Vadim Ogranovich wrote:
Dear R-Users,
I need to find a smooth function f() and coefficients a_i that give the best
fit to
y ~ a_0 + a_1*f(x_1) + a_2*f(x_2)
Note that it is the same non-linear transformation f() that is applied to
both x_1 and x_2.
So my first question is how can I do it in R?
A more general question is this: suppose I have a utility function U(a_i,
f()), where f() is say a spline. Is there a general optimizer that could
find an extremum of such U()? If not, how easy it would be to hack up
something like this? Would it become easier if U() depended on f() only,
i.e. no a_i terms?
Thanks, Vadim
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Vadim It seems to me that ls (linear least squares) will be enourgh. You have to find linear coefficients of three vectors - first consisting of all ones , second and third filled with values f(x_1) and f(x_2). Answer to more general question will be ?optim (in general). You have to write a function that have as a result a sum of residuals between y values to be fit and modelled values and find minimum of this function. This is what optim exactly do.
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