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I have a Poisson regression model, and I would like to measure the discrepancy between actual counts and predicted counts. For binary classification model, the log-loss metrics fits for this purpose. Is there any metrics alike for Poisson models? Similarly, is there any package or is possible to code a function in R for it? Thanks in advance

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    $\begingroup$ The log-loss is the log-likelihood of the bernoulli distribution. You want the log-likelihood of the poisson distribution. $\endgroup$ – Matthew Drury Apr 26 '17 at 20:48
  • $\begingroup$ It really depends on what aspects of the original you want equivalence of. The present answer offers a very sensible choice, but it really depends on what you mean by "equivalent" $\endgroup$ – Glen_b Apr 27 '17 at 1:18
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When fitting a GLM, the deviance is something you'd like to see as low as possible. I believe for a binomial GLM, the binomial deviance is already the log loss. If you run a Poisson GLM, the Poisson deviance should be the number you're looking for. It's spit out by default in glm() in R.

Check it out what it actually is here.

A bonus benefit to using deviance, is that you can use it to compare models via a $\chi^2$ test.

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