Hi,

Thanks for your feedback. You are absolutely right. I too didn't like the
"Assume non-negative" option since its constrains the other parameter as
well. But then for the particular problem in question that constraint was
necessary. As you correctly put it, I think, we have to build a Solver model
for a problem at hand, instead of trying to build a model that would be
global.

Another idea occurred to me for analyzing your data. Even though I
generally prefer to analyze data as-is and not use linear (or other)
transformations as for as possible, here I think a linear transformation
works well.

In column C, I calculated y values using the formula =$F$2*LN(A2-$E$2),
where E2 and F2 contain 'a' and 'b' respectively. Here, I didn't use the
dummy parameter 'aprime'. For calculating the SSR however, I used the
following formula [corresponding to the linear transform of y = b*ln(x-a) ,
i.e., (x-a) = exp(y/b)].

=SUMXMY2(A22:A36-$E$19,EXP(B22:B36/$F$19))

I started with the guess values a=1 and b=1 (SSR = 2108). When Solver is
invoked (with no constraints), the following result was obtained:

a=2.996056603, b=2.001589552, SSR=0.00621783

Of course, one has to expect slight differences in the values of the
parameters obtained from nonlinear and linear analyses of real-life data (due
to different error-distributions in the raw and transformed data, which is
not taken into account in these optimizations).

Regards,
B. R. Ramachandran


"MrShorty" wrote:


Thanks,

That's an interesting idea, to build the conditions into the
spreadsheet model rather than into the solver model. One thing I
didn't like about your approach for this problem is the "assume
non-negative" option, because it applies to both parameters. A
different data set may require b to be less than 0, but your particular
solver model wouldn't find it. You would have to either add a
bprime=-b, or alter the formulas in column 3. Neither of which is a
bad solution, but I would probably rather have a single constraint
aprime=0 rather than the dual constraint aprime=0 and b=0. Of
course, at that point, there's not a lot of difference between a single
constraint a<=3.049999 and aprime=0. On the other hand, we have to
remember that we are building a Solver model to solve the problem at
hand, and solve future problems when we come to them.


--
MrShorty
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