[R] Testing Nonlinear Restrictions

[Spencer Graves]

	  What kind of nonlinear restriction?  Can you solve for one or more of 
the parameters in terms of the other(s) [either directly or implicitly]? 
  If yes, then let

	  fit1 <- nls(... full model ... )
	  fit2 <- nls(... restricted model ...)

	  anova(fit1, fit2)

	  If my memory is correct, Doug Bates, in his PhD dissertation ~25 
years ago, decomposed the nonlinearity in nonlinear least squares into 
"intrinsic curvature" and "parameter effects curvature".  The Wald test 
is distorted by both sources types of nonlinearity, but the standard 
likelihood ratio anova is affected only by "intrinsic curvature", and 
not "parameter effects" (provided the algorithm actually converges 
appropriately).  Moreover, by reanalyzing a fair number of published 
data sets, Doug demostrated that in a nearly all practical application, 
the parameter effects curvature was much larger than the intrinsic 
curvature, and the latter was close to negligible in nearly all cases, 
while the parameter effects curvature was often of sufficient magnitude 
to substantively distort the answers.  For more information, see Bates & 
Watts (1988) Nonlinear Regression Analysis and Its Applications (Wiley).

	  hope this helps.   	
	  spencer graves	

Jacho-Chavez,DT (pgr) wrote:

> Dear all,
> 
> I'm interested in testing 2 nonlinear restrictions on coefficients of a nls object. Is there a package for doing this? Something in the lines of `test(nls object, res=c("res 1","res 2"),...)'
> I only found the function delta.method in the alr3 library that calculates the se of a singleton nonlinear restriction of a nls object using the delta method.
> 
> Thanks in advanced for your help and suggestions.
> 
> 
> David
> 
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