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This question already has an answer here:

I've got a couple different models (poisson regression vs. OLS linear model on log-transformed DV) and trying to compare the two. They both provide reasonably good fit to the data.

I have heard people state that you cannot use AIC/BIC to compare these two but cannot seem to find a reference to this effect. They are different kinds of models, so I'm curious to know how one should go about making the decision between them.

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marked as duplicate by kjetil b halvorsen, Michael Chernick, Peter Flom regression May 19 at 13:17

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    $\begingroup$ AIC/BIC can be used here, but standard software may omit "constants" in the log likelihood that could matter for the comparison. In your case this is probably the "jacobian" of the transformation. $\endgroup$ – probabilityislogic Dec 30 '17 at 6:18
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OLS is not a probabilistic model as it does not have an associated likelihood function. Unless you assume a normal model for the errors in a linear regression model (thus you get the same estimators for the regression coefficients), then you cannot compare it to the Poisson regression model.

If you assume the normal model, then you still cannot justify the comparison on the basis of AIC/BIC as the linear regression model assumes continuous responses, while the Poisson regression model is a discrete model. Thus, the models cannot be compared in terms of these information criteria (which require same support to properly define the Kullback Liebler divergence).

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