[R-sig-eco] Time series and GLS

[Scott Foster]

Hi,

Just a few quick thoughts.

*) your success.gls model contains a linear effect for year.  Is this 
really likely over the time period you mention?  I would highly doubt it 
(but this is really just a guess).  If this is not the case then your 
residuals are likely to show falsely high autocorrelation, not because 
it is there but because the residuals come from an inappropriate mean model.
*) With the previous point in mind: have you considered using GAM 
models?  It seems like a perfect application as you can specify 
different smooth functions for each of the populations and then see if 
they really are all that different (through LRTs).
*) The GLS function will assume normality (albeit correlated).  Is this 
really all that believable?  In the GAM framework you could specify 
binomial data, an assumption that is much more likely to make sense.  Of 
course, your data may contain enough nests sampled and a favourable 
probability of success, to make the normality assumption very plausible.
*) The GAM model, when viewed as a random effects model, does specify a 
correlation structure amongst the outcomes.  It may not be the most 
appropriate correlation structure, nor even *an* appropriate structure 
but it may be a suitable starting place.  Most analysts would consider 
it a useful finishing place too (but you can extend the GAM model -- 
Richard Morton has done some work in this line although I can't find the 
reference right now). 

Be careful taking acf of residuals in GAM models -- the residuals from 
the model conditional on the random effects may not tell much about the 
correlation structure (need the marginal distribution for this).

I just notice that Kingsford Jones has sent through some more pointers.  
They are excellent suggestions, especially the one about plotting up 
your data -- visualisation is much more important than formal testing 
(in my opinion).  I believe that the above points are complementary to 
Kingsford's comments.

I hope that this helps,

Scott

PS  An excellent reference for GAMs is Simon Wood's Book (with 
accompanying R package).


LisaB wrote:
> Thanks Kinsford.  I thought it would be appropriate.  As a follow up
> question: My first thought is to set up the data file with three columns:
> year, population (A,B), and nest success and then to input the following
> formula: success.gls=gls(success~year*population).  This would allow me to
> test for the effect of year for each population and then also test for
> differences between the two populations.  My questions are 1) have I
> specified the model right for those questions and 2) would the acf function
> calculate the autocorrelation correctly even though my 'year' in the data
> file is repeated twice (once for each value of nest success/population)? 
> Thanks. Lisa (hope all is well with you)
>
>
> Kingsford Jones wrote:
>   
>> The gls function in nlme fits a general linear model, so yes you can
>> have categorical predictors (the advantage over the lm function is the
>> error covariance matrix may have non-zero off-diagonals, such as with
>> an autocorrelation structure, and non-constant diagonals).
>>
>> hth,
>> Kingsford Jones
>>
>> On Fri, Jan 1, 2010 at 2:44 PM, LisaB <lisabaril at hotmail.com> wrote:
>>     
>>> Hello -
>>>
>>> I need to analyze some time series data in an ANOVA framework, but am
>>> unsure
>>> of how to go about it.  I have data on nest success (response) over a 22
>>> year period for two populations.  For each year I have one value of nest
>>> success per population.  I am interested in determining 1) whether there
>>> are
>>> differences in nest success over time between these two populations and
>>> 2)
>>> what are the trends for each population over time.  My thought is to use
>>> GLS
>>> and model temporal autocorrelation if the acf function indicates this is
>>> an
>>> issue, but since population is a categorical variable I'm unsure if this
>>> is
>>> appropriate.  Any advice would be much appreciated. Thank you. Lisa
>>>
>>>
>>>
>>>
>>> --
>>> View this message in context:
>>> http://n2.nabble.com/Time-series-and-GLS-tp4240700p4240700.html
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>>>
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>
>   

-- 
Scott Foster
CSIRO Mathematical and Information Sciences
GPO Box 1538
Castray Esplanade
Hobart 7001
Tasmania 
Australia

Phone:     (03) 6232 5178
Fax:       (03) 6232 5000
Email:     scott.foster at csiro.au