# Are these 2 quasi poisson glm identical?

Approach 1:

lm.fit <- glm(response ~ 1, offset=log(lam), family="quasipoisson")
summary(lm.fit)


Approach 2: Feed summary.glm with a pearson dispersion.

lm.fit <- glm(response ~ 1, offset=log(lam), family="poisson")
summary(lm.fit,
dispersion=sum(residuals(lm.fit, type="pearson")^2)/df.residual(lm.fit))


First of all, they are not both quasipoisson. The first approach is indeed a quasipoisson but the 2nd lm.fit is called a poisson GLM. In approah 1 since you are fitting a quasipoisson, there will be no log-likelihood and therefore there is not any AIC to report in the 1st summary(lm.fit) you wrote.
However, in the 2nd approach since you fitted a poisson GLM first, there will be a log-likelihood and even if you plug in the estimated dispersion effect in the summary, you can still see the AIC criteria in the output of your 2nd summary(lm.fit).