From: glenn andrews <ga_at_aggies.com>

Date: Sun, 30 Mar 2008 07:31:19 -0500

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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Sun 30 Mar 2008 - 12:39:01 GMT

Date: Sun, 30 Mar 2008 07:31:19 -0500

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
**>
**>
**>>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/>
**>>>-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
**>>>r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html <http://www.ci.tuwien.ac.at/%7Ehornik/R/R-FAQ.html>
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*

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