Interpretation confidence intervals empirical bayes estimates multilevel model

[Elena Strippoli]

Dear all,
I'm working with a multilevel poisson model using random effect approach (first level the patient and 34 hospitals at the second level). Here I provide an example of the code I am using:

mepoisson outcome treatment sex age || hospital: , irr exp(personyear)

I would like to explore whether there are differences among hospitals and which hospitals differ the most (by excess or defect) once adjusted for the variables in the model.
Using postestimation commands I can retrieve the empirical bayes estimates of the random effect and their standard error.

predict re_hosp, reffects reses(se_hosp)
gen lb_hosp= re_hosp-1.96* se_hosp
gen ub_hosp= re_hosp+1.96* se_hosp

I have two doubts about this:
1) Can I exponentiate the empirical bayes estimates (i.e., exp(re_hosp)) in order to read them as irr (I suppose that STATA gives me re_hosp prediction as logarithm)
2) Can I directly compare the confidence intervals to the 0 value to asses whether the hospital XYZ is significantly different from the average represented by the fixed part of the model?
Thank you for your attention

[Leonardo Guizzetti]

Please don't edit your question to nothing. The forum is designed to now allow you to delete posts so that they can serve as a record for future people who come across the thread to hopefully get some help.

[Erik Ruzek]

I would suggest you look at the PDF documentation for mepoisson postestimation. They give a very nice example of how one might work with predictions from a model. Remember that the empirical Bayes predictions are how much the hospital differs from the fixed constant (_cons) and so you will need to manually add the _b[_cons] to re_hosp and re_ses to recover the model-based estimates. I would not personally exponentiate those, but that is not based on anything other than I am unsure if that will give you what you want. In terms of looking for "significance," people have been known to use the approach you describe whereby hospitals with 95% CIs outside the fixed effect constant estimate are considered significantly different from the "average" hospital.

Another nice thing you can do is get a prediction for each hospital in the original metric of the outcome using:

predict mu, mu

Unfortunately, you do not get standard errors for this prediction, but it does put the predictions on the original, hopefully meaningful scale of the DV. And the prediction incorporates information about both the fixed and random effects in your model.

[Elena Strippoli]

Thank you,
thank you for the example on posteestimation commands. Unfortunately, I need to show the random part separately from the fixed part (so the predict mu command is not useful for me). I was not able to find examples in the litterature or in other forums.
If I am not mistaken in the meglm formula for the poisson distribution, the link function is always the logarithm. The incidence rate (=event/personsears), when all the covariates are set to 0, should be exp(_cons). So I wonder if exp(_cons+re_hosp) can be the incidence in the individual hospital including the random effect. I tried with the reported example, this interpretation seems to work. At least te exponential of exp(_b[_cons] + re) is at least on the same scale of the mean of the indipendent variable.

Thanks again, now I found a lot of examples of caterpillar plot interpreted as you said (also in the litterature).