[R] Singular Gradient in nls

From: glenn andrews <ga_at_aggies.com>
Date: Fri, 28 Mar 2008 14:33:07 -0500

//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?



/> 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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Received on Fri 28 Mar 2008 - 19:39:29 GMT

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