Non-constant variance and non-Gaussian errors
Hi Paul, Take a look at gam() from package mgcv (gam = generalized additive models), maybe this will help you. GAMs can work with other distributions as well. Generalized additive models consist of a random component, an additive component, and a link function relating these two components. The response Y, the random component, is assumed to have a density in the exponential family. I am not sure about errors, though. This modeling package uses penalized versions of the least squares or maximum ?likelihood / IRLS methods. The penalizing or smoothing factor is calculated by minimizing the generalized cross validation (GCV), or the information criterion (AIC) scores using a Newton type optimization based on exact first and second derivatives, as described in Wood (2008). Wood, S.N. (2004) Stable and efficient multiple smoothing parameter estimation for generalized additive models.Journal of the American Statistical Association. 99:673-686. Wood, S.N. (2006) Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC. Wood, S.N. (2008) Fast stable direct fitting and smoothness selection for generalized additive models. Journal of the Royal Statistical Society (B) 70(2): - . Hope this helps some, Monica ----------------------------------------------------------- Message: 94 Date: Wed, 3 Sep 2008 09:24:10 +0100 From: "Paul Suckling" Subject: Re: [R] Non-constant variance and non-Gaussian errors with gnls To: r-help at r-project.org Message-ID: Content-Type: text/plain; charset=UTF-8 Well, it looks like I am partly answering my own question. gnls is clearly not going to be the right method to use to try out a non-Gaussian error structure. The "ls"=Least Squares in "gnls" means minimising the sum of the square of the residuals ... which is equivalent to assuming a Gaussian error structure and maximising the likelihood. So gnls is implicitly Gaussian. Still, there must be some packages out there that can be applied to non-linear regression with not-necessarily-Gaussian error structures and weighting, although I appreciate that that's a difficult problem to solve. Does anyone here know of any? Thank you, Paul 2008/9/2 Paul Suckling :
I have been using the nls function to fit some simple non-linear regression models for properties of graphite bricks to historical datasets. I have then been using these fits to obtain mean predictions for the properties of the bricks a short time into the future. I have also been calculating approximate prediction intervals. The information I have suggests that the assumption of a normal distribution with constant variance is not necessarily the most appropriate. I would like to see if I can obtain improved fits and hence more accurate predictions and prediction intervals by experimenting with a) a non-constant (time dependent) variance and b) a non-normal error distribution. It looks to me like the gnls function from the nlme R package is probably the appropriate one to use for both these situations. However, I have looked at the gnls help files/documentation and am still left unsure as to how to specify the arguments of the gnls function in order to achieve what I want. In particular, I am unsure how to use the params argument. Is anyone here able to help me out or point me to some documentation that is likely to help me achieve this? Thank you.
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