Poisson regression Goodness of Fit

[thesis]

Hi,

Currently I'm running a poisson regression and I would like to check the goodness of fit. However according to literature R2 is not usefull, Rodriguez (2007) supposes Pearson's Chi Squared Statistic might be a good alternative. Unfortenately this statistic is not presented in the Eviews output.
Therefore I have some questions

1. Is it correct the R2 is not a usefull goodness of fit measure for poisson?
2. What statistic might be a good alternative in these poisson regressions?
3. How do I calculate this alternative in Eviews? (For example Pearson's Chi Squared)

[EViews Glenn]

The Pearson statistic is reported if you estimate your Poisson using the GLM estimator.

Alternately, if your Poisson count equation is EQ01, with dependent variable is Y, forecast from your Poisson (say into the series YF),

Code: Select all

eq01.forecast yf

This gets you the expected values of the dependent variable. Then compute

Code: Select all

series pearson_residsq = (y-yf)^2/yf

to get the squared Pearson residuals, and

Code: Select all

scalar pearson = @sum(pearson_residsq)/eq01.@df

to get the Pearson statistic.

[thesis]

Thank you very much Glenn!! This works! However another question pops up: I read the Eviews guide, to get a better understanding of this GLM estimator. GLM is moslty used in combination with the Negative Binomial method (QML) which is an alternative in case of overdispersion.

I do not really understand this GLM estimator. It can be used together with the Poisson method as well. The probabilities change dramatically by using the GLM estimor, so how does this work?

So:

- Where and when do you use the GLM estimator for?
- Is the GLM in combination with Poisson already an alternative to correct for overdispersion?

[EViews Glenn]

I won't go into a long discussion of the GLM methodology, but basically, it's a framework for thinking about a variety of common nonlinear specifications (Logit, Poisson, ..., not just a particular form of the negative binomial) as particular generalizations of least squares. But it's not really doing a different model. Thus, estimating the GLM Poisson specification is an equivalent method of doing the the ML Poisson that you have estimated using COUNT. Putting the model in the GLM framework, however, unifies thinking about these models and has a number of conceptual advantages, in particular, highlighting various quasi-ML robustness results that come from the fact that the model is a member of the exponential family.

I'm not certain what you mean by the probabilities change as well...

Lastly, the GLM Poisson is the same model as the COUNT Poisson ML so overdispersion isn't accounted for. Thus, to correct for overdispersion, you'll have to use the negative binomial in either the COUNT or the GLM framework. Note that the negative binomial in the latter framework only supports QMLE. Note also that some of the QMLE remedies we offer in the COUNT framework come directly from the GLM theory.

I highly recommend the monograph on GLM by McCullagh and Nelder that we cite. I am also very fond of the Wooldridge discussion of QML count models. The latter is well-worth the price of admission.

McCullagh, Peter, and J. A. Nelder (1989). Generalized Linear Models, Second Edition. London: Chapman
& Hall.

Wooldridge, Jeffrey M. (1997). “Quasi-Likelihood Methods for Count Data,” Chapter 8 in M. Hashem
Pesaran and P. Schmidt (eds.) Handbook of Applied Econometrics, Volume 2, Malden, MA: Blackwell,
352–406.

[thesupremes]

Hi I need help I’m really new in the use of these program and actually I’m not economist I’m Environmental Biologist, so I’m totally lost.
Well my problem is these I don’t know if the value of Pearson statistics is indicating a good or bad fit.
I know this question is more statistical but I’m really desperate. I did a GML Poisson regression and my results are the next. Because i have no idea of how to do it in the Count Data model (I’m using (Eviews 7)




Coefficient Std. Error z-Statistic Prob.

C(1) 2.167030 0.120942 17.91793 0.0000
C(2) -2.39E-05 4.21E-06 -5.677737 0.0000
C(3) 1.72E-05 1.59E-06 10.82665 0.0000
C(4) 0.646290 0.079441 8.135524 0.0000
C(5) -0.644312 0.085060 -7.574753 0.0000

Mean dependent var 7.915789 S.D. dependent var 11.61131
Sum squared resid 10589.99 Log likelihood -559.4750
Akaike info criterion 11.88369 Schwarz criterion 12.01810
Hannan-Quinn criter. 11.93800 Deviance 804.7061
Deviance statistic 8.941179 Restr. deviance 1011.543
LR statistic 206.8368 Prob(LR statistic) 0.000000
Pearson SSR 1033.486 Pearson statistic 11.48318
Dispersion 1.000000

[Nitzan04]

How can i know what is the significant level of the value from the pearson chi square test?

[EViews Glenn]

The scaled deviance (and in this case the unscaled deviance) and Pearson SSRs should, for this model, both be approximately Chi-Square(n-p).