Poisson Regression Calculator

Poisson regression online with rate ratios, offsets and dispersion check.

Open the Poisson Regression (counts) calculator

When to use it

Use when the outcome is a non-negative count (number of insect visits, lesions per leaf, customer arrivals per hour, weed seedlings per quadrat) and you have one or more continuous or categorical predictors. The Poisson model assumes the variance equals the mean; the link is log so coefficients act multiplicatively on the rate.

When NOT to use it

Do not use when the variance is much larger than the mean (overdispersion); use Negative Binomial regression instead. Do not use when many counts are exactly zero beyond what Poisson predicts (zero inflation); use a zero-inflated Poisson (ZIP) or Hurdle model. Do not coerce a binary outcome into a count; use logistic. For rare events with offset exposure (events per person-year) include log(exposure) as an offset.

What you get

Coefficient table with log-rate estimates, standard errors, Wald z, two-sided p, 95 percent CIs; rate ratios (exp(b)) with CIs; null and residual deviance with the model likelihood-ratio chi-square; Pearson dispersion statistic (variance/mean ratio); over-dispersion warning when dispersion exceeds about 1.5; AIC.

How to interpret the output

A rate ratio above 1 means the predictor increases the event rate; below 1 decreases. Pearson dispersion close to 1 supports the Poisson assumption; values above 1.5 strongly suggest overdispersion and a switch to negative binomial. The model assumes log-linear effects; check residual diagnostics for non-linearity. Cameron and Trivedi (2013) is the standard reference.

Common pitfalls

Skipping the dispersion check; Poisson with overdispersed data gives anti-conservative SEs.
Forgetting to include log(exposure) as an offset for rate outcomes (events per person-year).
Reporting log-rate coefficients without the rate ratios.
Using Poisson on continuous outcomes that happen to be non-negative (it expects integer counts).

Try it in StatVeda

The Poisson Regression (counts) engine runs entirely in the browser. No signup, no install, no data sent to a server. Paste your data, hit Run, copy the output.

Open Poisson Regression (counts)

References

Cameron, A. C. and Trivedi, P. K. (2013). Regression Analysis of Count Data, 2nd edition. Cambridge University Press, Cambridge.
McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd edition. Chapman and Hall, London.
Agresti, A. (2013). Categorical Data Analysis, 3rd edition. John Wiley and Sons, Hoboken. Chapter 4.