"Suzanne Szak" <szak@ncbi.nlm.nih.gov> writes:
> With the data shown below, I'm trying to find a least squares fit (using the
> function nls) using the formula:
>
> CV = sqrt(S^2/U2 + F^2)
>
> using the starting parameters S=0.03 and F=6e-008.
So the contribution of F to the sum is on the order of 10^(-15), which
gets lost in the roundoff.
> I continue to get the error "singular gradient matrix". What does this
> error indicate? I've tried changing the starting parameters w/o any luck.
> In fact, the S and F values above were determined using Excel.
The error message indicates that the gradient matrix (derivative of
the predicted response with respect to the parameters - a matrix with
48 rows and 2 columns in your case) is computationally singular. The
derivative of the response with respect to F is essentially zero.
Notice that the non-zero values of CV range from 0.012 up to 1.2. One
of the assumptions when using nonlinear least squares is that the
variability in the response is approximately constant over the range
of the observed responses. This seems unlikely here. You may want to
consider transforming the response in some way. Even then it is
unlikely that you will be able to compute a meaningful estimate of F.
Your observations 6 and 30
U2 CV
6 1.4929143669 0.000000000
30 1.4271015812 0.024381877
are at roughly the same U2 values but have CV values that differ by
about 0.025. It is not reasonable to expect to estimate an additive
shift parameter that is on the order of 10^(-8).
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