Sometimes there is some meaning to the parameters that help you estimate them.  Like one parameter may be the maximum y value of the curve, or one might be the y value when x is 0. 

What I've done that's worked is to set up a spreadsheet and plot in Excel or something similar. 

I have cells for the each of the parameters, and then a column of x values (same range as my data) and a column of y values that are calculated by being hot-linked to the cells with the parameters. 

Then a plot of the data I'm trying to fit and the curve produced by  the x and y columns in the spreadsheet. 

Everything is hot-linked, so that I can change the parameters and the plot automatically changes.  It's usually not too difficult to find reasonable starting parameters this way, because it's easy to see if tweaking the parameters improves the fit.

I would suggest linearizing your model and estimate the parameters under this simple model with OLS and then plug these estimates in as starting values. B1-B2*exp(-B3*x) is approximately equal to B1-B2*(1-B3x)=B1-B2+B2*B3x. Now, estimate y=A1+A2x which would provide you with indirect estimates of B2 and B3. As a starting value to B1 you could simply take the mean of y for the subset where x is equal or near to 0. If this approach is not working, make a second (instead of first as above) order Taylor expansion of exp() and estimate this linear model and derive the values for B1-B3 in the same fashion as above.

Ken,

Thank you for replying. I have a second problem which I am enclosing. When the initial values for the OLS model do not work I really don't know what to do. YourTaylor expansion suggestion does not make sense to me. I don't understand what you are doing. Can you look at the enclosed please.  I am pretty good at linear models but nonlinear models is not going well.

Mary

I do not have SAS installed presently, and I am not clear on which of the variables in the excelfile are to be in the model, but I can provide a detailed explanation for how to get the initial values for the parameters sought by exploiting the idea of linearization. Take first a look at the link to Wikipedia description of Taylar expansions and particularly to "List of Maclaurin series of some common functions".

A second order expansion of exp(x)=1+x+0.5x^2. This provides an approximation being linear, now apply this to your model: B1-B2exp(-B3x) is approximately equal to B1-B2+B2*B3x-0.5*B2*B3^2*x^2. So now your model is linear, and can be re-written as y=A1+A2x+A3x^2+e. Then you estimate this model by OLS to get estimates a1, a2, a3. Now it remains to re-convert this A-estimates into initial values for your B-parameters. A3=-0.5*B2*B3^2; A2=B2*B3; A1=B1-B2 and we apply some substitution. We note first that by dividing A3 with A2 we free the B3 parameter -> b3=-2*a3/a2. Upon having fixed b3 we readily get b2=a2/b3=-a2^2 / 2*a3 and finally b1=a1-b2=a1+a2^2 / 2*a3. There you have b1, b2, and b3 as good initial values for your estimation of the non-linear model in SAS.

As the procedure relies on an approximation, there is of course an issue of how good is this approximation and the answer is: If B3 is close to zero the initial values will be close to the final Estimates, however if it is far away from zero then the approximation is less good and more iterations would typically be required in the stimation procedure.

Hopefully, it is all clear now.

/kenneth

https://en.wikipedia.org/wiki/Taylor_series

your problem is a mixture of linear and non linear. Using a grid search is possible but will be quite lengthy, specially because you have as much as 14 or so parameters.

not all of your parameters in the non linear part are necessary. P_TV and P_PDEs are quite close to one, you could fix them to one (tentatively),  P_UR is very close to zero and should be skipped (with the variable UR and the coefficient B7). The P_DTC is larger but with a huge standard deviation, you probably may fix it at 2 or 4 for the moment. Your problem will turn to be a linear one. The solution of it wil probably provide a better starting point, which you are looking for if I understood you well.