[R] Non-constant variance and non-Gaussian errors

[roger koenker]

You might also consider the additive model fitting with rqss() in the  
package quantreg.

url:    www.econ.uiuc.edu/~roger            Roger Koenker
email    rkoenker at uiuc.edu            Department of Economics
vox:     217-333-4558                University of Illinois
fax:       217-244-6678                Champaign, IL 61820



On Sep 3, 2008, at 12:01 PM, Monica Pisica wrote:

>
> 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.
>>
>
>
>
>
> _________________________________________________________________
>
> Live.
>
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