Negative binomial regression is used to model count dependent variables. A count variable, for example, the number of years in poverty, is assumed to follow a Poisson distribution. The Poisson distribution has the feature that its mean equals its variance. Since the variance of a count variable is often empirically larger than its mean, a situation known as over-dispersion (Hausman, Hall and Griliches, 1984), in a negative binomial regression, the Poisson parameter is assumed to follow a Gamma distribution. In our study, two outcome variables are of the nature of count data: years in poverty between the ages of 25-29, and years on welfare between the ages of 21-33.
An estimated coefficient from a negative binomial regression is interpreted as percentage changes in the outcome variable given a unit change in an explanatory variable. To keep the interpretation comparable, we present results from negative binomial regressions in the form of marginal effects. Marginal effects measure changes in an outcome variable resulting from a unit change in an independent variable. For example, in estimating the number of years in poverty, we obtained a marginal effect of -0.231 for males relative to females (whose marginal effect is set to 0), which means male respondents on average spent 0.231 years less in poverty compared with female respondents. In essence, the interpretation of marginal effects is equivalent to estimated coefficients in linear models.