I've created nice little nonlinear model relating survival probability to length in salmon. I fit it assuming binomial errors and maximizing 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?

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?