Dear Group Members,
Forgive me if I am a little bit out of subject. I am looking for a good
way to test the homogeneity of two variance-covariance matrices using R,
prior to a Hotelling T test. Youll probably tell me that it is better
to use a robust version of T, but I have no precise idea of the
statistical behaviour of my variables, because they are parameters from
the harmonics of Fourier series used to describe the outlines of
specimens. I rather like to explore precisely these harmonics parameters.
It is known that Boxs M-test of homogeneity of variance-covariance
matrices is oversensitive to heteroscedasticity and to deviation from
multivariate normality and that it I not useful (Everitt, 2005 ; Seber,
1984 ; Layard, 1974). I have tried a quick and dirty intuitive
comparison between two covariance matrices and I am seeking the opinion
of professional statisticians about this stuff. The idea is to compare
the two matrices using the absolute value of their difference, then to
make a quadratic form using a unity vector and its transpose. One obtain
a scalar that must be close to zero if the two covariance matrices are
homogeneous :
Let S1 and S2 be two variance-covariance matrices of dimension n,
Let a be a vector of n ones : a <- rep(1, times = n)
b = a * |S1 S2| * a, i.e. in R:
b <- a %*% abs(S1 S2) %*% a
Is b distributed following a chi-square distribution? Is this idea total
crap? Did someone tried this before and published something?
My data gave two 77 x 77 covariance matrices and b = 0.003243, a value
close to 0, hence I expect my two covariance matrices are homogeneous.
Am I right?
If this comparison is incorrect, could someone suggest a useful way to
make this comparison using R?
Thank you in advance for your comments.
Franck
_______________________________
Dr Franck BAMEUL
Le Clos d'Ornon
7 rue Frdric Mistral
F-33140 VILLENAVE D'ORNON
France
fbameul at wanadoo.fr
06 89 88 16 73 (personnel)
05 57 19 57 20 (professionnel)
05 57 19 57 27 (fax)
