Filipe J. Marques

Instructions and examples for the implementation of approximations for the likelihood ratio statistic for testing the equality of several covariance matrices

These modules were developed using the software Mathematica version 10.0 and allow the computation of approximations for the distribution of the likelihood ratio test statistic Λ (and also for its negative logarithm W = logΛ) used to test the equality of several covariance matrices in the balanced and unbalanced cases. Only one simple module is required for the computation of the probability density and cumulative distribution functions of Λ and W. The use of this module requires the Numerical Calculus package. Before executing this module, it should be used the following instruction Needs["NumericalCalculus`"].

File with instructions and examples: HERE

To run the function EqMatrices[Samples ,type ,p ,m ,x ] in Figure 1 it is necessary to define the following parameters

i) Samples - is a vector with the samples size considered for each population;

ii) type - can assume two values 1 or 2; if type=1 the output will be of the probability density function in a given value x; if type=2 the output will be of the cumulative distribution function in a given value x;

iii) p - the number of variables in each of the populations;

iv) m - the number of exact moments matched by the approximating distribution;

v) x - the running value.

The computational module can be found HERE