[R] Singular Gradient in nls

[glenn andrews]

Is the nls() algorithm based on a weighted non-linear least squares -- I 
noticed you mentioned a weighted gradient matrix?

Glenn


Katharine Mullen wrote:

>sorry, the below should read:
>
> A QR decomposition is done on the weighted gradient matrix; if the
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>>estimate of the rank that results is less than min( the number of
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>columns in
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>>the gradient (the number of nonlinear parameters), the
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>number
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>>of rows (the number of observations) ) , nls stops.
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>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:
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>>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:
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>>>//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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