[R-sig-ME] Combining spatial and temporal correlation

[Highland Statistics]

> Date: Thu, 26 May 2011 18:50:50 +0200
> From: Jens Oldeland<oldeland at gmx.de>
> To: r-sig-mixed-models at r-project.org
> Subject: [R-sig-ME] Combining spatial and temporal correlation
> 	structures -	possible?
> Message-ID:<4DDE84EA.2050308 at gmx.de>
> Content-Type: text/plain; charset=ISO-8859-15; format=flowed
>
> Dear Mixed-Model SIG
>
> I am trying to use serial and spatial correlation structures in a gamm
> model.
>
> g2<- gamm(sqrt(pp10M.day) ~
>            s(tempsurf, bs="cr"),
>            data=data,
>            random= list(Station= ~1),
>            correlation=corARMA(form = ~ 1|Station, p =2,q=1),
>            family=gaussian,
>            control=lmc)
>
> how do I put in my spatial correlation structure?
>
> correlation=corExp(form = ~ Station,nugget=T)
>
> I tried using correlation=list()  but did not suceed. I did not find
> anything in Zuur or Pinheiro&  Bates etc.
>
> would be glad if someone has an idea (or even says that it is not possible)
>
>
> best,
> Jens
>
>
>
> ------------------------------
>
> Message: 5
> Date: Thu, 26 May 2011 14:00:48 -0400
> From: Ben Bolker<bbolker at gmail.com>
> To: r-sig-mixed-models at r-project.org
> Subject: Re: [R-sig-ME] Combining spatial and temporal correlation
> 	structures - possible?
> Message-ID:<4DDE9550.1000507 at gmail.com>
> Content-Type: text/plain; charset=ISO-8859-1
>
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> On 05/26/2011 12:50 PM, Jens Oldeland wrote:
>> Dear Mixed-Model SIG
>>
>> I am trying to use serial and spatial correlation structures in a gamm
>> model.
>>
>> g2<- gamm(sqrt(pp10M.day) ~
>>           s(tempsurf, bs="cr"),
>>           data=data,
>>           random= list(Station= ~1),
>>           correlation=corARMA(form = ~ 1|Station, p =2,q=1),
>>           family=gaussian,
>>           control=lmc)
>>
>> how do I put in my spatial correlation structure?
>>
>> correlation=corExp(form = ~ Station,nugget=T)
>>
>> I tried using correlation=list()  but did not suceed. I did not find
>> anything in Zuur or Pinheiro&  Bates etc.
>>
>> would be glad if someone has an idea (or even says that it is not possible)
>>
>    I won't say it's impossible, but it's probably pretty tricky.
> Spatio-temporal correlation structures are a research frontier (in my
> opinoin at least). Separable correlation structures are easier than
> non-separable ones (library("sos"); findFn("{spatio-temporal
> correlation}") finds the ramps package ...
>     I think you'd probably have to build your own corClass. If you do
> decide to go this route, I would strongly recommend looking at some
> simple examples in packages *outside* of nlme -- e.g. the ape package --
> findFn("corClasses") is a good start.
>     However, my recommendation would be to try to model the spatial
> correlation via a spatial GAM (see examples in Simon Wood's book), and
> leave the correlation stuff for the temporal component.
>
>    I'd be happy to hear other ideas.
>
>    Ben Bolker

I would try to do this in a Bayesian context:
1. Fit a low rank thin plate spline
2. Add the random effect
3. Add an extra residual term epsilon..and impose a residual CAR 
correlation structure. You can now fill in a matrix C for the 
correlation however you want (though you have to follow some 
rules).....spatial correlation...or temporal correlation...or both.
4. Let your computer run...and run...and run

You can do this in R2WinBUGS. We are on the point to finish a book with 
only case studies on this stuff. Great fun!

An alternative approach to deal with the spatial-temporal correlation is 
to impose a spatial correlation on the residuals and let the parameters 
of the model change over time. Not sure how that would work with 
smoothers though.

The latest book from Cressie & Wikle (Statistics for Spatio-Temporal 
Data) may give you some ideas.

Alain










-- 

Dr. Alain F. Zuur
First author of:

1. Analysing Ecological Data (2007).
Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p.
URL: www.springer.com/0-387-45967-7


2. Mixed effects models and extensions in ecology with R. (2009).
Zuur, AF, Ieno, EN, Walker, N, Saveliev, AA, and Smith, GM. Springer.
http://www.springer.com/life+sci/ecology/book/978-0-387-87457-9


3. A Beginner's Guide to R (2009).
Zuur, AF, Ieno, EN, Meesters, EHWG. Springer
http://www.springer.com/statistics/computational/book/978-0-387-93836-3


Other books: http://www.highstat.com/books.htm


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