ABSTRACT
The negative binomial regression model uses a mixture of the Poisson and gamma distributions to estimate the variance. If the data are overdispersed, it will usually estimate a wider confidence interval compared with Poisson regression. Its ability to predict counts for overdispersed data is illustrated using an example regarding munition workers during World War I. But when an offset is used, the negative binomial model may re-weight rates differently compared with Poisson regression. Instead of creating averages by weighting stratum rates using person-time, the negative binomial model weights rates more equally if the numerator counts are greater than 1. On average, more weight is given to rates with smaller count numerators (rates that are often less precise) and less weight to rates with large count numerators. If numerator counts are sufficiently large, the reweighting assigns equal weight to all observations, much like ordinary least squares linear regression. This behavior can produce estimates different from methods that rely upon person-time weighting.
