Dear Pedro,
Thanks so much! Your comments got me headed in right direction.
First, I converted Dates to a day-of-year format and sorted by Date.
Second, I gave it a group structure, using:
fvfm <- groupedData(FvFm ~ Date | Tree/Exposure, perm.fvfm)
head(fvfm)
Grouped Data: FvFm ~ Date | Tree/Exposure
Tree Exposure Date FvFm
1 1 N 44 0.7950
2 1 S 44 0.7750
3 1 N 51 0.7790
4 1 S 51 0.6980
5 1 N 58 0.7725
6 1 S 58 0.6475
I needed to nest Exposure in Tree, otherwise I got the following error
when running the GLS:
Error in Initialize.corAR1(X[[i]], ...) :
covariate must have unique values within groups for "corAR1" objects
Then I ran GLS as:
gls.fvfm<-gls(FvFm ~ Exposure, correlation = corAR1(form = ~Date|Tree/
Exposure), data = perm.fvfm);summary(gls.fvfm)
which gave me:
Generalized least squares fit by REML
Model: FvFm ~ Exposure
Data: perm.fvfm
AIC BIC logLik
-306.1793 -294.356 157.0896
Correlation Structure: ARMA(1,0)
Formula: ~Date | Tree/Exposure
Parameter estimate(s):
Phi1
0
Coefficients:
Value Std.Error t-value p-value
(Intercept) 0.7780694 0.009153179 85.00538 0.0000
ExposureS -0.0214861 0.012944549 -1.65986 0.0991
Correlation:
(Intr)
ExposureS -0.707
Standardized residuals:
Min Q1 Med Q3 Max
-4.0182078 -0.3630604 0.2468685 0.6717131 2.0139322
Residual standard error: 0.0776673
Degrees of freedom: 144 total; 142 residual
I?m interpreting this to mean that Exposure is marginally significant,
with S < N (which is what I?ve observed).
Once again, much thanks!
Rick
On Jun 16, 2019, at 9:45 AM, Pedro Pequeno <pacolipe at gmail.com> wrote:
Dear Richard,
your question could be handled using a linear model incorporating a
temporal autcorrelation structure within trees. However, I don't think
using "tree" as random factor (e.g. in lme()) would be very helpful here
because random factors assume a compound symmetry autocorrelation structure
(same correlation for any temporal distance), which is probably overly
simplistic for long time series. Instead, you could use Generalized Least
Squares, gls() in R, which is a standard choice in such cases. For instance:
gls(FvFm ~ Exposure, correlation = corAR1(form = ~time|Tree), data =
perm.fvfm)
This will fit a model assuming a first-order autoregressive correlation
structure, i.e. residual autocorrelation should decrease as the temporal
distance between them increases. Notice that "time" should be the temporal
order of observations within trees, so you will have to convert your "Date"
to this format first. For other correlation structures, relevant R
functions and examples similar to yours, see Zuur et al. (2009), "Mixed
effects models and extensions in ecology with R".
Best wishes,
Pedro
Em sex, 14 de jun de 2019 ?s 14:42, Richard Boyce <boycer at nku.edu>
escreveu:
I?m measuring chlorophyll fluorescence (FvFm), my measured variable, on N
and S exposures (treatment variable) of 4 red cedar trees. Here?s what the
beginning of the data file looks like:
head(perm.fvfm).
Tree Exposure Date FvFm
1 1 S 13.Feb 0.775
2 1 N 13.Feb 0.795
3 2 S 13.Feb 0.737
4 2 N 13.Feb 0.759
5 3 S 13.Feb 0.615
6 3 N 13.Feb 0.712
If I were just doing this one time, this would be a randomized block
design, where trees were the blocks (random variable) and exposure was the
treatment variable (fixed variable). Actually, since there are only two
treatment levels, it would be a paired t-test.
However, I?ve repeated this on many dates (18 so far this year). So this
also requires a repeated-measures design, with trees as subjects.
Repeated-measures, however, usually have time (date) as a within-subject
variable and then some other treatment that is a between-subjects variable.
I don?t have have a between-subjects variable, however, as all subjects
(trees) get both levels of exposure and all levels of time (date).
I?ve searched the web, but there is not a lot out there for this kind of
design. It looks like lm, lme, lmer, and permuco in R might all work, but
advice for how to set up the Error() or random variable designations are
confusing and sometimes contradictory. Any advice would be much appreciated!
Thanks,
Rick Boyce