Nonlinear regression and goodness-of-fit (a mixed real and theoretical problem)

Dear Sirs/Madams:

I'm going to show you a real problem that I have at my research laboratory

and that is a theoretical problem too (statistics). A very interesting problem.

It is well known that when we fit experimental data to a linear model

we can use the R2 (R squared) value in order to compare the goodness-of-fit

of this fitted particular model to the data in front of other linear models.

However, when we fit experimental data to a **NONLINEAR **model the

R2 is not well defined. In fact, the underlying hypothesis that

SST=SSE+SSR (total variance=explained variance+residual variance)

is not true in this case.

Some authors had proposed to use an R2-like parameter

for nonlinear models: plot experimental values in front

of the predicted values (using a fitted model) and getting

the linear regression (R2) of this plot.

I must highlight that this R2 (from now on R2*) is not the conventional R2

that we usually now.

My experimental data is a phyiscal parameter (i.e.: flow)

in front of time (400 values of time).

I'm trying to fit this data to some nonlinear models (no mather what models).

The fact is that when I apply this R2* criteria, I got

very good R2* in all cases (>90%).

However, if I see the predicted curves (using the

fitted models) I see very clear that some models

does not fit good (despite its R2 is very high).

It is to say, very high R2 but very bad

graphical fitting.

I have read some technical books, for example:

__"Nonlinear regression" (G.A.F. Seber by Wiley Series).__

But the authors of those books offer a way of comparing two models

(one model in front of another model *each time*) by means of contrast

of hypothesis.

The fact is that I have a lot of models and

a lot of experiments and these kind of

test is very tedious.

I must highlight too that the methods of __those books__

__suppose that the residual data is normaly distributed__,

but **my residual data does not follow a particular distribution.**

Does anyone know a parameter that can

express the goodness-of-fit of a **nonlinea**r model

to a experimental data **without** the need of comparing models (among them)

by contrasting of hypothesis and** wihout** the assumption that the residuals are normally distributed ?

I will be very pleased if anyone can help me.

Thanks in advance.