Bootstrap for Regularized Partial Correlation Networks

Fast, single-call bootstrap for EBICglasso partial correlation networks. Combines nonparametric edge/centrality bootstrap, case-dropping stability analysis, edge/centrality difference tests, predictability CIs, and thresholded network into one function. Designed as a faster alternative to bootnet with richer output.

Usage

boot_glasso(
  x,
  iter = 1000L,
  cs_iter = 500L,
  cs_drop = seq(0.1, 0.9, by = 0.1),
  alpha = 0.05,
  gamma = 0.5,
  nlambda = 100L,
  centrality = c("strength", "expected_influence", "betweenness", "closeness"),
  centrality_fn = NULL,
  cor_method = "pearson",
  ncores = 1L,
  seed = NULL
)

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

# S3 method for class 'boot_glasso'
summary(object, type = "edges", ...)

# S3 method for class 'boot_glasso'
plot(x, type = "edges", measure = NULL, ...)

Arguments

x: A data frame, numeric matrix (observations x variables), or a netobject with method = "glasso". For the print() and plot() methods: an object of class boot_glasso.
iter: Integer. Number of nonparametric bootstrap iterations (default: 1000).
cs_iter: Integer. Total number of case-dropping iterations (default: 500). Following bootnet, each iteration draws one drop proportion at random from cs_drop, so the iterations are spread across the proportions rather than repeated cs_iter times at each one.
cs_drop: Numeric vector. Drop proportions for CS-coefficient computation (default: seq(0.1, 0.9, by = 0.1)).
alpha: Numeric. Significance level for CIs (default: 0.05).
gamma: Numeric. EBIC hyperparameter (default: 0.5).
nlambda: Integer. Number of lambda values in the regularization path (default: 100).
centrality: Character vector. Centrality measures to compute. All four built-in measures ("strength", "expected_influence", "betweenness", "closeness") are computed internally with no extra dependencies and are always taken from the built-in path even if centrality_fn is supplied. Names that are not one of these four are valid only when a centrality_fn is supplied; that function is then responsible for returning them. Default: c("strength", "expected_influence", "betweenness", "closeness").
centrality_fn: Optional function. A custom centrality function that takes a weight matrix and returns a named list of centrality vectors. When NULL (default), all four built-in measures are computed internally: "strength"/"expected_influence" via rowSums, and "betweenness"/"closeness" via an internal Floyd-Warshall shortest-path routine. When provided, the function is called as centrality_fn(mat) and is used only for requested measures that are not one of the four built-ins; it should return a named list (e.g., list(my_metric = ...)).
cor_method: Character. Correlation method: "pearson" (default), "spearman", or "kendall".
ncores: Integer. Number of parallel cores for mclapply (default: 1, sequential).
seed: Integer or NULL. RNG seed for reproducibility.
...: In plot.boot_glasso(): Additional arguments passed to plotting functions. For type = "edge_diff" and type = "centrality_diff", accepts order: "sample" (default, sorted by value) or "id" (alphabetical). In print.boot_glasso() and summary.boot_glasso(): Additional arguments (ignored).
object: For the summary() method: an object of class boot_glasso.
type: In summary.boot_glasso(): Character. Summary type: "edges" (default), "centrality", "cs", "predictability", or "all". In plot.boot_glasso(): Character. Plot type: "edges" (default), "stability", "edge_diff", "centrality_diff", or "inclusion".
measure: Character. Centrality measure for type = "centrality_diff" (default: first available measure).

