Bootstrap confidence intervals for circular concentration

Computes nonparametric bootstrap confidence intervals for the concentration of each group, for both the von Mises maximum-likelihood concentration \(\kappa\) and the mean resultant length \(R\). Angles are resampled with replacement and the interval is the percentile envelope of the bootstrap estimates. Unlike the normal-approximation se_kappa from vonmises_fit, it makes no distributional assumption and stays usable at low concentration or small sample size, where that approximation is unreliable and where \(\hat\kappa\)/\(\hat R\) carry a known upward bias.

Usage

boot_kappa_ci(
  hd,
  group_col = NULL,
  angle_col = "heading",
  conf = 0.95,
  R = 999L,
  axial = FALSE
)

Arguments

hd

Data frame containing headings in radians.

group_col

Column(s) to group by. NULL (default) treats the whole data frame as one group.

angle_col

Name of the heading column. Default "heading".

conf

Confidence level. Default 0.95.

R

Number of bootstrap resamples. Default 999. Set the RNG seed with set.seed for reproducible intervals.

axial

Logical; when TRUE, treat the angles as axial (bidirectional, mod-pi): concentration is estimated in the doubled-angle frame (about the axis) and, like vonmises_fit, is not rescaled. Default FALSE (directional).

Value

Data frame with columns group_col (if supplied), kappa (von Mises MLE concentration), kappa_ci_lo/kappa_ci_hi (conf-level percentile CI on \(\kappa\)), kappa_bias, resultant_R (mean resultant length in \([0,1]\)), R_ci_lo/R_ci_hi, R_bias, and n. Groups with fewer than two finite angles yield an all-NA row.

Details

The kappa_bias/R_bias columns report the bootstrap estimate of that bias (bootstrap mean minus the sample estimate); the intervals themselves are the raw percentile envelope and are not bias-shifted.

See also

boot_mean_ci, boot_kappa_contrast, vonmises_fit, circ_dispersion, test_concentration