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Re: eigenstructure table in linear model fit

• To: mathgroup at smc.vnet.net
• Subject: [mg115962] Re: eigenstructure table in linear model fit
• From: Darren Glosemeyer <darreng at wolfram.com>
• Date: Thu, 27 Jan 2011 03:42:24 -0500 (EST)

On 1/20/2011 5:28 AM, richard i pelletier wrote:
> Hi,
>
> Can anyone tell me how the eigenstructure table, a property of linear
> model fit, is computed? I can't find the details of the computation in
> the documentation.
>
> Furthermore, the documentation seems wrong. It is an easy verification
> that the eigenvalues listed in the eigenstructure table are those of the
> _data_ correlation matrix, rather than of the _parameter_ correlation
> matrix. (I used the well-known Hald data.)
>
> Or am I making a foolish mistake?
>
> Thanks,
>
> rip
>

The most complete description in the docs is:

""EigenstructureTable" gives the eigenvalues, condition indices, and 
variance partitions for the nonconstant basis functions. The Index 
column gives the square root of the ratios of the eigenvalues to the 
largest eigenvalue. The column for each basis function gives the 
proportion of variation in that basis function explained by the 
associated eigenvector. "EigenstructureTablePartitions" gives the values 
in the variance partitioning for all basis functions in the table."

in tutorial/StatisticalModelAnalysis.

Note that the table includes information about the nonconstant basis 
functions. I've checked that the code uses the design matrix. If the 
nonconstant basis functions are the same as the predictor variables in 
your example, I wonder if this might account for what you are observing?

Darren Glosemeyer
Wolfram Research