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Compare Network-Level Statistics of Two Networks

Source: R/vertex_bootstrap.R
vertex_compare.Rd

Snijders & Borgatti (1999) two-network test: each network's statistics get vertex-bootstrap standard errors, and each difference is tested with $$z = (\hat{\theta}_x - \hat{\theta}_y) / \sqrt{SE_x^2 + SE_y^2}$$ against a standard normal reference. This is the comparison the vertex bootstrap was originally proposed for: deciding whether two observed networks differ in density, centralization, reciprocity, or any other whole-network descriptive.

Usage

vertex_compare(
  x,
  y,
  iter = 1000L,
  ci_level = 0.05,
  statistics = NULL,
  statistic_fn = NULL,
  directed = NULL,
  seed = NULL,
  labels = c("x", "y")
)

Arguments

x, y

The two networks: netobjects, cograph_networks, square weight matrices, or precomputed net_vertex_bootstrap objects (then iter, statistics, statistic_fn, directed, and seed are ignored for that argument). The two sides must cover exactly the same statistics; a mismatch (e.g., a directed network's reciprocity against an undirected one, or precomputed objects built with different statistics selections) is an error, never a silent subset.

iter

Integer. Number of bootstrap replicates (default 1000).

ci_level

Numeric. Significance level for the confidence intervals (default 0.05 for 95% CIs).

statistics

Character vector selecting built-in statistics (see Details). Default: all applicable to the network's directedness.

statistic_fn

Optional named list of functions, each taking the weight matrix and returning a single numeric value. Computed alongside the built-ins.

directed

Logical or NULL. Directedness of the network. NULL (default) reads x$directed when available, otherwise falls back to matrix symmetry.

seed

Integer or NULL. RNG seed for reproducibility.

labels

Character vector of length 2 naming the networks in the output (default c("x", "y")).

Value

An object of class "net_vertex_comparison" containing:

summary

Tidy data frame, one row per statistic: statistic, the two observed values, diff, se_diff, z, p_value, and a normal-approximation confidence interval for the difference.

x, y

The two net_vertex_bootstrap results.

labels, ci_level

Configuration.

When both bootstrap SEs are zero (a statistic with no resampling variation in either network) z and p_value are NA.

References

Snijders, T. A. B., & Borgatti, S. P. (1999). Non-parametric standard errors and tests for network statistics. Connections, 22(2), 161-170.

See also

vertex_bootstrap, nct for the permutation-based comparison of edge-level structure when raw data are available, permutation.

Examples

states <- c("plan", "code", "debug", "test")
s1 <- data.frame(
  T1 = rep(states, 5), T2 = rep(rev(states), 5),
  T3 = rep(states[c(2, 3, 4, 1)], 5)
)
s2 <- data.frame(
  T1 = rep(states[c(3, 1, 4, 2)], 5), T2 = rep(states, 5),
  T3 = rep(states[c(4, 3, 1, 2)], 5)
)
net1 <- build_network(s1, method = "relative")
net2 <- build_network(s2, method = "relative")
cmp <- vertex_compare(net1, net2, iter = 100, seed = 1)
cmp$summary
#>        statistic observed_x observed_y        diff    se_diff          z
#> 1        density  0.5000000  0.5833333 -0.08333333 0.25478584 -0.3270721
#> 2    mean_weight  0.5000000  0.5714286 -0.07142857 0.09622256 -0.7423267
#> 3 centralization  0.3333333  0.0000000  0.33333333 0.24140627  1.3807981
#> 4    reciprocity  1.0000000  0.2500000  0.75000000 0.35488859  2.1133393
#>      p_value    ci_lower  ci_upper
#> 1 0.74361337 -0.58270441 0.4160377
#> 2 0.45788942 -0.26002131 0.1171642
#> 3 0.16734104 -0.13981427 0.8064809
#> 4 0.03457174  0.05443114 1.4455689