I've created nice little nonlinear model relating survival probability to length in salmon. I fit it assuming binomial errors and minimizing the negative log likelihood. I've been asked to compare it to someone else's model, where they binned the data and fit a straight line to it. However, the lowest bin includes the long left tail of the length distribution, and would predict 0 (or negative) chance of survival for those fish, were they not lumped into a bin with higher length average---but some of those fish do survive. That said, for some data sets, the linear model does quite well on the binned data.
I'd like to compare these models, but I can't use AIC because the linear model's invalidity makes its AIC explode. I could truncate the data--it is a very small proportion of the data, or I could bin the data and calculate an AIC for my model assuming normal errors, but I don't really feel great about either of those. Are there other options, or are these choices not so bad?