Hmm. Interesting. Well rank-based non-parametrics is not my strength,
so I cannot really comment much on the results of -somersd-.
-bootstrap- won't be better, and it is actually quite difficult with
the survey data to bootstrap them properly. I've been tried to hammer
that into Stata users heads at the last couple of meetings, but you
must have skipped my presentations :)). I'd be still be more inclined
to stick to the jackknife, so you will need something like
program define partial_tau, eclass properties( svyj )
* run the three somersd commands
* to get temp scalars `tau_xy', etc.
* put them together to say
tempname ptau
mat `ptau' = (`tau_xy' -
`tau_xz'*`tau_yz')/sqrt((1-`tau_xz'^2)*(1-`tau_yz'^2))
ereturn post `ptau'
end
I am not entirely sure this will work. If it does not, ask Jeff
Pitblado for some help, he would know all the guts of -svy jackknife-
processing.
If the covariance matrix is singular, the general theory would
probably suggest taking higher order expansions. And that you
certainly don't want to do. However my asymptotic intuition says here
that a degenerate covariance matrix of the taus does not necessarily
imply that you will have problems with the variance of the result.
On 1/21/09, Feiveson, Alan H. (JSC-SK311) <[email protected]> wrote:
> Stas - Thanks for your further comments and the reference. With
> -somersd- and the fun(), cluster(), and wstrata() options I can get
> pairwise estimates of the "correct" covriance matrix obtained by
> jackknife, as I described earlier - but it turns out that (at least for
> the one time I tried it) the 3 x 3 matrix is singular! So to do the
> jackknife on all three taus or on the partial tau, it looks as though I
> would need to modify the current -somersd-, Another alternative is to
> use -bootstrap- on -somersd- with the appropriate options, but this is
> wasteful since I only need the point estimates for each resampled data
> set, not jackknife-within-jackknife standard errors. But the advantage
> of bootstrapping -somersd- is that I will have the necessary informaiton
> to compare the two methods as you suggest. Of course there is also the
> issue of which transformation to use. It was also interesting to read
> your discussion about what is "asympotic". The application I have in
> mind is more like #strata going to infinity with #units per stratum
> bounded.
>
> By the way, I just now realized what you were talking about with respect
> to "1, 3, 4" oops!
>
> Al
>
>
--
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.
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