= Solution
Because models 1 and 3 are full likelihood models for the same response, one can compare their <Akaike information criterion> values; that favors model 1. One can also compare held-out count prediction by <K-fold cross-validation>, using a common loss such as Poisson deviance or negative log predictive density.
The AIC comparison cannot include model 2 because a Quasi-Poisson fit specifies only mean and variance and has no full likelihood. Cross-validation can compare model 2 with model 3 if all predictions are scored by the same proper out-of-sample loss.
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