Bootstrap a Network Estimate

Non-parametric bootstrap for any network estimated by build_network. Works with all built-in methods (transition and association) as well as custom registered estimators.

For transition methods ("relative", "frequency", "co_occurrence"), uses a fast pre-computation strategy: per-sequence count matrices are computed once, and each bootstrap iteration only resamples sequences via colSums (C-level) plus lightweight post-processing. Data must be in wide format for transition bootstrap; use convert_sequence_format to convert long-format data first.

For association methods ("cor", "pcor", "glasso", and custom estimators), the full estimator is called on resampled rows each iteration.

If a transition network contains only one sequence, the function warns that such a network is not recommended for bootstrap or other confirmatory testing.

Usage

bootstrap_network(
  x,
  iter = 1000L,
  ci_level = 0.05,
  inference = "stability",
  consistency_range = c(0.75, 1.25),
  edge_threshold = NULL,
  seed = NULL,
  boundary = c("inclusive", "strict"),
  ci_method = c("percentile", "basic"),
  actor = NULL
)

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

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

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

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

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

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

Arguments

x: A netobject from build_network. The data, method, params, scaling, threshold, and level are all extracted from this object. A cograph_network is coerced first; a netobject_group or mcml bootstraps every constituent network, and a wtna_mixed bootstraps both of its components (see Value). For the print() method: an object of class net_bootstrap, net_bootstrap_group or wtna_boot_mixed.
iter: Integer. Number of bootstrap iterations (default: 1000).
ci_level: Numeric. Significance level for CIs and p-values (default: 0.05).
inference: Character. "stability" (default) tests whether bootstrap replicates fall within a multiplicative consistency range around the original weight. "threshold" tests whether replicates exceed a fixed edge threshold.
consistency_range: Numeric vector of length 2. Multiplicative bounds for stability inference (default: c(0.75, 1.25)).
edge_threshold: Numeric or NULL. Fixed threshold for inference = "threshold". If NULL, defaults to the 10th percentile of absolute original edge weights.
seed: Integer or NULL. RNG seed for reproducibility.
boundary: Character. Comparison rule when computing the consistency-range p-value. "inclusive" (default, tna-compatible) counts iterations that meet the bound ($\le$ / $\ge$); "strict" counts only iterations strictly outside ($<$ / $>$).
ci_method: Character. Method for the edge-weight confidence intervals. "percentile" (default) uses the empirical bootstrap quantiles (Efron). "basic" reflects those quantiles around the observed weight, $(2\hat{\theta} - q_{1-\alpha/2}, 2\hat{\theta} - q_{\alpha/2})$ (Davison & Hinkley 1997, eq. 5.6), which corrects first-order bootstrap bias but can produce bounds outside the natural weight range near boundaries (e.g., below 0 for transition probabilities close to 0).
actor: Character or NULL. Name of the column identifying the actor each sequence belongs to (e.g. "student_id" for sessions nested in students, "Group" for students nested in teams), looked up in the network's $metadata or wide sequence data. When supplied, whole actors are resampled; see the section Nested data and actor. Default NULL: sequences are resampled individually.
...: In print.net_bootstrap(), print.wtna_boot_mixed(), summary.net_bootstrap() and summary.wtna_boot_mixed(): Additional arguments (ignored). In print.net_bootstrap_group() and summary.net_bootstrap_group(): Ignored.
object: For the summary() method: an object of class net_bootstrap, net_bootstrap_group or wtna_boot_mixed.

