        0          0       1       FALSE
#> 5   V2 V4        0        0          0       1       FALSE
#> 6   V3 V4        0        0          0       1       FALSE