Negative Binomial Regression & Nonlinearity

[Alaina DeBiasi]

Negative binomial regression - which relies on the log-link function - models the expected value of Y (given Xs) as an exponential function. Does this mean that negative binomial regression captures nonlinear (i.e., exponential) relationships?

[Clyde Schechter]

Does this mean that negative binomial regression captures nonlinear (i.e., exponential) relationships?

I'm not sure what you mean by this question. But it is true that in a negative binomial regression, the relationship between the value of a predictor and the expected outcome is an exponential function. In particular, a unit increase in a predictor is associated with a fixed multiplicative change in the outcome, not an additive change. Is that what you were asking?