nlme model specification

Dear R-sig-eco:

Many thanks to all of those who took the time to reply to my question.  The diversity of replies has made me go back and try to clarify my question.  Apologies for the length of the e-mail.  Thanks in advance to anyone willing to plow through this and understand it.  If you're ever in Middlebury I'll buy you a beer.

To repeat, I have 300 trees, ranging in size from 10 - 150 cm diameter (big trees).  To simplify my original question, let's say I want to understand the relationship between growth and two variables, diameter (continuous) and vine load (ordinal index from 1-4). I'd also like to know the relative importance of diameter vs. vine load, e.g. by partial R2.  If I had one year of data, this would be a simple regression.

However, I have 9 years of annual measurements on the trees.  It's as if I have the above analysis repeated 9 times.  There was no initial treatment, so I view these 9 years as a random sample of the years in the life of the tree, and unlike most examples of repeated measures I have read, the time effect is of no interest whatsoever. That is, I am not interested in viewing xyplot(growth ~ time|id).  I don't expect to see any consistent directional response to time.  In a way, it's as if the 9 years represent blocks, (except that it's the same 300 trees in each block) -- this is why I view the yr as a random effect, and as the grouping variable.

If I were to graph the data, I would use xyplot(growth ~ diameter|yr) to see what I am most interested in.  Grouping by individual doesn't make sense to me here because each individual only represents a very small slice of the full range of measurements - e.g. over the ten years, each tree only grows from 10 cm - 14 cm, so I can't really estimate the growth vs. diameter relationship for each tree.  xyplot(growth ~ diameter|id) would not be useful. This is why I don't consider the individual to be the grouping variable, but perhaps I am wrong on this.

So, now, as before, I am back to

fit <- lme(fixed = growth ~ diameter * vines, random = ~ 1|year)

I'm expecting that this will estimate separate intercepts for each year.  Which is what I want (I would like to fit separate slopes by year too, but that model didn't converge).

I guess what I'm most concerned about is whether the significance tests obtained for each term use the appropriate error term and the appropriate degrees of freedom.  I'm currently using something like the following command to test the effect of diameter

anova(fit.full.model, update(fit.full.model, . ~ vines))

But maybe I'm way off base there.

Thanks very much!

Matt Landis

-----Original Message-----
From: r-sig-ecology-bounces at r-project.org
[mailto:r-sig-ecology-bounces at r-project.org] On Behalf Of
Landis, R Matthew
Sent: Wednesday, May 21, 2008 1:55 PM
To: 'r-sig-ecology at r-project.org'
Subject: [R-sig-eco] nlme model specification

Greetings R-eco folks,

I'm trying to analyze a dataset on tree growth rates to see
which factors are important (and their relative importance
too, if I can get that), and I'm having some trouble figuring
out how to specify the model, despite having carefully read
Pinheiro and Bates, the help files for nlme, Crawley's book on
Statistics with S, MASS, and other books besides.

The dataset consists of ~ 300 trees measured annually for 10
years.  So, I have 9 pseudo-replicated intervals over which to
assess growth (about 2700 rows in the dataset).  There are 5
different explanatory factors, which are a combination of
continuous variables and categorical factors.  Some of these
vary with time.  In the end, I would like to get both
coefficient estimates and partial R2 (or some other way of
ranking them) for each factor.  Unlike most time-series
examples in the books, I am not interested in how growth
varies with time, nor am I particular interested in
interactions of explanatory factors with time.

Based on this, I've convinced myself that I should specify the
model as:

fit <- lme(fixed = growth ~ (x1 + x2 + x3+ x4 + x5)^2, random
= ~1|year, method = 'ML')

Year is clearly a random effect, and is the grouping variable
for the analysis.  Each of the other coefficients is "inner"
to this variable.  I'm ignoring individual tree as a grouping
factor, since I don't want to estimate separate coefficients
for each tree.  Does this sound like the correct way to do this?

Thanks for any help.  Apologies if this is more of a
statistics question and less of an R question.

Matt Landis

****************************************************
R. Matthew Landis, Ph.D.
Dept. Biology
Middlebury College
Middlebury, VT 05753

tel.: 802.443.3484
**************************************************


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