I have fit a poisson regression model to my count data. The distribution of my dependent variable followed Poisson distribution and mean is almost equal to variance. But when I fit a Poisson regression model, some of goodness of fit test like deviance and pearson chi-square test showed that was not the case though my model fits reasonable well to the data and the profiles seem like the way its supposed to.

I read on one of the pages that deviance test is wrong about 94% of the time. Is there any other way to asses the validity of the model?

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#### Best Answer

In the case of overdispersion, you can use quasi-poisson models where the mean and variance can be decoupled. Regarding fit, I usually compare my model using Pearson’s residuals (which is what this post recommends too: Why goodness of fit via deviance and chisq is poor for poisson regression (glm)?).

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