Good morning fellow SPLus fans,
I'd like to thank Douglas Bates, Ed Jones, David O. Nelson, Bob Byers, and
Dave Fournier for helping me out with my question from last week; their
suggestions and input really turned my day around after I spent some hours
of frustration trying to figure out the problem by myself.
The problem I had was that when I attempted to use the nls() function to
perform a nonlinear least squares regression, I was getting the error
"Singular gradient matrix."
This error indicates that the "gradient matrix (derivative of the predicted
response with respect to the parameters) is computationally singular."
[D.B.] That is, one of my starting parameters (called 'F') was so low, and
the step values SPlus used to tweak it were so small, that no difference in
the sum of squares was detected by SPlus; the derivative with respect to F
was essentially zero. Suggestions included transforming my original
function to a linear function by squaring both sides, and then performing
linear regression analysis. Or, because the 'F' parameter is so low, it can
essentially be omitted from the analysis and the function fit using the one
other parameter only. Another error that may be encountered in such a case
is "Step factor reduced below minimum" which also seems to indicate that a
parameter's value is too low to be improved.
Of note, Dave Fournier was able to solve for both of my nonlinear parameters
using his AD Model Builder software which can be used to make DLLs or shared
libraries that can be run from SPLus. This may be helpful to those of you
who routinely perform a lot of nonlinear parameter estimations.
Thanks again,
Suzanne
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