R help - Jul 2002 - nls() singular graident matrix error

R-helpers;

	I used Proc Model in SAS to fit the following model to data:

		proc model data = dbsmv;
                        a = a1*F**2;
                        b = b1*F + b2*T + b3*F*T;
                        tph2 = tph1 *((1 - exp(-a*age2)) / (1 -
exp(-a*age)))**-b;
		fit  tph2;

	and yielded the following estimated parameters after iterations:

	a1 = -0.15943, a2 = -1.8177, b1 = -0.01911, b2 = - 0.01494, b3 0.036427 with
SEE = 4.7492 and MSE = 0.0111 (427 d.f). The model fits well
to the data.
	

	Trying to duplicate the model in R using nls(), I took the following
steps:

	Foo <- deriv( ~ tph1 * ((1 - exp(-(a1*N^a2)*age2))/ (1 -
exp(-(a1*N^a2)*age)))^(-(b1*N + b2*T +
            b3*F*T)),
c("a1","a2","b1","b2","b3"),
function(tph1, age2, age,
T, N, a1, a2, b1, b2, b3) {})

	Foo.nls <- nls(tph2 ~ Foo(tph1,N, T, a1, a2, b1, b2, b3), data dbsmv,
    start = c(a1 = -0.15943, a2 = -1.8177, b1 = -0.01911, b2 = - 0.01494, b3
= 0.036427))	

	The nls() failed due to 
	"Error in nlsModel(formula, mf, start) : singular gradient matrix at
initial parameter estimates".

	Any workaround for the singularity problem? 

	Thanks in advance,

Richard


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Richard,


Trying to duplicate the model in R using nls(), I took the following  steps:
        Foo <- deriv( ~ tph1 * ((1 - exp(-(a1*N^a2)*age2))/ (1 -
exp(-(a1*N^a2)*age)))^(-(b1*N + b2*T +
            b3*F*T)),
c("a1","a2","b1","b2","b3"),
function(tph1, age2, age,
T, N, a1, a2, b1, b2, b3) {})


I had a similar problem, and tracked it down to a known bug in deriv, which
does not correctly handle unary minus signs. To check is this is the
problem,
rewrite
  exp(-(a1*N^a2)*age2))
as

  exp((-1)*(a1*N^a2)*age2))

(for all similar cases)

Even if this does not help (there might be other errors around), check
the resulting derivatives if they are correct. I never use derive unchecked,
but only to generate an expression and paste that expression into my
program.

Dieter

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