Extreme difference: Log-binomial vs robust Poisson regression poisson-regression

[Marios Politis]

Hi all,
More a statistics than a STATA programming question: I am working on cross-sectional data and I have fit the 1.log-binomial regression model, 2.robust Poisson regression and the 3. logistic regression model. My outcome is rare (<1%) and the data are clustered in two levels. My question is: why while all results are similar (PR and POR) only the robust Poisson regression provides a significant result? Can I use any model without justification?
Thanks

[Carlo Lazzaro]

Marios:
as usual, no details from poster's side causes the reply to be guess-work driven.
If robust Poisson means a -poisson- with non-default standard errors, this may be the/one explanation.

[Marios Politis]

Sorry for the confusion, you are right, Carlo.
So, bellow are the codes for every model. The outcome is rare and I believe that's the reason that the results are almost identical for all models. However, the robust poisson model provide considerably significant results, whereas the other do not.

logistic regression: meglm result ib1.tertiles_all i.1.Sex i.contact i.past i.agegroupreg i.screening ib1.health_insurance|| district :, family(binomial) link (logit) eform
robust Poisson regression: meglm result ib1.tertiles_all i.1.Sex i.contact i.past i.agegroupreg i.screening ib1.health_insurance || district :, family(poisson) vce(robust) irr
log-binomial regression: xi: gllamm result i.tert2 i.tert3 i.sexreg1 i.contact i.past i.agegroupreg i.screening i.hi1 ,link(log) fam(binom)i(dist) eform

[Carlo Lazzaro]

Marios:
1) you ran three different models. Therefore, different results are perfectly legal;
2) you -meglm- code, -poisson- family, applies clustered-robust standard errors, whose validity depends on the number of clusters (30-50, at least) (see https://cameron.econ.ucdavis.edu/res...5_February.pdf).
For a smaller number of clusters, the cluster-robust standar errors can be even more misleading than their default counterparts.

[Marios Politis]

Thank you for your answer. My data are 13.000 individuals clustered into 40 wards and then in 4 districts. Which one of the levels should I consider for choosing the robust standard error function?

[Carlo Lazzaro]

Marios:
thanks for clarifying.
4 district are not enough to go cluster-robust.
You should go back to default standard errors.

[Marios Politis]

Thanks for your prompt response / feedback Carlo.