Singular Gradient in nls

sorry, the below should read:

A QR decomposition is done on the weighted gradient matrix; if the
 

estimate of the rank that results is less than min( the number of
   

columns in
 

the gradient (the number of nonlinear parameters), the
   

number
 

of rows (the number of observations) ) , nls stops.
   

so you look at the number of observations, and the number of parameters,
and take the smaller of the two.  if the estimated rank of the weighted
gradient is small than this number, you stop.

On Fri, 28 Mar 2008, Katharine Mullen wrote:

 

A QR decomposition is done on the weighted gradient matrix; if the
estimate of the rank that results is less than the number of columns in
the gradient (the number of nonlinear parameters), or less than the number
of rows (the number of observations), nls stops.

You can see the calls in the source code of nlsModel
(https://svn.r-project.org/R/trunk/src/library/stats/R/nls.R).

On Fri, 28 Mar 2008, glenn andrews wrote:

   

//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 at 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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