Fits five candidate models to a heading sample and ranks them by the small-sample-corrected Akaike information criterion (AICc):
- uniform
no preferred direction (k = 0).
- unimodal
one von Mises mode (k = 2).
- axial
symmetric bimodal von Mises, two equal antipodal modes (k = 2).
- unimodal_uniform
a directed von Mises mode over a uniform background, \(p\,vM(\mu,\kappa) + (1-p)\,U\) (k = 3).
- bimodal
an asymmetric two-component von Mises mixture with free means, concentrations, and weight (k = 5).
The mixture models (unimodal_uniform, bimodal) are fitted by
numerical maximum likelihood; the other three are closed-form. This model set
mirrors the Schnute-Groot family implemented by the CircMLE package
(Fitak & Johnsen 2017): uniform = M1, unimodal = single von
Mises, axial = symmetric bimodal, unimodal_uniform = a directed
component over a uniform background, and bimodal = a free two-component
mixture.
Value
Tidy data frame, one row per candidate model (five rows, or five per
group when group_col is supplied), sorted by AICc ascending (best first;
NA last). Columns: group_col (if supplied), model,
n, k (free parameters), logLik, AIC, AICc,
BIC, dAICc (AICc minus the group minimum), and weight
(Akaike weight). AICc/weight are NA for a model whose
fit failed or when n - k - 1 <= 0; remaining weights sum to 1.
Details
Parameters for uniform, unimodal, and axial are estimated
with vonmises_fit (the axial model via its axial = TRUE
doubled-angle fit) and likelihoods with the circular package densities.
The table reports model comparison only; obtain the fitted parameters of a
chosen model from vonmises_fit.
References
Burnham, K.P. & Anderson, D.R. (2002). Model Selection and Multimodel Inference, 2nd ed. Springer.
Schnute, J.T. & Groot, K. (1992). Statistical analysis of animal orientation data. Animal Behaviour, 43(1), 15-33.
Fitak, R.R. & Johnsen, S. (2017). Bringing the analysis of animal orientation data full circle: model-based approaches with maximum likelihood. Journal of Experimental Biology, 220(21), 3878-3882.