# st: Query about negative binomial and poisson with an without survey weighted data

 From "Jason Ferris" To Subject st: Query about negative binomial and poisson with an without survey weighted data Date Tue, 21 Jul 2009 14:42:34 +1000

```Hi all,
I was looking at some data trying to determine the degree of
overdispersion when I noticed that the point estimate and standard error
for a svy: nbreg and a svy: poisson with only the outcome variable were
the same.  When I ran this without svy (i.e., nbreg and poisson) they
differed.  Can someone tell me why the survey approach produces
identical results?  Below, I have done this with a Stata dataset
(alq99_00) and got the same results.

Jason Ferris
AER Centre for Alcohol Policy Research
Turning Point Alcohol and Drug Centre
Victoria, Australia

Example:
* using stata-press dataset alq99_00

. webuse alq99_00, clear

. gen drinkdays=alq120q if alq120q<=365
(6451 missing values generated)

. svyset

pweight: wtmec2yr
VCE: linearized
Single unit: missing
Strata 1: sdmvstra
SU 1: sdmvpsu
FPC 1: <zero>

************
* weighted *
************

. svy: nbreg drinkdays
(running nbreg on estimation sample)

Survey: Negative binomial regression

Number of strata   =        13                  Number of obs      =
3948
Number of PSUs     =        27                  Population size    =
96361343
Design df          =
14
F(   0,     14)    =
.
Prob > F           =
.

------------------------------------------------------------------------
------
|             Linearized
drinkdays |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------+----------------------------------------------------------
------
_cons |   1.081066   .0578862    18.68   0.000     .9569123
1.205219
-------------+----------------------------------------------------------
------
/lnalpha |   .2746654   .0887549                       .084305
.4650257
-------------+----------------------------------------------------------
------
alpha |    1.31609   .1168095                      1.087961
1.592055
------------------------------------------------------------------------
------

. svy: poisson drinkdays
(running poisson on estimation sample)

Survey: Poisson regression

Number of strata   =        13                  Number of obs      =
3948
Number of PSUs     =        27                  Population size    =
96361343
Design df          =
14
F(   0,     14)    =
.
Prob > F           =
.

------------------------------------------------------------------------
------
|             Linearized
drinkdays |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------+----------------------------------------------------------
------
_cons |   1.081066   .0578862    18.68   0.000     .9569123
1.205219
------------------------------------------------------------------------
------

**************
* unweighted *
**************

. nbreg drinkdays, nolog

Negative binomial regression                      Number of obs   =
3514
LR chi2(0)      =
0.00
Dispersion     = mean                             Prob > chi2     =
.
Log likelihood = -8053.3652                       Pseudo R2       =
0.0000

------------------------------------------------------------------------
------
drinkdays |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------
------
_cons |    1.19019   .0232271    51.24   0.000     1.144666
1.235714
-------------+----------------------------------------------------------
------
/lnalpha |   .4647593    .029011                      .4078988
.5216197
-------------+----------------------------------------------------------
------
alpha |   1.591631   .0461748                      1.503655
1.684754
------------------------------------------------------------------------
------
Likelihood-ratio test of alpha=0:  chibar2(01) = 2.0e+04 Prob>=chibar2 =
0.000

. poisson drinkdays, nolog

Poisson regression                                Number of obs   =
3514
LR chi2(0)      =
0.00
Prob > chi2     =
.
Log likelihood = -18257.672                       Pseudo R2       =
0.0000

------------------------------------------------------------------------
------
drinkdays |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------
------
_cons |    1.19019   .0093036   127.93   0.000     1.171955
1.208425
------------------------------------------------------------------------
------

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