How do you interpret the Pearson goodness of fit test p-value for Poisson Regressions?

[anisha arya]

Hi,

For data:

* Example generated by -dataex-. For more info, type help dataex
clear
input float count_selectoptionsh byte treatment long businessincome_num float(ff_dummy albvisit_dummy) long takerisk_num byte(educ ownership)
1 2 . 0 0  7 5 3
0 1 5 0 0  4 6 1
5 2 5 0 0  7 6 2
0 1 6 0 0  . . .
3 1 0 0 1  7 7 1
4 3 1 0 0  6 7 1
2 3 1 0 0  4 4 3
5 2 3 0 1  6 5 1
1 3 1 0 0  6 6 2
1 2 1 0 1  7 3 4
2 1 . . 0  6 . 1
0 1 2 1 1  3 2 2
1 2 1 0 0  7 3 1
4 3 1 0 1  5 4 4
0 1 1 0 1  5 . 1
4 2 2 0 0  2 6 4
1 1 1 0 1  6 6 1
0 1 1 0 0  4 4 2
4 2 2 0 0  7 6 1
3 1 6 0 0  9 5 3
2 1 2 0 0  6 3 1
0 1 1 0 1  5 2 1
1 2 1 0 0  4 . 1
2 3 1 0 0  7 6 1
0 1 6 0 0  5 6 3
1 2 1 0 1  7 7 2
3 1 2 0 1  7 5 1
2 1 . 0 1  8 3 1
1 2 6 0 1  5 . 3
0 1 . 0 1  5 6 2
1 1 . 0 0  6 6 1
2 1 . 0 1  7 6 1
3 1 . 0 0  5 3 2
1 2 . 0 1  5 4 4
2 3 6 0 0  7 3 3
2 1 1 0 1  5 6 1
2 3 . . 0  5 5 1
1 1 6 1 1  8 6 1
5 1 0 1 1  5 7 4
3 3 1 0 0  9 5 1
3 2 6 0 0  8 6 2
4 3 6 0 1  7 6 2
7 1 6 0 0  5 6 2
2 1 2 0 0  5 5 3
0 1 1 0 1  6 5 2
2 1 5 0 1  9 6 2
4 2 6 0 1 10 5 1
3 1 6 0 1  7 6 2
4 2 1 0 1  7 4 4
0 3 1 0 1  1 . 1
2 2 3 0 0  9 5 3
1 1 2 0 1  8 4 4
1 3 3 0 0  3 6 1
0 1 1 . 1  5 . 4
1 3 . 0 0  6 7 3
0 2 6 0 1 10 3 3
4 2 6 0 0  7 6 1
3 2 1 0 1  8 5 2
3 3 6 0 1  6 5 3
2 2 2 0 1  8 5 2
2 3 3 0 0  5 7 1
1 3 6 0 0  8 3 3
1 1 1 0 0  5 7 2
5 3 1 1 1  3 7 2
7 2 . 0 1 10 7 3
1 2 1 0 0  5 3 1
2 2 1 0 1  7 3 2
1 3 1 0 1  7 . 1
2 2 6 0 1  6 7 3
2 1 3 0 0  5 5 1
4 2 . 0 1  9 5 4
2 2 2 0 0  7 6 2
2 1 . 0 1  3 4 1
2 2 . 0 0  5 6 1
3 1 5 0 1  4 5 4
0 2 6 0 0  7 6 1
1 3 6 0 0  5 5 3
1 1 . 0 0  7 6 1
1 3 1 0 0  4 . 4
4 2 3 0 0  8 6 1
2 3 1 0 0  5 4 1
1 1 . 0 0  5 1 3
1 1 . 1 1  6 6 1
3 3 3 0 0  7 4 4
1 3 . . 0  6 . 1
4 2 0 0 1  5 4 2
2 2 5 0 0  6 7 2
3 3 6 0 0  7 6 2
0 3 . 0 1  9 5 1
0 1 6 0 0  8 7 3
1 1 6 0 1  4 4 2
1 3 6 . 0  6 4 3
1 3 2 0 0  7 6 2
2 2 1 0 0  7 5 2
2 3 . 1 1  8 5 2
4 1 6 1 0  7 6 2
7 2 . 0 1  6 7 2
5 3 6 0 0  6 7 2
1 3 . 0 0  6 7 1
2 3 6 0 0  7 3 4
end
label values treatment treatment
label def treatment 1 "Control", modify
label def treatment 2 "Video", modify
label def treatment 3 "Video + Nudge", modify
label values businessincome_num junk
label values takerisk_num junk
label values educ educ
label def educ 1 "Completed Primary", modify
label def educ 2 "Some Secondary", modify
label def educ 3 "Completed Secondary School", modify
label def educ 4 "Vocational or Similar", modify
label def educ 5 "Some University but no degree", modify
label def educ 6 "University Bachelors Degree", modify
label def educ 7 "Graduate or professional degree (MA, MS, MBA, PhD, JD, MD, DDS)", modify
label values ownership ownership
label def ownership 1 "Fully owned", modify
label def ownership 2 "Mostly owned, some tenanted", modify
label def ownership 3 "Some tenanted, mostly owned", modify
label def ownership 4 "Fully tenanted", modify

I have poisson results:

 poisson count_selectoptionsh b1.treatment businessincome_num ff_dummy albvisit_dummy takerisk_num educ ow
> nership, vce (robust)

Iteration 0:  Log pseudolikelihood =  -621.2712  
Iteration 1:  Log pseudolikelihood = -621.27114  

Poisson regression                                      Number of obs =    391
                                                        Wald chi2(8)  =  47.41
                                                        Prob > chi2   = 0.0000
Log pseudolikelihood = -621.27114                       Pseudo R2     = 0.0321

--------------------------------------------------------------------------------------
                     |               Robust
count_selectoptionsh | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
---------------------+----------------------------------------------------------------
           treatment |
              Video  |   .2279497   .0905258     2.52   0.012     .0505223    .4053771
      Video + Nudge  |   .0889809   .0896911     0.99   0.321    -.0868103    .2647721
                     |
  businessincome_num |   .0523736   .0173785     3.01   0.003     .0183124    .0864347
            ff_dummy |    .277089   .1379644     2.01   0.045     .0066837    .5474942
      albvisit_dummy |   .1570745   .0706869     2.22   0.026     .0185306    .2956183
        takerisk_num |   .0191169   .0223749     0.85   0.393    -.0247372    .0629709
                educ |   .0796836   .0292534     2.72   0.006      .022348    .1370191
           ownership |   .0291635   .0363037     0.80   0.422    -.0419904    .1003174
               _cons |  -.3456968   .2298975    -1.50   0.133    -.7962877     .104894
--------------------------------------------------------------------------------------

. estat gof

         Deviance goodness-of-fit =  377.4179
         Prob > chi2(382)         =    0.5566

         Pearson goodness-of-fit  =  350.1423
         Prob > chi2(382)         =    0.8774

.

I am wondering if this is a good model for my data. Can it be ascertained from the Pearson test? If yes, how do I interpret the results?

[Dimitriy V. Masterov]

Take a look at example 1 in the poisson postestimation pdf for interpretation.