Exlaining xtnbreg dispersion statistics in layman's terms

[James Wo]

Hello Everyone,

For a paper, I have estimated a series of longitudinal negative binomial regression models using Stata's xtnbreg command. However, for reporting purposes, I have the following questions:

1) Unlike the output provided by nbreg, the xtnbreg model provides "/ln_r" and "/ln_s" as well as "r" and "s". Which of these statistics would you report for a journal publication?

2) Also, can someone please provide layman's interpretations of the xtnbreg dispersion statistics? Unfortunately, the stata manual simply reads "/ln_r and /ln_s for longitudinal negative binomial regression (the Stata command: xtnbreg) refer to ln(r) and ln(s), where the inverse of one plus the dispersion is assumed to follow a Beta(r, s) distribution"

***If anyone can provide the answer to the above questions, or point me in the right direction, it would be much appreciated.

Thanks much!
James

[Clyde Schechter]

1) Unlike the output provided by nbreg, the xtnbreg model provides "/ln_r" and "/ln_s" as well as "r" and "s". Which of these statistics would you report for a journal publication?

I think that depends on the journal and who reads it and who reviews it. Since you are asking in your second question for a layman's interpretation, I'm guessing that your target audience is not deeply familiar with statistics. When I publish in clinical journals, I would not report anything about technical details like that. The readers would never understand it, and given their interests it would not be a worthwhile use of their time for them to read a long enough explanation to actually get it across. If you are writing for a statistically savvy audience, I'd probably show r and s rather than their logarithms, although such an audience would probably be unphased by either.

2) Also, can someone please provide layman's interpretations of the xtnbreg dispersion statistics? Unfortunately, the stata manual simply reads "/ln_r and /ln_s for longitudinal negative binomial regression (the Stata command: xtnbreg) refer to ln(r) and ln(s), where the inverse of one plus the dispersion is assumed to follow a Beta(r, s) distribution"

This strikes me as a bit like asking for instructions in layman's terms on how to build a Higgs boson detector in your garage. The explanation in the Stata manual is clear to anyone trained in statistics. An explanation of all of this in layman's terms would, I think, run to several pages, as one would have to first introduce the whole concept of overdispersion and why it is a problem, and how the negative binomial model deals with it. Then one would have to go on and explain beta distributions (and maybe even distributions themselves). It seems to me that any audience for your work that actually would care about this level of detail will already understand it as explained in the Stata manual. If you are writing for a hybrid audience of lay people and technical people, you could skip it in the main body of your work and include the details in an appendix.