On Wed, 20 Mar 2019 08:02:45 +0000 akshay kulkarni <akshay...@hotmail.com> wrote:
> formulaDH5 <- as.formula(HM1 ~ (a + (b * ((HM2 + 0.3)^(1/2)))) + > (A*sin(w*HM3 + c) + C)) The problem with this formula is simple: the partial derivative with respect to `a` is the same as the partial derivative with respect to `C`. This makes the regression problem have an infinite number of solutions, all of them satisfying equation \lambda_1 * a + \lambda_2 * C + \lambda_3 = 0 for some values of \lambda_i. Gradient-based optimizers (which both nls and nlsLM are) don't like problems with non-unique solutions, especially when the model function has same partial derivative with respect to different variables, making them indistinguishable. Solution: remove one of the variables. > > formulaDH3 > HM1 ~ (a + (b * ((HM2 + 0.3)^(1/3)))) * (c * log(HM3 + 27)) The problem with this formula is similar, albeit slightly different. Suppose that (a, b, c) is a solution. Then (\lambda * a, \lambda * b, c / \lambda) is also a solution for any real \lambda. Once again, removing `c` should get rid of ambiguity. > I've checked the Internet for a method of getting the starting > values, but they are not comprehensive....any resources for how to > find the starting values? Starting values depend on the particular function you are trying to fit. The usual approach seems to be in transforming the formula and getting rid of parts you can safely assume to be small until it looks like linear regression, or applying domain specific knowledge (e.g. when trying to it a peak function, look for the biggest local maximum in the dataset). If you cannot do that, there also are global optimization algorithms (see `nloptr`), though they still perform better on some problems and worse on others. It certainly helps to have upper and lower bounds on all parameter values. I've heard about a scientific group creating a pool of many initial Levenberg-Marquardt parameter estimates, then improving them using a genetic algorithm. The whole thing "converged overnight" on a powerful desktop computer. -- Best regards, Ivan ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
