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I'm in the process of learning about Poisson regression and i am wondering if anyone here could give me some valuable advice on model selection. I'm looking for values and tests like the Hosmer-Lemeshow test and the Roc curve for logistic regression but instead more appropriate for count data.

What's your process when comparing two Poisson regressions? Surely your selection cannot be only based on AIC values?

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  • $\begingroup$ If your question has been answered to your satisfaction, you can accept an answer by clicking the check mark under the voting arrows. $\endgroup$ – Kodiologist Jul 18 '17 at 16:24
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You might want to use the following for assessment of fit:

  • Analysis of residual statistics
    • Graph residuals (e.g: standardised Pearson or Anscombe residuals) by prediction
    • Look for nonrandom patterns
  • Likelihood ratio test
  • Use score test to test for overdispersion
  • Use Lagrange Multiplier Test to test for overdispersion
  • Use chi-square test to assess predicted against observed counts

You might want to use AIC or BIC for model selection criteria.

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Surely your selection cannot be only based on AIC values?

Sure it can, assuming you're using the same dataset for both. Any generic model-selection method applies just as well when one or more of the models is a Poisson regression model. What made you think otherwise?

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  • $\begingroup$ What would you then do if the models came from different datasets? $\endgroup$ – Janono Apr 11 '17 at 10:39
  • $\begingroup$ @Janono The whole idea of model selection requires you to be comparing models on the same data. $\endgroup$ – Kodiologist Apr 11 '17 at 14:27

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