My response variable showed significant underdispersion, which was due to uneven sampling. I searched for the right models and was advised to fit a COM Poisson model, as quasi-Poisson and other generalisations might be too optimistic. I am now wondering whether the evaluation of my model in terms of explanatory power and fit needs to be done differently than with standard procedures for GLMs (measured using likelihood ratio tests, chi-square tests, and deviations). I ask this because I cannot find any literature that is not too specific or doesn't require too much prior knowledge.

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