Estimates the mean direction \(\mu\) and concentration \(\kappa\) of a
von Mises distribution via maximum likelihood, together with asymptotic
standard errors and a confidence interval on \(\mu\). Intended as a
parametric companion to circ_dispersion: where
circ_dispersion returns the empirical resultant length R and
circular SD, vonmises_fit returns the MLE \(\hat{\kappa}\) with
its uncertainty.
Usage
vonmises_fit(hd, group_col = NULL, angle_col = "heading", conf = 0.95)
Arguments
- hd
Data frame containing headings in radians.
- group_col
Column(s) to group by. NULL fits a single model to
all rows.
- angle_col
Name of the heading column. Default "heading".
- conf
Confidence level for the interval on \(\mu\).
Default 0.95.
Value
Data frame with columns group_col (if supplied), mu
(MLE mean direction, radians), mu_deg (degrees), kappa
(MLE concentration), se_mu, se_kappa (asymptotic standard
errors), ci_lo and ci_hi (conf-level interval on
\(\mu\), radians), n.
Details
\(\kappa = 0\) corresponds to a uniform distribution (no preferred
direction); larger values indicate increasing concentration. The confidence
interval on \(\mu\) uses a normal approximation and is unreliable for
\(\kappa < 0.5\) or small samples.