Evaluate the stability of the causal order from bootstrap

Aggregates the causal order (causal_order) estimated in each bootstrap sample and quantifies how stable the order is. Returns the rank distribution of each variable, the precedence probabilities for variable pairs, and an overall stability score.

Usage

get_causal_order_stability(result, labels = NULL)

Arguments

result

A BootstrapResult object (run with the current version)

labels

A vector of variable names (if NULL, x0, x1, ... are generated automatically)

Value

A list of class causal_order_stability, containing:

• rank_summary: A summary of the rank of each variable (variable, mean_rank, sd_rank, median_rank, mode_rank). Sorted in ascending order of mean_rank (from upstream). A rank of 1 is the most upstream.

• precedence_matrix: A precedence probability matrix. P[i, j] is the proportion of bootstrap samples in which variable i was located upstream of (before) variable j.

• stability_score: An overall stability score, from 0 (random order) to 1 (order agrees across all samples). The closer the precedence probability of each variable pair is to 0/1, the higher the score.

• n_sampling: The number of bootstrap samples.

Examples

dat <- generate_lingam_sample_6()
bs <- lingam_direct_bootstrap(dat$data, n_sampling = 30L, reg_method = "ols", seed = 42)
#> Bootstrap: 30 iterations, method=ols (sequential)
#>   iteration 1 / 30
#>   iteration 10 / 30
#>   iteration 20 / 30
#>   iteration 30 / 30
#> Completed in 0.2 seconds.
get_causal_order_stability(bs, labels = names(dat$data))
#> === Causal Order Stability ===
#> Bootstrap samples:       30
#> Overall stability score: 0.680  (0 = random, 1 = fully stable)
#> 
#> Rank summary (sorted by mean rank; 1 = most upstream):
#>  variable mean_rank sd_rank median_rank mode_rank
#>        x3      1.17    0.91         1.0         1
#>        x0      2.57    0.57         3.0         3
#>        x2      2.93    0.98         2.5         2
#>        x5      4.33    1.32         4.0         3
#>        x4      4.87    0.86         5.0         5
#>        x1      5.13    1.11         5.0         6
#> 
#> Precedence probability P[i, j] = P(variable i precedes j):
#>      x0   x1   x2   x3   x4   x5
#> x0 0.00 0.97 0.47 0.03 0.97 1.00
#> x1 0.03 0.00 0.03 0.03 0.40 0.37
#> x2 0.53 0.97 0.00 0.03 0.97 0.57
#> x3 0.97 0.97 0.97 0.00 0.97 0.97
#> x4 0.03 0.60 0.03 0.03 0.00 0.43
#> x5 0.00 0.63 0.43 0.03 0.57 0.00