[R-sig-ME] Mixed models for repeated measures with missing values

[Hongmei Chen]

Dear mixed model users,

I have a question concerning using mixed models for repeated measures 
with missing values. I would like to test the effects of plant diversity 
(Div., continuous) on root growth rate (Y, continuous) over time (Time). 
However, time is not evenly spaced, thus I think it is better to use 
Time as a continuous term. In addition, the root growth rate - time 
relationship was not linear. Thus I used poly (Time, N) to account for 
the non-linear relationship.  Besides, the plots were randomly arranged 
in the 4 blocks, I would also like to account for the potential block 
effect.

I use lme from nlme for the data analyses.
I first tested the polynomial order by increasing n from 2 to 3. 
However, AIC suggest that I should use 5 or 6. I am afraid I will over 
fit the data. thus I chose ploy(Time, 3).
Mod1 <- lme (Y ~ Div * ploy(Time, 3), random = ~1|block/plot, method="ML")

Because of repeated measurement, I included e.g. correlation= corRatio 
(form=~Time, nugget=T) to account for the dependence. I tested different 
correlation structures and chose the one with lowest AIC.
Mod2 <- lme (Y ~ Div * ploy(Time, 3), random = ~1|block/plot, 
method="REML", correlation=  corRatio (form=~Time, nugget=T))

After checking the residuals, I still could see some trend in time, and 
heterogeneity in residuals e.g. at different time. I further included 
"weights" argument in the model.
Mod3 <- lme (Y ~ Div * ploy(Time, 3), random = ~1|block/plot, 
method="REML", correlation=  corRatio (form=~Time, nugget=T), 
weights=varIdent(form=~1|plot))

My questions are
1) Should I go for higher order in polynomial term? For example 4
2) For the random term, I used the simplest one. Would you consider 
other options e.g. random = ~ploy(Time, 3)|block/plot
3) Can I use time as a continuous term in fixed part but as a factor in 
the random part or in the weights argument  like: 
weights=varIdent(form=~1|as.factor(Time))

Because of the missing observation values, I could only used mixed 
models for my data. I have googled this is for quite a long time but 
could not find a good example or solution. Any suggestions are welcome.

Kind regards,
Hongmei Chen

-- 
Hongmei Chen
Spezielle Botanik und Funktionelle Biodiversität Institut für Biologie
Universität Leipzig
Johannisallee 21-23
04103 Leipzig

Tel: ++49 341 9738589
Fax: ++49 341 9738549
Email: hongmei.chen at uni-leipzig.de