//Referring to the response  posted many years ago, copied below, what 
is the specific criterium used for singularity of the gradient matrix?  
Is a Singular Value Decomposition used to determine the singular 
values?  Is it the gradient matrix condition number  or some other 
criterion for determining singularity?
//

//Glenn
//

/
/

/> What does the error 'singular gradient' mean during a nonlinear 
regression? /

The gradient matrix to which the message refers is the derivative of
the vector of predicted values with respect to the vector of
parameters at the current parameter estimates. If you have 20
observations and three parameters, this will be a matrix with 20 rows
and three columns.

For the model to be estimable in a region of the current estimates,
this matrix must have full column rank. When it fails to have full
column rank the "singular gradient" message is given and the
iterations stop.

Generally this indicates that the model is overparameterized or that
the starting estimates were poorly chosen. Try using trace = TRUE in
the call to nls and watching the progress of the iterations. This
will often show that the estimates are wandering into unreasonable
regions of the parameter space.

-- 
Douglas Bates                            bates@stat.wisc.edu
Statistics Department                    608/262-2598
University of Wisconsin - Madison        http://www.stat.wisc.edu/~bates/ <http://www.stat.wisc.edu/%7Ebates/>
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