Centrality Stability Coefficient (CS-coefficient)

Estimates the stability of centrality indices under case-dropping. For each drop proportion, sequences are randomly removed and the network is re-estimated. The correlation between the original and subset centrality values is computed. The CS-coefficient is the maximum proportion of cases that can be dropped while maintaining a correlation above threshold in at least certainty of bootstrap samples.

For transition methods, uses pre-computed per-sequence count matrices for fast resampling. Strength centralities (InStrength, OutStrength) are computed directly from the matrix without igraph.

Usage

centrality_stability(
  x,
  measures = c("InStrength", "OutStrength", "Betweenness"),
  iter = 1000L,
  drop_prop = seq(0.1, 0.9, by = 0.1),
  threshold = 0.7,
  certainty = 0.95,
  method = "pearson",
  centrality_fn = NULL,
  loops = FALSE,
  normalize = FALSE,
  invert = TRUE,
  normalize_diffusion = TRUE,
  seed = NULL
)

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

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

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

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

# S3 method for class 'net_stability'
plot(x, ...)

Arguments

x: A netobject from build_network, a cograph_network, or a netobject_group / mcml (each constituent network is assessed and a net_stability_group is returned). For the print() and plot() methods: an object of class net_stability or net_stability_group.
measures: Character vector. Centrality measures to assess. Defaults to c("InStrength", "OutStrength", "Betweenness"). Pass "all" for every built-in measure: "OutStrength", "InStrength", "ClosenessIn", "ClosenessOut", "Closeness", "Betweenness", "BetweennessRSP", "Diffusion", and "Clustering". The legacy aliases "InCloseness" and "OutCloseness" are also accepted. Custom measures beyond these are valid only when a centrality_fn is supplied to resolve them.
iter: Integer. Number of bootstrap iterations per drop proportion (default: 1000).
drop_prop: Numeric vector. Proportions of cases to drop (default: seq(0.1, 0.9, by = 0.1)).
threshold: Numeric. Minimum correlation to consider stable (default: 0.7).
certainty: Numeric. Required proportion of iterations above threshold (default: 0.95).
method: Character. Correlation method: "pearson", "spearman", or "kendall" (default: "pearson").
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 built-in measures are computed internally: "InStrength"/"OutStrength" via colSums/rowSums, "Betweenness"/ "ClosenessIn"/"ClosenessOut"/"Closeness" via an internal Floyd-Warshall shortest-path routine, and "BetweennessRSP", "Diffusion" and "Clustering" from the weight matrix directly. When provided, the function is called as centrality_fn(mat) and is used only for requested measures that are not one of the built-ins; it should return a named list (e.g., list(my_metric = ...)).
loops: Logical. If FALSE (default), self-loops (diagonal) are excluded from centrality computation. This does not modify the stored matrix.
normalize: Logical. Range-normalize all requested measures using the same transformation as tna::centralities(normalize = TRUE). Default: FALSE.
invert: Logical. Invert weights for shortest-path measures? Default: TRUE, matching tna.
normalize_diffusion: Logical. Range-normalize Diffusion even when normalize = FALSE. Default: TRUE.
seed: Integer or NULL. RNG seed for reproducibility.
...: In plot.net_stability(), print.net_stability(), print.net_stability_group(), summary.net_stability() and summary.net_stability_group(): Additional arguments (ignored).
object: For the summary() method: an object of class net_stability_group or net_stability.

Value

An object of class "net_stability": a list with

cs: Named numeric vector of CS-coefficients, one per retained measure.
correlations: Named list of iter x length(drop_prop) matrices of correlation values, one per retained measure.
measures: Character vector of the measures actually assessed (see the zero-variance rule below).
drop_prop: Drop proportions used.
threshold: Stability threshold.
certainty: Required certainty level.
iter: Number of iterations.
method: Correlation method.

A netobject_group or mcml input instead returns a "net_stability_group": a named list of one net_stability per constituent network.

Zero-variance measures are handled by two different rules, both long-standing behaviour. When some requested measures have zero variance on the original network (for example "OutStrength" on a row-normalised transition network), those measures are dropped: $cs, $correlations and $measures cover only the retained ones. When every requested measure has zero variance a warning is issued and all requested names are returned with cs = 0 and all-NA correlation matrices.

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

In print.net_stability_group(): The input x invisibly.

In summary.net_stability_group(): A data frame with columns group, measure, drop_prop, mean_cor, sd_cor, prop_above.

In summary.net_stability(): A data frame with columns measure, drop_prop, mean_cor, sd_cor, prop_above.

In plot.net_stability(): A ggplot object (invisibly).

Methods

plot.net_stability(): Plots mean correlation vs drop proportion for each centrality measure. The CS-coefficient is marked where the curve crosses the threshold.
summary.net_stability(): Returns the mean correlation at each drop proportion for each measure.
summary.net_stability_group(): Per-network stability as a tidy data frame. Stacks summary() results for each network with a group column.

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

Examples

seqs <- data.frame(
  T1 = c("plan", "code", "debug", "plan", "test", "code"),
  T2 = c("code", "debug", "code", "plan", "code", "test"),
  T3 = c("debug", "code", "plan", "code", "debug", "plan"),
  T4 = c("test", "plan", "test", "debug", "plan", "code")
)
net <- build_network(seqs, method = "relative")
cs <- centrality_stability(net, iter = 10, drop_prop = 0.3, seed = 1)
# \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")
cs <- centrality_stability(net, iter = 100, seed = 42,
  measures = c("InStrength", "OutStrength"))
print(cs)
#> Centrality Stability (100 iterations, threshold = 0.7)
#>   Drop proportions: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9
#> 
#>   CS-coefficients:
#>     InStrength       0.00
#>     OutStrength      0.30
# }