Is Quasi-Poisson the same thing as fitting a Poisson GEE model?

Question

The title says it all. I'm wondering if someone can help me understand the difference (if there even is one) between a Quasi-Poisson model and fitting a Poisson Regression Model using GEE? It is my understanding that both of these methods can be effective ways for handling over/under-dispersion and they seem similar, but I can't tell if they are the same thing or not.

I'm really surprised no one has addressed this? As often as I see the terms quasi-poisson and GEE used in the literature, maybe I'm not the only one confused by the seemingly dual usage of these terms?

Answer 1

Quasi-poisson GLM is a special case of Poisson GEE.

The specification of GEE (copied from wikipedia) is that

$$U(\beta)=\sum_i \frac{\partial\mu_{ij}}{\partial \beta_k} V_i(Y_i-\mu_i(\beta))$$

where $V_i$ is the variance of observation $i$. In the case that these are a constant multiple of the (standard dispersion) poisson mean, this reduces to a poisson GLM with a dispersion parameter. However, the GEE is more general than that; it can cope when there is additional variance structure on top of this.