Negative Binomial Regression
Also known as: NB regression, NB2 regression, negatif binom regresyonu
Negative Binomial Regression is a generalized linear model for count outcomes that extends Poisson regression to handle overdispersion, where the variance of the counts exceeds their mean. Developed in the GLM tradition and treated in depth by Hilbe (2011), it adds a dispersion parameter so that inference stays valid when Poisson would understate the spread of the data.
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When to use it
Use negative binomial regression when the outcome is a non-negative integer count and the counts are overdispersed — that is, the variance clearly exceeds the mean (Var(Y) > E(Y)). It suits cross-sectional or panel data with independent observations and a reasonably large sample (about 100 or more). A practical screening step is to fit a Poisson model first and check the dispersion: a Pearson chi-square divided by residual degrees of freedom well above 1 (roughly > 1.5) signals that the negative binomial is warranted; if dispersion is near 1, plain Poisson suffices.
Strengths & limitations
- Correctly handles overdispersed count data where Poisson would produce standard errors that are too small.
- Coefficients exponentiate into incidence rate ratios (IRR), giving a direct multiplicative interpretation of each predictor on the event rate.
- Nests Poisson as a special case (α → 0), so it can be compared against Poisson via AIC to confirm whether the extra dispersion parameter is needed.
- Requires a non-negative integer (count) outcome; it is not appropriate for continuous or binary responses.
- Needs a fairly large sample (about 100 or more) for stable estimation of both the coefficients and the dispersion parameter.
- Assumes independent observations and does not, on its own, address an excess of zeros beyond what overdispersion explains.
Frequently asked
How is negative binomial regression different from Poisson regression?
Poisson regression forces the variance to equal the mean. Negative binomial regression adds a dispersion parameter α so the variance can grow as μ + αμ², which fits overdispersed counts (Var > Mean). As α approaches 0 the negative binomial collapses back to Poisson.
How do I know if I need the negative binomial instead of Poisson?
Fit a Poisson model first and inspect the dispersion: the Pearson chi-square divided by the residual degrees of freedom should be near 1. A ratio well above 1 (roughly above 1.5) indicates overdispersion and favours the negative binomial; comparing AIC between the two models confirms the choice.
What does an exponentiated coefficient mean?
Because of the log link, exp(β) is an incidence rate ratio (IRR): the multiplicative change in the expected count for a one-unit increase in that predictor. An IRR of 1.2 means the rate rises by about 20 percent, holding the other predictors fixed.
What if my data have far too many zeros?
Overdispersion and excess zeros are different problems. If a structural surplus of zeros remains after accounting for dispersion, a zero-inflated or hurdle count model is usually more appropriate than a plain negative binomial.
Sources
- Hilbe, J. M. (2011). Negative Binomial Regression (2nd ed.). Cambridge University Press. DOI: 10.1017/CBO9780511973420 ↗
How to cite this page
ScholarGate. (2026, June 1). Negative Binomial Regression. ScholarGate. https://scholargate.app/en/econometrics/negative-binomial-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.
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