Hi all. I have a question about the behavior of -regress- with
iweights. It seems peculiar to me, and isn't documented anywhere I can
find, and I wonder if anyone can see any logic to it.
The behavior is the treatment of the sample size. Iweights are not
normalized, and in principle the sample size N can take non-integer
values.
If I recall correctly, Stata allows only integer values of N to be
posted with the obs() option of -ereturn-. If iweights generates a
non-integer N, -regress- rounds down before posting. That makes sense
to me.
But what I don't understand is why -regress- seems to use the same
rounded-down N for calculations of things like the var-cov matrix and
the error variance. Wouldn't it make sense to use the more precise,
unrounded N when calculating them?
In practice, iweights are, I think, used mostly by programmers, so this
is probably relevant only to those who are using -regress- to produce
these things.
An example using the toy auto dataset is below.
I am using Stata 11 but this behavior of -regress- appears in earlier
versions of Stata as well.
--Mark
Prof. Mark E. Schaffer FRSE
Department of Economics
School of Management & Languages
Heriot-Watt University
Edinburgh EH14 4AS UK
44-131-451-3494 direct
44-131-451-3296 fax
http://ideas.repec.org/e/psc51.html
*********** EXAMPLE **************
. sysuse auto, clear
(1978 Automobile Data)
. qui reg mpg weight [iweight=headroom]
. predict double e, resid
. gen double e2=e^2
. qui sum e2 [iweight=headroom], meanonly
. di r(sum_w)
221.5
. di e(N)
221
. scalar s2unrounded=r(sum)/(221.5-2)
. scalar s2rounded =r(sum)/(221-2)
. di sqrt(s2unrounded)
3.2509661
. di sqrt(s2rounded)
3.2546751
. di e(rmse)
3.2546751
.
. mat accum XX = weight [iweight=headroom]
(obs=221.5)
. mat XXinv=syminv(XX)
. mat Vunrounded = XXinv*s2unrounded
. mat list Vunrounded
symmetric Vunrounded[2,2]
weight _cons
weight 8.109e-08
_cons -.00025336 .83926154
. mat Vrounded = XXinv*s2rounded
. mat list Vrounded
symmetric Vrounded[2,2]
weight _cons
weight 8.128e-08
_cons -.00025394 .84117766
. mat list e(V)
symmetric e(V)[2,2]
weight _cons
weight 8.128e-08
_cons -.00025394 .84117766
--
Heriot-Watt University is a Scottish charity
registered under charity number SC000278.
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