Poisson and Negbin - opposite estimation

[nitu pun]

Hi,

I have done Poisson ML and NB2 estimation.

Cameron and Trivedi 2010 says that the estimation should be similar (NB2 estimation should be around 15% of Poisson ML).

However, my Poisson ML and NB2 estimation give opposite estimation. One says the main variable of interest increases and the other says decreases.

Would someone be able to tell me what could possibly be going wrong?

Many thanks,


N

[Jeff Wooldridge]

Nitu: I'm not sure what that Cameron and Trivedi comment refers to. Can you cite a page? Because if the NB2 model is correct, the estimates should be similar because the Poisson estimates are consistent if the NB2 model is correct. The opposite is not true. That's why, for estimating effects on the mean -- the majority of applications, I think -- I always prefer Poisson regression with robust standard errors. Are CT referring to standard errors (which, again, would leave me a bit puzzled).

It is pretty rare to see sign changes when comparing Poisson and NB2. But the NB2 estimates could be badly biased if the variance-mean relationship is complicated. In particular, if there is underdispersion (variance less than mean) for all or some values of x, NB2 can be off.

Try this command for Poisson regression:

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

In the upper right-hand-corner, what does Stata report for the statistic (1/df) Pearson?

And don't listen to people who say not to use Poisson regression. They're thinking of requiring all features of the Poisson distribution to be correct, whereas none need to be for estimation of the mean parameters.

Oh, and as others on here will tell you, please read the FAQ about how to post here and you'll get faster, better answers.

JW

[nitu pun]

This is CT 2010 pg.578. CT are referring to coefficients (not standard errors).

I tried dropping some explanatory variables from my model and the P and NB coefficient estimates are similar. However the standard errors of NB are slighter larger than the P (CT say that it should be the opposite "indicating efficiency gains due to using a more appropriate parametric model".)

I entered the code and Stata reports 31.46233 for (1/df) Pearson.

N

[Jeff Wooldridge]

That's a very large value for that Pearson statistic suggesting severe overdispersion. Are you using the Poisson robust standard errors and comparing those to the NB2 usual MLE standard errors? If the NB2 ones are larger that shows NB2 is very unlikely to be the correct model.

What happens when you use NB1? I can't really help more without seeing some output.

[nitu pun]

I used Poisson robust standard errors and NB2 robust standard errors. NB1 give me an opposite estimation to Poisson ML and NB2 (which I do not want).

Here are my results:
Poisson

NB2

NB1

[Jeff Wooldridge]

Nitu: I assume you're referring to the coefficient on "no." You have to remember that estimates are uncertain; that's why we have standard errors and confidence intervals. In all three estimations the coefficient is quite insignficant; it's not even close to being statistically different from zero. That's effectively telling us that, if you obtained a different sample -- or, in your case, use a different estimation method -- it would not be at all unusual to see a sign flip. If you random sample 10,000 units from a normal population with a mean of zero, you'll get a negative estimate roughly half of the time and a positive estimate the other half. That's essentially what is happening to you. You can also apply nonlinear least squares using the glm command with fam(normal) and link(log) as a fourth estimator. Frankly, I don't know what the sign on "no" would be, and it wouldn't tell us much unless it somehow was statistically different from zero (unlikely).

Note that, on the statistically significant variables, the signs line up and the magnitudes are reasonably close, too.

By the wage, is agen1sq the square of agen1? Is "no" a function of these variables? If either is true I may have a suggestion for how to get much better results. You should center agen1 about its mean before squaring it, unless agen1 = 0 is the most interesting value.

Finally, while it makes sense to use "robust" for poisson, you should know you're admitting the estimates in the NB1 and NB2 cases are inconsistent if you use a robust option. That's because, theoretically, NB1 and NB2 are not robust quasi-MLEs. This is a minor point, though, and to me it makes sense to admit all models are, at best, approximations.

[nitu pun]

The agenlsq is the square of agenl (age non-linear). The 'no' refers to not receiving payment i.e. WFP. So the population that didn't receive the payment had higher GP visits. I will try all that have suggested. Thanks.