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Re: st: Vector degrees of freedom in Stata


From   "Stas Kolenikov" <[email protected]>
To   [email protected]
Subject   Re: st: Vector degrees of freedom in Stata
Date   Wed, 11 Apr 2007 08:46:48 -0500

Well a different line of thought would be towards scalar degrees of
freedom arguing that # of clusters is too conservative, while # of
observations is too liberal, so the effective degrees of freedom are
somewhere it between. I know there's been thinking along those lines
in the mixed models literature, motivated for instance by the need to
come up with some reasonable numbers to go into the information
criteria for model selection, but I have not been following that
literature.

Yet another view on the effective degrees of freedom is suggested in
the statistical learning and data mining literature where they show
that the effective degrees of freedom for a non/semi-parametric model
can be found as E(\partial \hat y_i/\partial y_i) = Cov( \hat y_i,
y_i), which can be checked to coincide with linear regressions
identities like # variables = trace[ X(X'X)^{-1}X' ]. See Hastie,
Tibshirani and Friedman's book on statistical learning (2001), or Ye
(JASA, 1998: http://www.citeulike.org/user/ctacmo/article/574999).

On 4/11/07, Newson, Roger B <[email protected]> wrote:
Fellow Statalisters (especially StataCorp):

At the German Stata Users' Group Meeting at Mannheim in 2006, whose Web
page is at
http://ideas.repec.org/s/boc/dsug06.html
Bobby Gutierrez gave a very interesting talk on -xtmixed-, downloadable
at
http://ideas.repec.org/p/boc/dsug06/05.html
which ended with a summary of possible future developments to watch out
for in future versions. One of these possible developments mentioned was
"Degrees of freedom calculations". This seems to indicate that somebody
at StataCorp is thinking of offering alternative degrees of freedom
formulas to the standard e(N_clust)-1 or e(N_clust)-colsof(e(b)), at
least for -xtmixed-.

--
Stas Kolenikov
http://stas.kolenikov.name
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