critical_angle: Compute the critical angle for the test of the angle between...

In fruciano/GeometricMorphometricsMix: Miscellaneous functions useful for geometric morphometrics

Compute the critical angle for the test of the angle between two multivariate vectors

Description

This function computes the angle below which two vectors would be "significantly similar" using Li 2011 test.

Usage

critical_angle(dimensions, alpha = 0.05, prec = "normal")

Arguments

dimensions	number of dimensions to use
alpha	significance level (by default 0.05)
prec	whether one has to use the internal R functions ("normal", default), or mpfr precision ("mpfr")

Details

This function considers the formulas in Li 2011 which have been used to perform a test of the angle between multivariate vectors. This is the test implemented in MorphoJ (Klingenberg 2011), in the R package Morpho (Schlager 2016), and in the function TestOfAngle of this package. The test produces a p value for the angle between two vectors (with significant values being "significantly similar").

This function reverts the logic of the formula/test and, given a number of dimensions (e.g., morphometric variables) and a level of significance (by default 0.05), it computes the angle below which the test would be significant.

Value

The function outputs the critical angle (in degrees)

Notice

In case of very many dimensions, there are numerical problems in performing the test. If prec="normal" the function uses internally the package Morpho (which should be installed) and these problems will start occurring above about 340 variables. If prec="mpfr" the function uses internally a custom function which requires the package Rmpfr (which should be installed). This allows the computation of extremely large or small numbers, it is currently set to a 120 bit precision and allows the computation using up to about 1200 variables (over this number, there will be problems even using the option "mpfr")

References

Klingenberg CP. 2011. MorphoJ: an integrated software package for geometric morphometrics. Mol Ecol Resour 11:353-357.

Li S. 2011. Concise formulas for the area and volume of a hyperspherical cap. Asian Journal of Mathematics and Statistics 4:66-70.

Schlager S. 2016. Morpho: Calculations and Visualisations Related to Geometric Morphometrics.

See Also

TestOfAngle

Examples

critical_angle(50)
# This is the angle below which two vectors (e.g., PCA axes)
# of 50 variables would be would be "significantly similar"

fruciano/GeometricMorphometricsMix documentation built on Jan. 31, 2024, 6:24 a.m.