Prediction interval (not confidence interval) calculations for glm w/ robust VCE model?

[sarah minion]

In reference to the two threads below, did anybody ever figure out how to get prediction intervals/individual intervals/the stdf command to work with margins in more complex models? I have a glm with poisson family and log link with robust variance estimator. I have been requested by a reviewer to add prediction intervals in one week but cannot find a solution as the predict + stdf command does not appear to work with robust VCE (https://www.statalist.org/forums/for...=1653449067985).


https://www.statalist.org/forums/for...argins-command
https://www.statalist.org/forums/for...able-after-mlr

[Joao Santos Silva]

Dear sarah minion,

I believe the answer to your question depends on whether you believe your data really follows a Poisson distribution. If that is the case, then you can use the properties of the Poisson distribution to get the interval. Otherwise (and I fear this is your case because you use robust standard errors), there is no way to do that because such intervals require very strong parametric assumptions that we cannot make if we are agnostic about the distribution of the data. An alternative would be to use quantile regression to compute the limits of the interval, but I do not know if you want to go that way.

Best wishes,

Joao

[sarah minion]

Hi Joao, Thanks for your answering my question so succinctly. At this point in my data analyses, I feel strongly about the distribution + robust standard errors and do not want to switch to quantile regression. I wanted to confirm that there wasn't an alternative I was missing within the bounds of my current model, and you have definitely answered that. Appreciate the help!

[Joao Santos Silva]

Dear sarah minion,

Just to clarify, you can use quantile regression to complement your analysis, not to replace it.

Best wishes,

Joao