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Re: Compare matrices using Chi square for Exploratory

  • To: mathgroup at smc.vnet.net
  • Subject: [mg114870] Re: Compare matrices using Chi square for Exploratory
  • From: Stuart Nettleton <Stuart.Nettleton at uts.edu.au>
  • Date: Tue, 21 Dec 2010 00:18:00 -0500 (EST)
  • References: <201012200539.AAA22748@smc.vnet.net>

A small addendum to my previous question with the issues that gave rise to  
my question about a simple approach to a whole-of-matrix comparison  
between original and recreated data.
I tracked down R's chi-squared comparison to Lawley & Maxwell (1962 &  
1971). Their Bartlett test suffers from a few disadvantages such as  
requiring the inverse of what I have discovered to be an ill-conditioned  
matrix or working from correlation matrices rather than original data.
My preference is to use Mathematica's elegant automatic Hypothesis tests  
in VarianceEquivalenceTest. At present this function compares vectors of  
data, rather than matrices. Mapping across each pair of original and  
recreated variables will lead to as many tests results as variables. This  
would be quite cumbersome and somewhat analogous to investigating the  
percentage of differences between correlation matrices that are greater  
than say 0.05, which is interesting but not a test upon which to accept or
reject the number of factors. Thus my question.
Many thanks to those who may be looking at this question.
BTW For those using a Version prior to 8.0, the first line of the package  
would need amendment to  
BeginPackage["zigzagefa`",{"MultivariateStatistics`"}]

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