[R] var-covar matrices comparison

[Peter Dalgaard]

David Duffy <David.Duffy at qimr.edu.au> writes:

> > Date: Mon, 20 Feb 2006 16:43:55 -0600
> > From: Aldi Kraja <aldi at wustl.edu>
> >
> > Hi,
> > Using package gclus in R, I have created some graphs that show the
> > trends within subgroups of data and correlations among 9 variables (v1-v9).
> > Being interested for more details on these data I have produced also the
> > var-covar matrices.
> > Question: From a pair of two subsets of data (with 9 variables each, I
> > have two var-covar matrices for each subgroup, that differ for a
> > treatment on one group (treatment A) vs (non-Treatment A).
> >
> > Is there a software that can compare if two var-covar matrices are
> > statistically the same?
> >
> 
> This can be done in various structural equation modelling packages.  I don't
> think it can be done automatically using the sem package, as that does not allow
> multiple groups.  You can roll your own LR test (assuming MVN):
> 
>   f <- (N-1) * (log(det(E)) - log(det(O)) + sum(diag((O %*% solve(E))))-p)
> 
>   N=size of group
>   p=number of variables
>   E=expected covariance matrix
>   O=observed covariance matrix

..and an asymptotic approximation to order n^-3 is found in TW
Anderson: An Introduction to Multivariate Statistical Analysis
(formula (7) section 10.5 in my 1958, 1st ed. reprint).

 
>   where in your example, E will be the observed covariance matrix for
>   the pooled groups.  There are GLS etc alternatives - see eg Bollen's book on
>   SEM.
> 
> | David Duffy (MBBS PhD)                                         ,-_|\
> | email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
> | Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
> | 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v
> 
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