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.
Examples
hd <- derive_headings(cpunctatus, rule = "distal", carry = "arc",
coords = "relative")
# Control (no stimulus) against the widest arc
circ_model_select(hd[hd$arc %in% c("0", "50"), ], group_col = "arc")
#> arc model n k logLik AIC AICc BIC dAICc
#> 4 50 unimodal_uniform 26 3 -25.31838 56.63676 57.72767 60.41105 0.0000000
#> 5 50 bimodal 26 5 -25.01426 60.02851 63.02851 66.31900 5.3008401
#> 3 50 axial 26 2 -35.64951 75.29902 75.82076 77.81522 18.0930879
#> 2 50 unimodal 26 2 -39.71644 83.43288 83.95462 85.94908 26.2269499
#> 1 50 uniform 26 0 -47.78480 95.56961 95.56961 95.56961 37.8419340
#> 11 0 uniform 35 0 -64.32570 128.65139 128.65139 128.65139 0.0000000
#> 41 0 unimodal_uniform 35 3 -61.16608 128.33216 129.10635 132.99820 0.4549588
#> 31 0 axial 35 2 -63.36687 130.73373 131.10873 133.84443 2.4573380
#> 21 0 unimodal 35 2 -64.15780 132.31560 132.69060 135.42630 4.0392093
#> 51 0 bimodal 35 5 NA NA NA NA NA
#> weight
#> 4 9.339324e-01
#> 5 6.595574e-02
#> 3 1.100149e-04
#> 2 1.884541e-06
#> 1 5.662965e-09
#> 11 4.500595e-01
#> 41 3.584898e-01
#> 31 1.317242e-01
#> 21 5.972646e-02
#> 51 NA