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Message: 5
Date: Sun, 3 Jan 2010 20:07:25 +1100
From: Scott Foster <scott.foster at csiro.au>
Subject: Re: [R-sig-eco] Time series and GLS
To: LisaB <lisabaril at hotmail.com>
Cc: "r-sig-ecology at r-project.org" <r-sig-ecology at r-project.org>
Message-ID: <4B405E4D.9080804 at csiro.au>
Content-Type: text/plain; charset="utf-8"; format=flowed
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
--
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