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Re: eigenstructure table in linear model fit

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115968] Re: eigenstructure table in linear model fit
  • From: richard i pelletier <bitbucket at comcast.net>
  • Date: Fri, 28 Jan 2011 06:11:20 -0500 (EST)
  • References: <ihrb56$8ru$1@smc.vnet.net>

In article <ihrb56$8ru$1 at smc.vnet.net>,
 Darren Glosemeyer <darreng at wolfram.com> wrote:
> 
> 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?
> 
Thanks for your replies, Darren.

I figured out for myself how the variance partitions were calculated,
but it was result of putting together a notebook to send you.

I do have a new question: can you provide a reference explaining what 
the eigenstructure table means? I now know _how_ it is calculated, but 
not _why_ it is a variance partition.

Writing out a careful explanation of what I did and didn't know gave me 
all the pieces of the puzzle. I had finished writing it out in a 
notebook, thought I would sleep on it before sending it, and then I 
finally stopped working.

Ten minutes later I realized there was an obvious calculation to try... 
and it worked.

I'm rather glad you didn't tell me how to calculate the variance 
partitions. I get a sharp thrill from working such things out for 
myself, and last night's solution was very satisfying.

I can send you the notebook, in case you're curious... but now it asks 
no questions. Instead, it concludes by showing exactly how the 
eigenstructure table is computed.

Thanks again. Trying to explain a problem to someone is often all you 
need in order to solve it.

(Posted and emailed.)

Vale,
   rip

-- 
email address is r i p 1 AT c o m c a s t DOT n e t


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