Comparing the fit of logistic regression model to a poisson regression model How do we compare the fit of the two models given that the explanatory variables are the same, except the response variable is different? (the response predicts an equivalent thing). We were told that we cannot use the change in deviance of the regression to compare the two models, though they didn't want to explain why when asked and I don't know either.
Any help is appreciated.
edit: apparently we're supposed to use the chi-probabilities, deviance (& ratios), mean deviance etc of the regression to deduce which is "better". I just don't understand how, if both p-values are equal
edit 2: For the logistic regression model i've used a binomial distribution and a logistic link function with a binary response (the capture or none-capture of an animal by a device/s), with a single explantory variable which is the location of the device (10 areas). and for the poisson regression model, i've used a log link function and a response which is the number of animals captured in all areas, with the same explanatory variable

If your responses are truly equivalent, you could generate poisson predictions, transform them into the equivalent variable for logistic regression, and compute classification accuracy, sensitivity, specificity, and F1. These metrics can be compared to metrics for the logistic regression model.
