# st: Odd iweights + regress behavior

 From "Schaffer, Mark E" To Subject st: Odd iweights + regress behavior Date Thu, 10 Dec 2009 14:29:08 -0000

```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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```