Value

An object of class "boot_glasso" containing:

original_pcor: Original partial correlation matrix.
original_precision: Original precision matrix.
original_centrality: Named list of original centrality vectors.
original_predictability: Named numeric vector of node R-squared.
edge_ci: Data frame of edge CIs (edge, weight, ci_lower, ci_upper, inclusion).
edge_inclusion: Named numeric vector of edge inclusion probabilities.
thresholded_pcor: Partial correlation matrix with non-significant edges zeroed.
centrality_ci: Named list of data frames (node, value, ci_lower, ci_upper) per centrality measure.
cs_coefficient: Named numeric vector of CS-coefficients per centrality measure.
cs_data: Data frame of case-dropping results, one row per drop proportion by measure, with columns drop_prop, measure, mean_cor, prop_above (fraction of that proportion's iterations correlating above 0.7) and n_samples (iterations that landed on that proportion).
edge_diff_p: Symmetric matrix of pairwise edge difference p-values; NULL when the network has more than 500 edges.
centrality_diff_p: Named list of symmetric p-value matrices per centrality measure.
predictability_ci: Data frame of node predictability CIs (node, r2, ci_lower, ci_upper).
boot_edges: iter x n_edges matrix of bootstrap edge weights.
boot_centrality: Named list of iter x p bootstrap centrality matrices.
boot_predictability: iter x p matrix of bootstrap R-squared.
nodes: Character vector of node names.
n: Sample size.
p: Number of variables.
iter: Number of nonparametric iterations.
cs_iter: Number of case-dropping iterations.
cs_drop: Drop proportions used.
alpha: Significance level.
gamma: EBIC hyperparameter.
nlambda: Lambda path length.
centrality_measures: Character vector of centrality measures.
cor_method: Correlation method.
lambda_path: Lambda sequence used.
lambda_selected: Selected lambda for original data.
timing: Named numeric vector with timing in seconds.

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

In summary.boot_glasso(): For type = "edges", the edge_ci data frame (edge, weight, ci_lower, ci_upper, inclusion) ordered by decreasing absolute weight; for "cs" the cs_data data frame; for "predictability" the predictability_ci data frame; for "centrality" a named list of one data frame per measure (node, value, ci_lower, ci_upper); for "all" a named list holding all four.

In plot.boot_glasso(): A ggplot object (returned, and so printed when the call is made at the top level).

Methods

plot.boot_glasso(): Plots bootstrap results for GLASSO networks.

References

Epskamp, S., Borsboom, D., & Fried, E. I. (2018). Estimating psychological networks and their accuracy: A tutorial paper. Behavior Research Methods 50(1), 195-212. doi:10.3758/s13428-017-0862-1 (source of the CS-coefficient and of the case-dropping, edge-difference and centrality-difference procedures reproduced here.)

Examples

set.seed(1)
dat <- as.data.frame(matrix(rnorm(60), ncol = 3))
net <- build_network(dat, method = "glasso")
bg <- boot_glasso(net, iter = 10, cs_iter = 5, centrality = "strength")
# \donttest{
set.seed(42)
mat <- matrix(rnorm(60), ncol = 4)
colnames(mat) <- LETTERS[1:4]
net <- build_network(as.data.frame(mat), method = "glasso")
# iter = 20 keeps the example fast; a real analysis uses 1000 or more.
boot <- boot_glasso(net, iter = 20, cs_iter = 10, seed = 42,
  centrality = c("strength", "expected_influence"))
print(boot)
#> GLASSO Bootstrap (20 iterations, 10 case-drop per proportion)
#>   Data: 15 x 4  |  Alpha: 0.05  |  Gamma: 0.50
#>   Edges: 0/6 significant (CI excludes zero)
#>   Mean inclusion probability: 0.34
#> 
#>   Centrality Stability (CS-coefficient):
#>     strength:              0.00 [Unstable]
#>     expected_influence:    0.00 [Unstable]
#> 
#>   Edge differences: 1/15 pairs significantly different
#>   Timing: 1.3s (bootstrap: 0.8s, case-drop: 0.4s)
summary(boot, type = "edges")
#>     edge weight    ci_lower  ci_upper inclusion
#> 1 A -- B      0 -0.11158199 0.2237170      0.35
#> 2 A -- C      0 -0.35185599 0.0000000      0.45
#> 3 B -- C      0 -0.30946821 0.2065199      0.25
#> 4 A -- D      0  0.00000000 0.3570903      0.50
#> 5 B -- D      0 -0.15048304 0.3105727      0.35
#> 6 C -- D      0 -0.03724162 0.1787669      0.15
# }