[R-sig-ME] multiple nested random factors

[Amanda Adams]

Hello!
I have been having a heck of a time figuring out how to estimate the 
proportion of variance from several random factors. I have a count data 
of the number of bat calls recorded at 3 sites, on 6 detectors, over 12 
nights. Detectors were at 2 heights.
If I understand nested factors correctly, Detectors are nested in Site 
and Night is nested in Site. Site/Detector and Site/Night are random 
factors and Height is a fixed factor.
Also, data is overdispersed so I am transforming number of calls as 
log(Calls+1).

'data.frame':   249 obs. of  11 variables:
  $ Night     : int  1 3 5 11 12 1 3 5 11 12 ...
  $ Night2    : int  1 2 3 4 5 1 2 3 4 5 ...
  $ Site      : int  1 1 1 1 1 1 1 1 1 1 ...
  $ Species   : int  1 1 1 1 1 1 1 1 1 1 ...
  $ Detector  : int  1 1 1 1 1 2 2 2 2 2 ...
  $ Height    : int  1 1 1 1 1 2 2 2 2 2 ...
  $ Calls     : int  6 444 236 12 143 5 815 712 30 142 ...
  $ f.Night   : Factor w/ 12 levels "1","2","3","4",..: 1 2 3 4 5 1 2 3 
4 5 ...
  $ f.Site    : Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 1 1 1 1 1 ...
  $ f.Detector: Factor w/ 6 levels "1","2","3","4",..: 1 1 1 1 1 2 2 2 2 
2 ...
  $ f.Height  : Factor w/ 2 levels "1","2": 1 1 1 1 1 2 2 2 2 2 ...

I then coded for the nested variables:
data$detector <- with(data, factor(f.Site:f.Detector))
data$night <- with(data, factor(f.Site:f.Night))

trans.log <- log(data$Calls+1)

model <- glmer(round(trans.log,digits=0)~ f.Height + (1|night) + 
(1|detector) +
     (1|f.Site) , data = data, family=poisson)

I am uncertain on a couple things. Are my nested variables correct? Can 
I correct for overdispersion with a transformation?

I was also wondering if there is a reference explaining why there is no 
residual variance term for the Poisson distribution. I saw the 
explanation on a forum, but was hoping there was something I could cite.

Any help or advice would be appreciated.
Thank you!
Amanda

-- 
Amanda Adams, MSc
PhD Candidate
Department of Biology
Western University
London, ON
Canada
N6A 5B7
Work (519) 661-2111 Ext: 81349