Goodness-of-fit test after Poisson

[Hm Saleh]

Hello guys,
I got this result and ran the Goodness-of-fit test after Poisson but the test is not significant. Is that mean we are not satisfied with the fit of my model?
thanks

[Jeff Wooldridge]

Three comments:

1. You should always used vce(robust) with Poisson regression. The standard errors may be larger or smaller than you're getting, but they'll be correct. I'm assuming you have no reason to cluster your standard errors.
2. The GOF statistics are quite statistically significant with very small p-values. This is expected with several large z (or t) statistics.
3. The GOF statistics don't tell you much that is useful. It says at least one variable is significant, but you can already see that. It's like the overall F statistic in a linear regression. Focus on the coefficients of the variables you care about and confidence intervals.
4. I just checked and the GOF statistic is not robust even if vce(robust) is used, making it even less useful. You can get a robust test of joint significance as follows:

poisson y x1 ... xK, vce(robust)
test x1 x2 ... xK

[Hm Saleh]

Thanks very much for your suggestions.
When I run the test command, I get an error message
test x1 x2 ... xK

[Hm Saleh]

Do I have to do the test to know if the Poisson model is satisfied?

[Jeff Wooldridge]

Please don't post screen shots. Post Stata output in between the code delimiters. Then I could copy and past rather than type the entire command line. See the FAQ about posting.

You can't use "i." in the test command. It has to be

test FAM_INCOME 1.HISPANIC 1.Married ... 2.EDUCATION 3.EDUCATION ...

Having said that, all you're testing is the null hypothesis that none of the variables help to predict N_CHILDREN. It's obvious that at least a few of the variables do. There's nothing about the "Poisson model" you're testing becausethe Poisson distribution doesn't have to be true. You're testing about the conditional expectation. But you still forgot to use the "vce(robust)" option.

[Hm Saleh]

Thank you very much for your response.

test ( FAM_INCOME 1.HISPANIC 1.Married 1.Divorced SHAREARNINGS 1.BLACK 2.EDUCATION 3.EDUCATION 4.EDUCATION 5.EDUCATION 2.AGE 3.AGE 4.AGE 5.AGE)


( 1) [N_CHILDREN]FAM_INCOME = 0
( 2) [N_CHILDREN]1.HISPANIC = 0
( 3) [N_CHILDREN]1.Married = 0
( 4) [N_CHILDREN]1.Divorced = 0
( 5) [N_CHILDREN]SHAREARNINGS = 0
( 6) [N_CHILDREN]1.BLACK = 0
( 7) [N_CHILDREN]2.EDUCATION = 0
( 8) [N_CHILDREN]3.EDUCATION = 0
( 9) [N_CHILDREN]4.EDUCATION = 0
(10) [N_CHILDREN]5.EDUCATION = 0
(11) [N_CHILDREN]2.AGE = 0
(12) [N_CHILDREN]3.AGE = 0
(13) [N_CHILDREN]4.AGE = 0
(14) [N_CHILDREN]5.AGE = 0

chi2( 14) = 190.87
Prob > chi2 = 0.0000



- The null hypothesis is given by my statement and in the output that each coefficient equals to zero simultaneously.

- The significance level of the test is close to 0, so we can strongly reject the hypothesis.

Do this result and interpretation make sense?

Thanks,