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 aNONLINEARmodel 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 modeleach 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 ofthose books

suppose that the residual data is normaly distributed,

butmy residual data does not follow a particular distribution.

Does anyone know a parameter that can

express the goodness-of-fit of anonlinear model

to a experimental datawithoutthe need of comparing models (among them)

by contrasting of hypothesis andwihoutthe assumption that the residuals are normally distributed ?

I will be very pleased if anyone can help me.

Thanks in advance.