Reported Convergence Measures
NLIN computes and reports four convergence measures
labeled R, PPC, RPC, and OBJECT.
- R
- is the primary convergence measure for the parameters.
It measures the degree to which the residuals are orthogonal to the
Jacobian columns, and it approaches 0 as the gradient of the
objective function becomes small.
R is defined as
![\sqrt{\frac{ r'X(X'X)^{-1}X'r } { {LOSS}^i }}](images/nlieq71.gif)
- PPC
- is the prospective parameter change measure.
PPC measures the maximum relative change in the parameters implied by
the parameter-change vector computed for the next iteration.
At the kth iteration, PPC is the maximum over the parameters
![\frac{|{\theta}^{k+1}_{i}- {\theta}^k_{i}|}{|{\theta}|^k_{i}+1E-6}](images/nlieq72.gif)
where
is the current value of the ith parameter and
is the prospective value of this parameter after
adding the change vector computed for the next iteration.
The parameter with the maximum prospective
relative change is displayed with the value of PPC, unless the PPC is
nearly 0.
- RPC
- is the retrospective parameter change measure.
RPC measures the maximum relative change in the parameters from the previous
iteration. At the kth iteration, RPC is the maximum over i of
![\frac{|{\theta}^k_{i}- {\theta}^{k-1}_{i}|}{|{\theta}^{k-1}_{i}+1E-6|}](images/nlieq75.gif)
where
is the current value of the ith parameter and
is the previous value of this parameter.
The name of the parameter with the maximum retrospective
relative change is displayed with the value of RPC, unless the RPC is nearly
0.
- OBJECT
- measures the relative change in the objective
function value between iterations:
![\frac{| O^k-O^{k-1}|}{| O^{k-1}+1E-6|}](images/nlieq77.gif)
where Ok-1 is the value of the objective function (Ok)
from the previous iteration. This is the old CONVERGEOBJ= criterion.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.