[R-sig-eco] nlme model specification

[Christian A. Parker]

Matthew
Please correct me if I am wrong (anyone) but because your observations 
are not independent across your desired groups (years) your error terms 
will be biased which will then influence your significant tests. So 
regardless of the factor that you are interested you would still want to 
account for the fact that all measurements were taken on the same trees 
each year by doing a repeated measures model of some sort.
Hope this helps,
-Chris

Landis, R Matthew wrote:
> 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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>>
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