Education 231C

Applied Categorical & Nonnormal Data Analysis

Negative Binomial Models

Negative Binomial Models

Negative binomial regression is used to estimate count models when the poisson estimation is inappropriate due to overdispersion (which is most of the time). In a poisson distribution the mean and variance are equal. When the variance is greater than the mean the distribution is said to display overdispersion. The nbreg command estimation includes an ancillary parameter α which is an estimate of the degree of overdispersion. For computational purposes, Stata estimates lnα which is then converted to α. When α is zero, negative binomial has the same distribution as poisson. The larger α is the greater the amount of overdispersion in the data.

When there is overdispersion the poisson estimates are inefficient with standard errors biased downward yielding spuriously large z-values.

The negative binomial distribution is given by

However, in the context of count regression models the negative binomial distribution can be thought of as a poisson distribution with unobserved heterogeneity which, in turn, can be conceptualized as a mixture of two probability distributions, poisson and gamma.

Negative Binomial Example

We will continue with the lahigh dataset.

Generalized Negative Binomial

It is possible to estimate a generalized version of the negative binomial model. The gnbreg command allows lnα to be modeled as a function of one or more variables.

Categorical Data Analysis Course

Phil Ender