[R-sig-ME] Specifying correlation structure

[Highland Statistics Ltd]

On 15/05/2012 12:59, Gang Chen wrote:
> Thanks for the comments!
>
> Currently I'm only trying to work on the model specification part with
> one subject. With multiple subjects, I can easily switch from gls to
> lme. Also the issue of corARMA or corAR1 or others is not important
> right now. Instead my focus is, how to correctly specify the
> correlation structure across the three conditions? You've kindly
> helped me out on imposing the same correlation structure for the three
> conditions. The only dangling part is, how to specify a different
> correlation structure for each condition while modeling the
> correlation similarity across the three conditions?

gls would use the same AR parameter (and therefore correlation 
structure) for all your conditions. If you use both random effects and 
AR1 then you would need to take a pen and paper to work out how exactly 
the correlation looks like (and also ensure that the two terms don't 
compete with each other). If you want to have different AR parameters, 
then one option would be to fit the model within an MCMC context. See 
our 2012 book (sperm whale chapter) for examples how to do this...or 
chapter 23 in our 2009 book for multiple AR parameters.

A random intercept and slope model would be an alternative (the 
correlation would depend on the covariate used as random slope)....but 
whether this is sensible for your data depends on your data, questions 
and your variables.


Alain

>
> Gang
>
>
> On Tue, May 15, 2012 at 12:15 PM, Gavin Simpson<gavin.simpson at ucl.ac.uk>  wrote:
>> On Tue, 2012-05-15 at 11:47 -0400, Highland Statistics Ltd wrote:
>>> Many thanks for the suggestion. It seems that gls does not like that either:
>>>
>>>> /  (fm<- gls(res ~ 1+reg1+reg2+reg3, correlation=corARMA(c(0.02, 0.03), form=~time|condition, p=1,q=1), data=Dat))
>>> /
>>> Error in model.frame.default(formula = ~time + condition + res + reg1 +  :
>>>     variable lengths differ (found for 'condition')
>> <snip />
>>
>>> That is because 'condition' is not in your Dat object. I guess it should be cond.
>>> Why corARMA and not corAR1?
>>>
>>> I'm actually not sure whether your modelling approach is correct. The
>>> unit is the subject....but the time | cond is imposing the correlation
>>> inside the observations from the same condition. Is that what you
>>> want? It would ignore any correlation between 2 observations from
>>> different
>>> conditions....but still from the same subject. But perhaps I did not
>>> fully understand your original post.
>> Those are good points Alain. My comment would be that the OP mentioned
>> that there was just a single subject; whether that was just the example
>> or a real property of the data, who knows? ;-)
>>
>> Like you, without further info, whether the nested ARMA(1,1) is
>> sufficient will depend on the OP providing more info.
>>
>> G
>>
>>> Alain
>>>
>>>
>>> /
>>>
>> --
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>>   Dr. Gavin Simpson             [t] +44 (0)20 7679 0522
>>   ECRC, UCL Geography,          [f] +44 (0)20 7679 0565
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>>
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-- 

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


4. Zero Inflated Models and Generalized Linear Mixed Models with R. (2012) Zuur, Saveliev, Ieno.
http://www.highstat.com/book4.htm

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


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