Value

An object of class "net_bootstrap" containing:

original: The original netobject.
mean: Bootstrap mean weight matrix.
sd: Bootstrap SD matrix.
p_values: P-value matrix.
significant: Original weights where p < ci_level, else 0.
ci_lower: Lower CI bound matrix.
ci_upper: Upper CI bound matrix.
cr_lower: Consistency range lower bound (stability only).
cr_upper: Consistency range upper bound (stability only).
summary: Long-format data frame, one row per non-zero original edge (undirected networks keep one row per unordered pair), with columns from, to, weight, mean, sd, p_value, sig, ci_lower, ci_upper, plus cr_lower and cr_upper when inference = "stability".
model: Pruned netobject (non-significant edges zeroed).
method, params, iter, ci_level, inference, ci_method: Bootstrap config.
consistency_range, edge_threshold: Inference parameters.
actor, n_actors: The actor column and its number of actors; NULL without actor.
clustering: Only with actor. One-row data frame: n_sequences, n_actors, icc, icc_ci_lower, icc_ci_upper, deff_edges.
clustering_edges: Only with actor. One row per edge of summary: from, to, icc, sd_actor, sd_sequence, deff.

A netobject_group or mcml input returns a "net_bootstrap_group" (named list of net_bootstrap results); a wtna_mixed input returns a "wtna_boot_mixed" with $transition and $cooccurrence results.

In print.net_bootstrap() and print.wtna_boot_mixed(): The input object, invisibly.

In summary.net_bootstrap(): The $summary data frame: one row per non-zero original edge, with columns from, to, weight, mean, sd, p_value, sig, ci_lower, ci_upper, plus cr_lower and cr_upper when the bootstrap used inference = "stability".

In print.net_bootstrap_group(): x invisibly.

In summary.net_bootstrap_group(): The per-group summaries stacked into one data frame: the columns of summary.net_bootstrap prefixed by a group column naming the network each row came from.

In summary.wtna_boot_mixed(): A list with $transition and $cooccurrence summary data frames.

Nested data and `actor`

The bootstrap resamples sequences as independent units. When sequences are nested in actors (sessions in students, students in teams), actor names the column identifying the actor, and whole actors are resampled with replacement, keeping all their sequences together: the cluster bootstrap that resamples at the top level only (Davison & Hinkley, 1997, section 3.8; Field & Welsh, 2007). The number of sequences per replicate then varies with the actors drawn.

With actor, the result also reports the nesting effect. The ICC is the proportion of the total variance that lies between actors (Shrout & Fleiss, 1979); an ICC close to 0 indicates little evidence of a nesting effect. It is computed as in permutation. The design effect is the ratio of the variance under the nested design to the variance had the sequences been sampled independently (Kish, 1965): here, the variance of the edge weights over actor-level replicates divided by their variance over sequence-level replicates drawn in the same run, reported as the median over edges. actor is available for transition networks ("relative", "frequency", "co_occurrence").

References

Davison, A. C., & Hinkley, D. V. (1997). Bootstrap Methods and Their Application. Cambridge University Press.

Field, C. A., & Welsh, A. H. (2007). Bootstrapping clustered data. Journal of the Royal Statistical Society: Series B, 69(3), 369-390.

Kish, L. (1965). Survey Sampling. Wiley.

Shrout, P. E., & Fleiss, J. L. (1979). Intraclass correlations: Uses in assessing rater reliability. Psychological Bulletin, 86(2), 420-428.

