I am looking for an appropriate measure of the "explained variance" of a Poisson GLM (using a log-link function).
I have found a number of different resources (both on this site and elsewhere) that discuss a number of different pseudo-$R^2$ measures, but nearly every site mentions the measures in relation to a logit-link function, and they don't discuss whether the pseudo-$R^2$ measures are appropriate for other link functions, such as log-link for my Poission distribution GLM.
For example, here are a few of the sites I've found:
My question is: Are any of the methods discussed at those links (in particular, the FAQ on the UCLA page) appropriate for a Poission GLM (using a log-link function)? Is any particular method more appropriate and/or standardly used than any other method?
This is for a research paper in which I am using a Poission GLM to analyze neural data. I am using the deviances of the models (calculated assuming a Poission distribution) to compare two models: One model (A) which includes 5 parameters that were left out of the other model (B). My interest (and the focus of the paper) is to show that that 5 parameters statistically improve the model fit. However, one of the reviewers would like an indication of how well both models fit the data.
If I were using OLS to fit my data the reviewer is effectively asking for the $R^2$ value for both the model with the 5 parameters and w/o the 5 parameters, to indicate how well either model explains the variance. It seems like a reasonable request to me. Lets say that, hypothetically, model B has an $R^2$ of 0.05 and model A has an $R^2$ of 0.25: even though that may be a statistically significant improvement, neither model does a good job of explaining the data. Alternatively, if model B has an $R^2$ of 0.5 and model A has an $R^2$ of 0.7, that could be interpreted in a very different way. I'm looking for the most appropriate measure that can be applied in a similar way to my GLM.