Hello,

I am having a lot of difficulty specifying a mixed effects model structure for analysing some soil nutrient data. I have been reading a lot about mixed effects models from books and the R mailing lists and I thought I had my design sorted until I had some feedback from reviewers that suggested otherwise. My design is as follows:

I have collected data from a fire experiment which has a randomised block design. There are three blocks of vegetation and each block is separated into 4 plots that get burnt at 4 different frequencies. I sampled soil from each of these 12 plots, however, I stratified my sampling by tree cover ('patch'). That is, I took 3 samples from beneath tree canopies and 3 samples away from canopies in each plot (the samples were actually composite samples made from bulking 8 individual soil samples collected over a 2 x 2m grid). I performed this sampling directly after the experimental burns were undertaken and at a further 4 other time points (2 weeks, 1 month, 3 months, 5 months) after the fires. At each time point I made sure that soil samples were collected a small distance away from the previous collections, but still  beneath the same canopy conditions.

Fire: factor with 4 levels: 1,2,5,0
Block: factor with 3 levels: A, B, C
Patch: factor with 2 levels: T, I
Replicate: factor with 3 levels: 1, 2, 3
Date (time since fire): 1, 12, 28, 55, 152

Total number of observation: 359 (one missing observation)

Response: soil amino acid concentration
Fixed effects: patch, date, fire

I wanted to treat block as a random effect and then because replicate samples taken from each patch type are nested within fire treatments I designed my random effects as block/fire/patch/replicate. However, because I took samples at different dates I wanted to account for the fact that samples collected from one time point are more closely related than samples collected at another time point. I also checked that there was no auto-correlation in my residuals using the corSpher correlation function (ie. that samples taken closer together e.g. days 1 and 12 are more highly correlated than samples taken further apart e.g. days 1 and 155) and I didn't find this to be a problem. The main difference of opinion has been where to place the 'date' term in the random effects. My original design was:

model1_lme<-lme (y~patch*date*fire ,random=~1|date/block/fire/patch/replicate)

but it was suggested that I should instead use:

model1_lme<-lme (y~patch*date*fire ,random=~1|block/fire/patch/replicate/date)
or
model1_lme<-lme (y~patch*date*fire ,random=~1|date/block/fire/patch/date/replicate)

Both these alternative models don't make sense to me but I am very new to mixed models so perhaps they are correct? Additionally, I understand that this group uses lmer and perhaps that is what I need to start using for these complicated designs? Lastly, I tried including date as a random covariate: random =~date|block/fire/patch/replicate but I receive the error:

Error in logLik.lmeStructInt(lmeSt, lmePars) :
  NA/NaN/Inf in foreign function call (arg 3)
In addition: There were 50 or more warnings (use warnings() to see the first 50)
> warnings()
Warning messages:
1: In logLik.lmeStructInt(lmeSt, lmePars) :
  Singular precision matrix in level -2, block 1
Etc

Any suggestions would be much appreciated, we don't have any statistics support in my lab so I feel very much in the dark when it comes to these things.
Thanks!
Anna
Dr Anna Richards
OCE Postdoctoral Fellow
CSIRO Ecosystem Sciences
Darwin, Australia


Dr Anna Richards
OCE Postdoctoral Fellow
CSIRO Ecosystem Sciences
Phone: +61 8 89448437 | Fax: +61 8 89448444 | Mobile: 0423 971 997
anna.richards@csiro.au<mailto:anna.richards@csiro.au> | www.csiro.au | www.csiro.au/people/Anna.Richards.html
Address: CSIRO Tropical Ecosystems Research Centre, 564 Vanderlin Drive, Berrimah NT 0828 Australia. (Postal address: PMB 44, Winnellie NT 0822)

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