[R-sig-eco] repeated measures mixed effects model

[Dunbar, Michael]

Hi Melissa

In your model formulation, I don't think TreeSpecies should be random. You have two tree species, and they have specific values. This is a big hint that tree species should be fixed. If you have an effect as both fixed and random, you need to think hard whether this is what you want.

Second, I can't work out what is IndivPlot. Is it an ID for individual trees? 

Thirdly, it's a not considered good form to call your model "model" in R (a minor point!)

>From the structure of the random effects and how the fixed effects slot in, lme "knows" for example that CO2 is a plot level effect.

If you have:
my. model <- lme(response ~ CO2 * TreeSpecies * year, random = ~ 1 | Group/IndivTree, data = x, na.action = na.omit, method = "REML")

Then I can't see a problem in following the standard approaches for model simplification. But I'm under the impression that for random effects, they set the structure of the data, so there is often little point in formally testing them. What might be of more interest is testing the fixed effects, in which case you will need to fit with method="ML". Finally, you've specified a three-way interaction, but it's worth thinking hard what this means and whether it is worth testing, as it will soak up a lot of degrees of freedom. 

Regards

Mike




-----Original Message-----
From: r-sig-ecology-bounces at r-project.org [mailto:r-sig-ecology-bounces at r-project.org] On Behalf Of m.martin at slf.ch
Sent: 24 February 2010 06:23
To: r-sig-ecology at r-project.org
Subject: [R-sig-eco] repeated measures mixed effects model

Dear All,

I have a question about model selection in a repeated measures linear  
mixed effects model. The field experiment was set up as a  
split-split-plot model with:
- 10 groups (each consisting 4 trees) - 5 of the groups are supplied  
with additional CO2 while the other 5 experience ambient conditions.  
Each individual elevated CO2 group is fed by one CO2 supply line,  
whereas ambient groups are simply trees relatively close together.
- each group consists of 2 trees of species A and 2 trees of species B
- repeated measurements were made on individual trees (year is a  
factor, as I am interested in whether the response differs across  
years rather than a trend over time)

The anova model with random intercepts I have used is:
model <- lme(response ~ CO2 * TreeSpecies * year, random = ~ 1 |  
Group/TreeSpecies/IndivPlot, data = x, na.action = na.omit, method =  
"REML")

I have been reading Zuur et al. 2009, and I would like to know if  
there is a way to use model selection to determine if the full nested  
design is necessary. They use likelihood ratio tests to compare  
models, removing the smallest nested level and then moving up. But in  
my repeated measures situation, this does not seem to work since  
repeated measurements were made on individual trees (lowest level).

One idea I had is to look at models of individual years and use  
likelihood ratio tests to see if TreeSpecies and Group actually  
contribute as random effects. As tests of all individual years  
indicate that these effects can be removed, could I then claim that  
the full repeated measures model also does not require these levels?  
This would leave a random structure of only: random = ~ 1 | IndivPlot

Thank you in advance for any suggestions!
Melissa

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