var-covar matrices comparison

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

  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   \_,-._/
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