Pairwise Chatterjee's xi correlation matrix — chatterjee

Computes the p x p asymmetric matrix of Chatterjee's xi correlations between all item pairs. Entry [j, k] is xi(item_j, item_k), which in general differs from xi(item_k, item_j); this asymmetry is what enables direction detection in subsequent graph-construction steps. Each off-diagonal entry is computed by xi_stable() to average over tie-breaking.

Usage

chatterjee_matrix(
  U,
  na = NULL,
  Z = NULL,
  w = NULL,
  B = 1000,
  seed = NULL,
  verbose = FALSE
)

Arguments

U: Either an exametrika object or raw data.
na: Values to be treated as missing.
Z: Missing indicator matrix.
w: Item weight vector.
B: Number of bootstrap replications per pair. Default 1000.
seed: Optional integer seed for reproducibility.
verbose: Logical. If TRUE, progress messages are displayed.

Value

A p x p numeric matrix with item labels as row/column names. The diagonal is 1; off-diagonal entries are asymmetric.

Details

Pairs are computed with pairwise-complete observations: for each pair (j, k), rows where either Q[i, j] or Q[i, k] is missing are excluded. The diagonal is set to 1.

References

Chatterjee, S. (2021). A new coefficient of correlation. Journal of the American Statistical Association, 116(536), 2009-2022.

Examples

# \donttest{
xi_mat <- chatterjee_matrix(J15S3810, B = 500, seed = 42)
# }