0
$\begingroup$

It's not clear how to build models when using the Stata gb2lfit module. Output includes two tables, parameter estimates and their logs. The significance tests can sometimes differ between the tables, with the paramter estimates being significant and the logs not. On which table ahould decisions about parameter significance be made?

Since it's possible that models with fewer than 4 parameters will fit the data, one also needs some way of comparing models. If only one log or parameter is not significant, is it then safe to assume that it is equal to 0 (log) or 1 (parameter)? If I constrain parameters as shown in the documetation, then how are models compared? Should the log pseudo-likelihood be utilized with the lowest value representing the best model?

Improve this question
$\endgroup$
6
  • $\begingroup$ Please note this question is in reference to gb2lfit, not gb2fit. Yes, Jenkins does demonstrate use of the Wald test, but he also shows a direct comparison of the Dagum and Singh-Maddala models. Not clear how the comparison is made and not clear how to judge parameter significance since tables of the logs and parameters are sometimes in disagreement. $\endgroup$
    – William Shakespeare
    Commented Sep 13, 2013 at 11:27
  • $\begingroup$ where did you find gb2lfit? findit did not find it. $\endgroup$
    – Maarten Buis
    Commented Sep 13, 2013 at 11:44
  • $\begingroup$ A Wald test is a comparison of these models, as one is just a constrained version of the other. If you do se log likelihood instead of log pseudo-likelihood, you can use the likelihood ratio test to compare them, but in your case you can only do the Wald test. $\endgroup$
    – Maarten Buis
    Commented Sep 13, 2013 at 11:47
  • $\begingroup$ Everything is at the JRSSA website. Gb2lfit is for truncated data. See: Jenkins, S. P., Burkhauser, R. V., Feng, S. and Larrimore, J. (2011), Measuring inequality using censored data: a multiple-imputation approach to estimation and inference. Journal of the Royal Statistical Society: Series A (Statistics in Society), 174: 63–81. $\endgroup$
    – William Shakespeare
    Commented Sep 13, 2013 at 12:12
  • $\begingroup$ I still cannot find the program, can you give a link? $\endgroup$
    – Maarten Buis
    Commented Sep 13, 2013 at 12:48

1 Answer 1

Reset to default
1
$\begingroup$

did you look at http://www.stata.com/meeting/2german/Jenkins.pdf ?

If you specify (cluster) robust standard errors and/or sampling weights you loose the capacity to compare likelihoods, see: http://www.stata.com/support/faqs/statistics/likelihood-ratio-test/ . In that case you need to use Wald tests, as was done in Stephen's presentation I linked to above. In Stata that would mean using the test command.

Regarding the first question: The top and bottom part of the table represent different null-hypotheses. The top part refers to the null-hypothesis log(parameter)=0, while the bottom part refers to the parameter=0. So you should get different p-values. They are both correct answers, it is just that the question is different. You should start with specifying the null hypothesis you want to check.

Improve this answer
$\endgroup$
3
  • $\begingroup$ Can you be a little more specific? What hypotheses are being tested? $\endgroup$
    – William Shakespeare
    Commented Sep 13, 2013 at 13:34
  • $\begingroup$ Let me be specific. My purpose is to determine how many parameters to retain in the model. Any of a, b, p or q could be equal to 1 (or the log of the parameter=0). However, when the p values for the parameter and its log disagree, it's not clear what to do. I would tend to want to look at the p values for the parameters, but the documentation for gb2lfit shows a test constraining the log to 0. Therein lies the confusion. $\endgroup$
    – William Shakespeare
    Commented Sep 13, 2013 at 14:14
  • $\begingroup$ There is no need for confusion: the p-values should be different because they test different null hypotheses. All you need to do is specify the null hypothesis you care about, and test that using the test command. What is being used by test are the log(parameters), so you will need to specify your null-hypothesis in terms of the log(parameter). If you prefer to use the parameter form, you will need to use gb2fit instead of gb2lfit. $\endgroup$
    – Maarten Buis
    Commented Sep 14, 2013 at 15:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.