Poisson

[Serena Gallo]

Hi Dear, I have a question. My dependent variable is a count variable. I want to choose between Poisson and NBREG and I have used the command "estat gof", this is the result:

Deviance goodness-of-fit = 226113.7
Prob > chi2(61) = 0.0000


Pearson goodness-of-fit = 286506.8
Prob > chi2(61) = 0.0000

Is NBREG the right model?

[Carlo Lazzaro]

Serena:
quoting from -help poisson postestimation##estatgof-:

estat gof performs a goodness-of-fit test of the model. Both the deviance statistic and the Pearson statistic are reported. If the tests are significant, the Poisson regression model is inappropriate.
Then you could try a negative binomial model; see [R] nbreg.

However, it is worth investigating whether the overdispersion is real or not (while in the first case -nbreg- is the way to go, in the latter -poisson- can still be a valid option and the over dispersion can be dealt with by dividing standard errors for a given constant and/or adding more predictors or interactions).
The deeply missed Joe Hilbe authored two relevant textbooks on count data regerssion model, from which I've learnt (and I'm still lerning) a lot:
https://www.stata.com/bookstore/nega...l-regression/;
https://www.stata.com/bookstore/modeling-count-data/.

[Serena Gallo]

Thanks very much for your suggestions. I don't understand how I can divide standard errors for a given constant, Can you provide me with any examples?

[Carlo Lazzaro]

Serena:
see Example 5, -glm- entry, Stata .pdf manual and/or:

https://www.stata.com/bookstore/modeling-count-data/. (pages 92-96).

[Jeff Wooldridge]

Serena: Using -estat gof- is an outdated way of choosing between Poisson and NBREG. It presumes that the NEGBIN model is correct and then it is a test of the Poisson distribution as a special (limiting) case of the NEGBIN distribution. But the NEGBIN distribution could be wrong. The variance/mean relationship could be very complicated, in which case NBREG is not even consistent. By contrast, the Poisson quasi-MLE is always consistent if you have the mean correct. Thus, Poisson regression is preferred regardless of the outcome of the specification test. In other words, I would use Poisson regression regardless of the outcome of the specification test because the test takes too narrow a view.

To Carlo's point about getting valid standard errors: use the vce(robust) option for poisson. This allows arbitrary misspecification of the Poisson distribution and gives the proper standard errors no matter what.

poisson y x1 ... xk, vce(robust)

Or, you can use the glm command:

glm y x1 ... xk, fam(poisson) vce(robust)

If you want to simply scale the MLE standard errors by a constant, use

glm y x1 ... xk, fam(poisson) sca(x2)

But this is still restrictive, and you are better off using the fully robust option.

[Serena Gallo]

Thanks a lot, Professor Wooldridge.
Your suggestions are very precious to me. I follow your advices by using Poisson regression with robust standard errors.