Modeling and Multivariate Methods - SAS

Chapter 9 Performing Nonlinear Regression 275
Statistical Details
Notes on Effective Nonlinear Modeling
We strongly encourage you to center polynomials.
Anywhere you have a complete polynomial term that is linear in the parameters, it is always good to center
the polynomials. This improves the condition of the numerical surface for optimization. For example, if you
have an expression like
a 1 + b 1 x + c 1 x 2
you should transform it to
a 2
+ b 2
( x – x) + c 2
( x–
x) 2
The two models are equivalent, apart from a transformation of the parameters, but the second model is far
easier to fit if the model is nonlinear.
The transformation of the parameters is easy to solve.
a 1
= a 2
– b 2
x + c 2
x
b 1
= b 2
– 2c 2
x
c 1
= c 2
If the number of iterations still goes to the maximum, increase the maximum number of iterations and
select Second Deriv Method from the red triangle menu.
There is really no one omnibus optimization method that works well on all problems. JMP has options like
Newton, QuasiNewton BFGS, QuasiNewton SR1, Second Deriv Method, and Numeric Derivatives
Only to expand the range of problems that are solvable by the Nonlinear Platform.
If the default settings are unable to converge to the solution for a particular problem, using various
combinations of these settings to increase the odds of obtaining convergence.
Some models are very sensitive to starting values of the parameters. Working on new starting values is often
effective. Edit the starting values and click Reset to see the effect. The plot often helps. Use the sliders to
visually modify the curve to fit better. The parameter profilers can help, but might be too slow for anything
but small data sets.