As I am browsing the resources online, I encounter as least three ways to detect overdispersion after fitting a Poisson regression model.
1) A regression approach proposed by Cameron and Trivedi, 1990
2) The Lagrange Multiplier test
3) A third test proposed by Greene found below
I found literature references to 1) and 2), but am having a hard time finding anything related to 3). Since every test has it own assumptions and limitations, would anyone shine some light on what passing/failing each test entails?