Examples

net <- build_network(data.frame(V1 = c("A","B","C"), V2 = c("B","C","A")),
  method = "relative")
boot <- bootstrap_network(net, iter = 10)
# \donttest{
set.seed(1)
seqs <- data.frame(
  V1 = sample(LETTERS[1:4], 30, TRUE), V2 = sample(LETTERS[1:4], 30, TRUE),
  V3 = sample(LETTERS[1:4], 30, TRUE), V4 = sample(LETTERS[1:4], 30, TRUE)
)
net <- build_network(seqs, method = "relative")
boot <- bootstrap_network(net, iter = 100)
print(boot)
#> Bootstrap Network  [Transition Network (relative) | directed]
#>   Iterations : 100  |  Nodes : 4
#>   Edges      : 0 significant / 16 total
#>   CI         : 95%  |  Inference: stability  |  CR [0.75, 1.25]
summary(boot)
#>    from to    weight      mean         sd   p_value   sig   ci_lower  ci_upper
#> 1     A  A 0.1304348 0.1274665 0.08074773 0.6831683 FALSE 0.00000000 0.3022826
#> 2     A  B 0.3043478 0.2997861 0.08278592 0.3663366 FALSE 0.14284091 0.4582168
#> 3     A  C 0.1304348 0.1418228 0.07482973 0.6732673 FALSE 0.00000000 0.3000000
#> 4     A  D 0.4347826 0.4309246 0.11390253 0.3267327 FALSE 0.24720280 0.6570000
#> 5     B  A 0.1724138 0.1737516 0.06474250 0.5346535 FALSE 0.07821429 0.3180000
#> 6     B  B 0.4137931 0.4205944 0.09336440 0.2970297 FALSE 0.23541667 0.5884848
#> 7     B  C 0.2068966 0.2050824 0.07346017 0.4752475 FALSE 0.06981818 0.3420833
#> 8     B  D 0.2068966 0.2005716 0.08216875 0.5049505 FALSE 0.05967023 0.3751667
#> 9     C  A 0.4000000 0.3857941 0.10757329 0.3861386 FALSE 0.17766798 0.6044118
#> 10    C  B 0.2000000 0.1884783 0.09391798 0.6534653 FALSE 0.04761905 0.3828755
#> 11    C  C 0.1500000 0.1571277 0.07338105 0.6039604 FALSE 0.00000000 0.2994885
#> 12    C  D 0.2500000 0.2686000 0.09868840 0.5544554 FALSE 0.10360963 0.4642308
#> 13    D  A 0.1666667 0.1651025 0.08394913 0.6336634 FALSE 0.02261905 0.3436275
#> 14    D  B 0.2222222 0.2362980 0.11192342 0.6930693 FALSE 0.00000000 0.4332589
#> 15    D  C 0.4444444 0.4507200 0.14203236 0.3861386 FALSE 0.18312325 0.7498039
#> 16    D  D 0.1666667 0.1478795 0.11004755 0.8118812 FALSE 0.00000000 0.3750000
#>      cr_lower  cr_upper
#> 1  0.09782609 0.1630435
#> 2  0.22826087 0.3804348
#> 3  0.09782609 0.1630435
#> 4  0.32608696 0.5434783
#> 5  0.12931034 0.2155172
#> 6  0.31034483 0.5172414
#> 7  0.15517241 0.2586207
#> 8  0.15517241 0.2586207
#> 9  0.30000000 0.5000000
#> 10 0.15000000 0.2500000
#> 11 0.11250000 0.1875000
#> 12 0.18750000 0.3125000
#> 13 0.12500000 0.2083333
#> 14 0.16666667 0.2777778
#> 15 0.33333333 0.5555556
#> 16 0.12500000 0.2083333

# Students nested in teams: resample whole teams
teams <- build_network(group_regulation_long, method = "relative",
                       actor = "Actor", action = "Action", time = "Time",
                       group = "Achiever")
bootstrap_network(teams, iter = 100, actor = "Group", seed = 1)
#>   Edge                   High      Low     
#>   --------------------------------------------
#>   synthesis→consensus   0.579     0.388   
#>   cohesion→consensus    0.536     0.451   
#>   adapt→consensus       0.519     0.458   
#>   consensus→plan        0.364     0.432   
#>   discuss→consensus     0.424     0.215   
#>   ... and 33 more shared significant edges
#> 
#> Grouped Bootstrap  [2 groups | 100 iterations | 95% CI]
#>   High                  41 sig / 76 total  |  Group: 100 actors, ICC -0.003, design effect 1.02
#>   Low                   44 sig / 75 total  |  Group: 100 actors, ICC -0.001, design effect 0.98
#>   Shared (all groups)   38 edges
# }