survey weighted negative binomial regression test for overdispersion

[Luis Mijares Castaneda]

I'm reposting, hoping someone can answer.

Hello, I had a quick question. I want to assess whether a count model using data from a survey suffers from overdispersion. Can I test for overdispersion using the alpha parameter from a survey-weighted nbreg model? I understand why the LR test is not produced when using survey-weighted data, but can I trust the alpha parameter to properly assess overdispersion? In the case below, because the confidence interval for the alpha parameter does not contain 0, is there evidence of overdispersion?

     
.  local contrls ///
>             c.ppage ///  
>             i.race_alt ///
>                       i.income ///
>                          i.personal_debt ///
>                          i.region ///
>                         i.housetype_alt /// 
>                          i.employment ///
>                          i.arrested ///
>                         i.asud /// 
>                          i.LifetimePTSDcriteria_positive ///
>                          i.any_lifetime_suicide_attempt ///
>                          

. svy: nbreg home_loss `contrls', exposure(total_years) irr  
(running nbreg on estimation sample)

Survey: Negative binomial regression

Number of strata =     1                          Number of obs   =      1,283
Number of PSUs   = 1,283                          Population size = 1,258.0535
                                                  Design df       =      1,282
                                                  F(19, 1264)     =       5.59
Dispersion: mean                                  Prob > F        =     0.0000

-------------------------------------------------------------------------------
              |             Linearized
    home_loss |        IRR   std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
        ppage |    .982977   .0126402    -1.34   0.182     .9584894     1.00809
              |
     race_alt |
 1.Non-White  |   1.858577   .5590613     2.06   0.040     1.030141     3.35324
              |
       income |
15,000-$~999  |   2.323929   1.060695     1.85   0.065     .9491779    5.689813
$30,000-~999  |   .8925358   .4195413    -0.24   0.809     .3549242     2.24448
 >= $60,0000  |   .2782457   .1839597    -1.93   0.053     .0760558    1.017946
              |
personal_debt |
2.less tha..  |   1.968493   .9617833     1.39   0.166     .7548373    5.133508
3.$15,00~000  |   1.336246   .7598767     0.51   0.610     .4379052    4.077487
4.$35,00~000  |   1.107194   .7143556     0.16   0.875     .3122585    3.925846
              |
       region |
     Midwest  |   2.420599   1.614974     1.33   0.185     .6538554    8.961153
       South  |   2.357167   1.494536     1.35   0.176     .6794933    8.177029
        West  |   .8547957   .6390102    -0.21   0.834      .197214    3.704989
              |
housetype_alt |
2.Apartmen..  |   1.482899   .5088747     1.15   0.251     .7563719    2.907285
     3.Other  |   1.184448   .8015107     0.25   0.803     .3140271    4.467501
              |
   employment |
Working pa..  |   .1982927   .1220356    -2.63   0.009     .0592864    .6632205
 Not working  |   .4308464    .184369    -1.97   0.049     .1860928    .9975055
              |
     arrested |
  1.Arrested  |   1.616884   .5399287     1.44   0.150     .8397831    3.113082
              |
         asud |
         Yes  |   1.941994   .8153613     1.58   0.114     .8521709     4.42557
              |
LifetimePTS~e |
         Yes  |   1.944238   .8600343     1.50   0.133     .8163272     4.63057
              |
any_lifeti~pt |
         Yes  |   4.136422   1.841605     3.19   0.001      1.72702    9.907229
        _cons |   .0172554   .0184194    -3.80   0.000     .0021254    .1400889
ln(total_y~s) |          1  (exposure)
--------------+----------------------------------------------------------------
     /lnalpha |   .8077066   .4349825                     -.0456491    1.661062
--------------+----------------------------------------------------------------
        alpha |   2.242759   .9755607                      .9553772    5.264901
-------------------------------------------------------------------------------
Note: Estimates are transformed only in the first equation to incidence-rate
      ratios.
Note: _cons estimates baseline incidence rate.

[Jeff Wooldridge]

Yes, Luis, if you want to use nbreg with svy, you can trust the Wald (asymptotic t statistic) to test the null that alpha is zero.the standard error properly accounts for the survey sampling. Since you’re very likely interested in the effects on the mean, I’d also use the fully robust svy: poisson, too.