BoxM.F {smsets}R Documentation

F approximation of Box's M test

Description

An R function which implements an F approximation for testing the homogeneity of covariance matrices by Box's M. This is an alternative approach to the chi square approximation which requires group sample-sizes to be at least 20.

Usage

BoxM.F(x, group)

Arguments

x

A data frame with p + 1 columns (one factor and p response variables).

group

The classification factor defining m samples or groups. It must be one of the columns in x.

Details

For m samples, the M statistic is given by the equation

M = \frac{\prod_{j=1}^{m} |\mathbf{C}_j|^{(n_{j}-1)/2}}{|\mathbf{C}|^{(n-m)/2}}

where

n_{j} is the sample size of the j-th sample,

|\mathbf{C}_j| is the determinant of the covariance matrix for the jth sample,

|\mathbf{C}| is the determinant of the pooled covariance matrix,

n is the total number of observations.

Large values of M provide evidence that the samples are not from populations with the same covariance matrix. In addition to the observed M-value itself, the F-approximation involves the sample sizes and the number of variables analyzed. See the reference for details. Box's test is sensitive to deviations from normality in the distribution of the variables.

Value

Returns an object of class "BoxM.F", a list containing the following components:

name A character string describing the function.
Cov.Mat A list containing the m sample covariance matrices
Cov.pooled The pooled covariance matrix
BoxM.stat The approximate F-statistic
F.BoxM The calculated F-statistic
df.v1 Numerator degrees of freedom for the F statistic
df.v2 Denominator degrees of freedom for the F statistic
Pvalue P-value for the F statistic
group a character string specifying the name of the classification factor defining groups.
levels.group a vector of length m, showing the levels in factor group.
data.name a character string giving the name of the data.
variables a character string vector containing the variable names.
data the data frame analyzed.

Author(s)

Jorge Navarro Alberto, ganava4@gmail.com

References

Manly, B.F.J., Navarro Alberto, J.A. and Gerow, K. (2024) Multivariate Statistical Methods. A Primer. 5th Edn. Chapman and Hall/CRC.

Examples

data(skulls)
resBoxM.F <- BoxM.F(skulls, Period)
# Brief output
resBoxM.F


[Package smsets version 1.2.3 Index]