[R] var-covar matrices comparison:

[Patrick Burns]

My first thought is to use a random permutation test.
In this setting the main question you need to ask is
what distance measure do you want to use between
variance matrices -- there are lots of choices.  One
that I've found useful is the absolute value of the
maximum eigenvalue of the difference of the matrices.

If you have a hypothesis about how the variances may
differ, then you should be able to come up with a more
powerful statistic.

Patrick Burns
patrick at burns-stat.com
+44 (0)20 8525 0696
http://www.burns-stat.com
(home of S Poetry and "A Guide for the Unwilling S User")

Aldi Kraja wrote:

>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?
>
>Below are a pair of two matrices, from several others.
>Thank you in advance for any input.
>Aldi
>
> First group var-covar matrix (the data were under treatment a)
>
>v1        v2                 v3          v4               v5       
>v6       v7            v8             v9
>
> 
>
>v1         730.87       3.406      -283.41        -74.68       
>107.57      -1355.13      -112.46      14.000       5.776
>
>v2             3.41      24.950       105.45       -121.31      
>-307.68       -285.40        29.65      -2.500      -7.796
>
>v3          -283.41     105.451      6292.19      -2676.46      
>-970.80      29296.23     10715.29       3.156     -66.313
>
>v4           -74.68    -121.307     -2676.46     124492.30     
>-2289.47     -20377.34      -409.71     183.500     563.102
>
>v5           107.57    -307.681      -970.80      -2289.47      
>7045.62      12118.09       954.51      38.258      96.355
>
>v6         -1355.13    -285.404     29296.23     -20377.34     
>12118.09     218555.93     70126.71     137.000    -130.667
>
>v7          -112.46      29.645     10715.29       -409.71       
>954.51      70126.71     28239.57      67.989     -26.370
>
>v8            14.00      -2.500         3.16        183.50        
>38.26        137.00        67.99      24.500       9.000
>
>v9             5.78      -7.796       -66.31        563.10        
>96.35       -130.67       -26.37       9.000      22.776
>
> 
>
> 
>
> Second group var-covar matrix (the data were NOT under treatment a)
>
>v1        v2                 v3          v4               v5       
>v6       v7            v8             v9
>
> 
>
>v1          2696.25       27.05       201.06       2745.54      
>-344.39        540.48        654.20      34.363       7.623
>
>v2            27.05       86.37       -96.89       -497.28     
>-1185.10      -3108.71       -910.38      -4.254      -9.115
>
>v3           201.06      -96.89     10647.26       8378.07      
> 595.81      66122.43      26237.21     -65.093     -51.998
>
>v4          2745.54     -497.28      8378.07     408391.25     
>-3887.28      40477.40      30652.01     450.539      50.311
>
>v5          -344.39    -1185.10       595.81      -3887.28     
>29204.00      65320.00      15238.41     -98.237     102.975
>
>v6           540.48    -3108.71     66122.43      40477.40     
>65320.00     549955.14     194691.90    -555.552     -95.210
>
>v7           654.20     -910.38     26237.21      30652.01     
>15238.41     194691.90      82698.88     -70.417     -75.585
>
>v8            34.36       -4.25       -65.09        450.54       
>-98.24       -555.55        -70.42      79.689       8.164
>
>v9             7.62       -9.11       -52.00         50.31       
>102.97        -95.21        -75.58       8.164      30.492
>
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