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Singular Gradient in nls
4 messages · glenn andrews, Katharine Mullen
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> Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._ [[alternative HTML version deleted]]
______________________________________________ R-help at r-project.org mailing list 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.
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> Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._ [[alternative HTML version deleted]]
______________________________________________ R-help at r-project.org mailing list 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.
______________________________________________ R-help at r-project.org mailing list 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.
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> Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._ [[alternative HTML version deleted]]
______________________________________________ R-help at r-project.org mailing list 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.
______________________________________________ R-help at r-project.org mailing list 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.