# Residual deviance: Poisson versus Quasi Poisson

There are numerous posts that have explained residual deviance and parameter estimates for the quasi Poisson. But since there is no probability distribution pertaining to the quasi Poisson and hence no likelihood, how exactly is the residual deviance computed?

• +1 Hmm I have read that the rationale for using a quasipoisson model is that you want to model the mean model $E(log(Y) | X) = \beta_0 + \beta_1 X$ and that the mean-variance relationship, rather than being $var(Y) = E(Y)$ is $var(Y) = \phi E(Y)$ i.e. Poisson assumption correct up to a constant. – AdamO Mar 6 '18 at 15:06