Directional (version 7.0)

Anova for (hyper-)spherical data: Analysis of variance for (hyper-)spherical data

Description

Analysis of variance for (hyper-)spherical data.

Usage

hcf.aov(x, ina, fc = TRUE)
hclr.aov(x, ina)
lr.aov(x, ina)
embed.aov(x, ina)
het.aov(x, ina)

Value

This is an "htest"class object. Thus it returns a list including:

statistic

The test statistic value.

parameter

The degree(s) of freedom of the test.

p.value

The p-value of the test.

alternative

A character with the alternative hypothesis.

method

A character with the test used.

data.name

A character vector with two elements.

Arguments

x

A matrix with the data in Euclidean coordinates, i.e. unit vectors.

ina

A numerical variable or a factor indicating the group of each vector.

fc

A boolean that indicates whether a corrected F test should be used or not.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris and Giorgos Athineou <[e-mail]>.

Details

The high concentration (hcf.aov), high concentration log-likelihood ratio (hclr.aov), log-likelihood ratio (lr.aov), embedding approach (embed.aov) or the non equal concentration parameters approach (het.aov) is used.

References

Mardia K. V. and Jupp P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.

Rumcheva P. and Presnell B. (2017). An improved test of equality of mean directions for the Langevin-von Mises-Fisher distribution. Australian & New Zealand Journal of Statistics, 59(1): 119--135.

Tsagris M. and Alenazi A. (2024). An investigation of hypothesis testing procedures for circular and spherical mean vectors. Communications in Statistics-Simulation and Computation, 53(3): 1387--1408.

See Also

hcf.boot, hcfboot, hclr.circaov,

Examples

x <- rvmf(60, rnorm(3), 15)
ina <- rep(1:3, each = 20)
hcf.aov(x, ina)
hcf.aov(x, ina, fc = FALSE)
lr.aov(x, ina)
embed.aov(x, ina)
het.aov(x, ina)