I've calibrated multiple times a model with three parameters: $a$, $b$ and $c$. I graphed each pair of resulting parameters to get an idea of the correlations and got these very strange plots: 
Here is a 3D plot:
I'd appreciate some thoughts on how to interpret these. Obviously there seems to be some extreme dependence, but are these results characteristic of anything? What conclusions can we draw from these?
The most striking feature seems to be that nonzero $a$ and nonzero $b$ seem to be mutually exclusive - that is, if $a$ is nonzero, $b$ must be 0 and vice versa. I can't think of a good example of this in the real world. It's not just an inverse relationship; it's an exclusionary one.
Have you tried taking a look at your original dataset in R? Seems really trivial and stupid, but sometimes R tends to misunderstand things and implements extra cases, leaves every second case out or something similar. Also, make sure you don't have a single comma or something left in the database, I did that once and got a similarly strange distribution for my parameters.
Hope this helps
