Robust Poisson Regression
Robust Poisson Regression with Sandwich Variance Estimator · Also known as: modified Poisson regression, Poisson regression with robust standard errors, log-binomial alternative, sandwich-variance Poisson
Robust Poisson regression fits a Poisson log-linear model to a binary outcome but replaces the model-based variance with the empirical sandwich estimator. This yields valid standard errors and risk ratios even though Poisson variance assumptions are technically violated for binary data. The approach, popularized by Zou (2004), is widely used in epidemiology as a numerically stable alternative to log-binomial regression.
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When to use it
Use robust Poisson regression when you have a binary outcome, want risk ratios rather than odds ratios, and log-binomial regression has failed to converge — which happens often when predictors are continuous or the outcome is common (prevalence > 10%). It is well suited to cross-sectional studies and prospective cohort studies with complete follow-up. Do not use it when the outcome is genuinely a count of events per unit time (use standard Poisson or negative binomial instead), or when the outcome is very rare (< 5%), where logistic odds ratios closely approximate risk ratios anyway. Avoid it when the log link predicts probabilities outside [0,1] for large portions of the data — check fitted values after estimation.
Strengths & limitations
- Produces directly interpretable risk ratios (relative risks) rather than odds ratios.
- Numerically more stable than log-binomial regression; IRLS rarely fails to converge.
- Sandwich variance estimator is robust to misspecification of the error distribution.
- Widely accepted in epidemiology and public health — results are understood by clinical audiences.
- Extends naturally to clustered or longitudinal data using GEE with a Poisson family and robust standard errors.
- Deliberately misspecifies the likelihood, so likelihood-ratio tests and AIC are not meaningful; use Wald tests with sandwich standard errors instead.
- Fitted probabilities can exceed 1 for extreme covariate patterns, indicating model instability in those regions.
- Less efficient than a correctly specified model when binary data truly follow a log-binomial distribution.
Frequently asked
Why not just use logistic regression and convert odds ratios to risk ratios?
Conversion formulas exist but require knowing the baseline risk and introduce additional uncertainty. When the outcome is common (prevalence > 10%), odds ratios overestimate risk ratios substantially, making conversion unreliable. Robust Poisson gives risk ratios directly without approximation.
How do I request robust standard errors in practice?
In R, use glm() with family=poisson(link='log') then wrap with sandwich::vcovHC() or use the coeftest() function from the lmtest package. In Stata, add the vce(robust) option to the poisson command.
What if fitted probabilities exceed 1?
This signals that the log-linear model extrapolates beyond a valid probability range for those covariate combinations. Check the range of predicted values with fitted(model). If many exceed 1, consider log-binomial regression, logistic regression, or restricting the covariate range.
Can I use this method with clustered data?
Yes. Specify cluster-robust standard errors (clustered sandwich estimator) or use generalized estimating equations (GEE) with a Poisson family, log link, and working independence or exchangeable correlation structure, requesting robust standard errors.
Is robust Poisson appropriate for rare outcomes?
For rare outcomes (prevalence < 5%), the odds ratio approximates the risk ratio closely, so logistic regression is usually sufficient and avoids the misspecification concerns of robust Poisson. The method is most valuable when the outcome is common.
Sources
- Zou, G. (2004). A modified Poisson regression approach to prospective studies with binary data. American Journal of Epidemiology, 159(7), 702-706. DOI: 10.1093/aje/kwh090 ↗
- Zou, G. Y., & Donner, A. (2013). Extension of the modified Poisson regression model to prospective studies with binary data: why it is simpler than it sounds. Journal of Clinical Epidemiology, 66(9), 1023-1028. link ↗
How to cite this page
ScholarGate. (2026, June 3). Robust Poisson Regression with Sandwich Variance Estimator. ScholarGate. https://scholargate.app/en/statistics/robust-poisson-regression
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Generalized Linear ModelStatistics↔ compare
- Logistic RegressionResearch Statistics↔ compare
- Negative Binomial RegressionEconometrics↔ compare
- Poisson RegressionEconometrics↔ compare
- Robust RegressionStatistics↔ compare