Edge-weight Case-dropping Stability

Computes a CS-coefficient for the edge-weight vector of a network: the maximum proportion of cases (rows of x$data) that can be dropped while the flattened edge-weight vector of the re-estimated network still correlates with the original above threshold in at least certainty of iterations.

Usage

casedrop_reliability(
  x,
  iter = 1000L,
  drop_prop = seq(0.1, 0.9, by = 0.1),
  threshold = 0.7,
  certainty = 0.95,
  method = c("spearman", "pearson", "kendall"),
  include_diag = FALSE,
  seed = NULL
)

# S3 method for class 'net_casedrop_reliability'
print(x, digits = 3, ...)

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

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

# S3 method for class 'net_casedrop_reliability_group'
summary(object, drop_prop = NULL, ...)

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

# S3 method for class 'net_casedrop_reliability'
plot(x, combined = TRUE, ...)

# S3 method for class 'net_casedrop_reliability_group'
plot(
  x,
  metric = c("correlation", "mean_abs_dev", "median_abs_dev", "max_abs_dev"),
  ...
)

Arguments

x: A netobject, cograph_network, netobject_group, or mcml. For the group types this function iterates over each element and returns a named list. For the print() and plot() methods: an object of class net_casedrop_reliability or net_casedrop_reliability_group (or its summary()).
iter: Integer. Iterations per drop proportion. Default 1000.
drop_prop: Numeric vector of proportions to evaluate. Each entry must lie strictly between 0 and 1. Default seq(0.1, 0.9, by = 0.1). In summary.net_casedrop_reliability_group(): Drop proportion at which to report the four metrics (mean +/- sd per network). Must be one of the drop proportions the object was built with. Defaults to the object's median grid value (the stored grid is used, not an assumed 0.7); pass an explicit value not in the grid to get an error listing the available proportions.
threshold: Numeric in [0, 1]. Minimum edge-vector correlation for an iteration to count as stable. Default 0.7.
certainty: Numeric in [0, 1]. Required fraction of iterations whose correlation must exceed threshold for a drop proportion to qualify. Default 0.95.
method: Correlation method: "pearson" (weight magnitudes), "spearman" (ranks, robust to scale), or "kendall". Default "spearman" because edge weights often span several orders of magnitude and rank stability is the typical target.
include_diag: Logical. Include diagonal (self-loop) edges in the edge vector. Default FALSE.
seed: Optional integer for reproducibility.
digits: Digits to display. Default 3.
...: In plot.net_casedrop_reliability(), plot.net_casedrop_reliability_group(), print.net_casedrop_reliability(), print.summary.net_casedrop_reliability_group(), summary.net_casedrop_reliability() and summary.net_casedrop_reliability_group(): Additional arguments (ignored). In print.net_casedrop_reliability_group(): Ignored.
object: For the summary() method: an object of class net_casedrop_reliability or net_casedrop_reliability_group.
combined: When TRUE (default), all four metrics are shown in one ggplot via facet_wrap(~ metric). When FALSE, returns a named list of four single-panel ggplots, one per metric.
metric: Which metric to plot. One of "correlation" (default), "mean_abs_dev", "median_abs_dev", "max_abs_dev".

Value

An object of class net_casedrop_reliability with:

cs: Scalar CS-coefficient - the maximum drop proportion for which the edge-vector correlation remains >= threshold in at least certainty of iterations. Zero if no proportion qualifies.
summary: Tidy data frame, one row per metric by drop proportion, with columns metric ("mean_abs_dev", "median_abs_dev", "correlation", "max_abs_dev"), drop_prop, mean, sd, median, mad, q025, q975.
metrics: Named list of four iter x length(drop_prop) matrices, one per metric, holding the raw per-iteration values.
correlations: iter x length(drop_prop) matrix of per- iteration correlations (the correlation entry of metrics).
drop_prop, threshold, certainty, iter, method, include_diag: Inputs.
n_cases: Number of cases resampled from (sequences for transition methods, rows of $data otherwise).
n_edges: Length of the edge vector assessed.

A netobject_group or mcml input instead returns a net_casedrop_reliability_group: a named list of one result per constituent network.

When the original edge vector has zero variance a warning is issued and the object is returned with cs = 0, an empty summary, and all-NA metric matrices.

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

In summary.net_casedrop_reliability(): A tidy data frame with columns metric, drop_prop, mean, sd summarising edge-weight stability across case-dropping iterations.

In summary.net_casedrop_reliability_group(): A data frame with one row per network containing cor, mean_abs_dev, median_abs_dev, max_abs_dev formatted as "mean +/- sd".

In plot.net_casedrop_reliability(): A ggplot object, or a named list of four ggplots when combined = FALSE.

In plot.net_casedrop_reliability_group(): A ggplot object.

Details

Complements centrality_stability(): that function asks whether centrality rankings are stable; this one asks whether the edge-weight structure itself is stable. For MCML-derived networks where each row of $data is one transition, this is case-dropping of edges.

For each drop_prop p and each iteration, a size n_cases * (1 - p) subset of $data rows is selected without replacement, the network is re-estimated using the same method/scaling/threshold as the input, and the upper/lower-triangle (directed: all off-diagonal entries) of the new weight matrix is flattened and correlated with the corresponding vector of the original matrix. The correlation method defaults to Spearman for robustness to the wide dynamic range of transition probabilities.

Unlike bootstrap CIs, case-dropping does not estimate sampling variance and so does not rely on the i.i.d. assumption. This makes it the appropriate robustness check for edgelist-derived networks (where rows of $data lack actor grouping), since dropping rows at random is a well-posed operation regardless of within-actor correlation.

Methods

plot.net_casedrop_reliability(): Plots the four model-level reliability metrics across drop proportions: correlation, mean_abs_dev, median_abs_dev, max_abs_dev. Each panel shows the per-iteration mean with a ribbon at mean +/- sd. The correlation panel includes a dashed horizontal line at the user's threshold (default 0.7).
plot.net_casedrop_reliability_group(): Overlay of per-cluster correlation curves across drop proportions. One colour per sub-network; ribbons show mean +/- sd across iterations. Dashed horizontal line marks the stability threshold (default 0.7).

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

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)
)
net <- build_network(seqs, method = "relative")
es  <- casedrop_reliability(net, iter = 50, drop_prop = c(0.1, 0.3, 0.5),
                      seed = 1)
print(es)
#> Edge-weight Case-dropping Stability
#>   Cases (rows of $data) : 30
#>   Edges assessed        : 12 (diagonal excluded)
#>   Iterations / prop     : 50
#>   Correlation method    : spearman
#>   CS-coefficient (r)    : 0.10  (threshold=0.70, certainty=0.95)
#> 
#> Model-level reliability across iterations (mean +/- sd per drop):
#>   drop_prop      p=0.1        p=0.3        p=0.5      
#>   mean|diff|      0.028+- 0.007   0.062+- 0.014   0.095+- 0.018
#>   MAD             0.021+- 0.008   0.052+- 0.014   0.085+- 0.023
#>   cor             0.927+- 0.045   0.820+- 0.078   0.688+- 0.161
#>   max|diff|       0.081+- 0.023   0.160+- 0.051   0.241+- 0.056