Dear All,

I am trying to fit a repeated-measures linear mixed effects model using 
lme and have some doubts about the ANOVA results. My experiment consists 
of 20 trees, which were assigned to ambient (A) or elevated (E) CO2 for 
9 years. The trees were then harvested and ring width was measured on 
multiple stem discs per tree, including several pre-treatment years. 
Therefore, my dataset has the following variables:

CO2 (A or E treatment)
ID (code for individual tree, 20 with E and 20 with A CO2)
yearCat (year of ring width, 2001-2009; set as categorical variable)
Disc (individual disc with ring width measurements, a-c except for one 
tree with 4 discs a-d)
rw (ring width measurement for individual year within disc within tree)
cov95to00 (mean ringwidth over pre-treatment years 1995 to 2000 for an 
individual disc)

I would like to analyze the effect of CO2 enrichment and whether it 
varied during the 9 years of treatment, using the pre-treatment ring 
width measured on individual discs as a covariable. So far, I have set 
up the following model, including corAR1 to account for auto-correlation 
of residuals between years:

rw.model <- lme(rw ~ cov95to00 + CO2 * yearCat, random = ~ 1 | ID/Disc, 
data = ringsyr, na.action = na.omit, method = "REML", corAR1())

However, the ANOVA output shows that year and CO2:yearCat are tested at 
the individual disc level, which means a very large denom DF, and I am 
not convinced this is correct.

numDF denDFF-value p-value
(Intercept)14128.025640.0048
cov95to001403.331490.0754
CO21182.705690.1173
yearCat8412 103.19579<.0001
CO2:yearCat84123.375340.0009

I also get huge confidence intervals (using the function intervals()) 
for the random effect associated with Disc or even the message "cannot 
get confidence intervals on var-cov components: Non-positive definite 
approximate variance-covariance", which makes me think the model 
structure might be incorrect.

While I am more confident in a model where measurements are averaged at 
the tree level (mean of all discs per tree for each year), I think a 
model with individual discs is better, especially because then I can use 
pre-treatment measurements that are specific to individual discs rather 
than averaged at the tree level. I get rather different ANOVA results 
when I average at the tree level.

I would be grateful for any suggestions about how to correctly apply lme 
in this situation.

Thank you,
Melissa


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