Dear all,

I am new to using mixed effects models and I would like to use a
multi-level model with nested random effects to look at variation in leaf
traits of 22 tree
 species across and within contrasting light environments. In total, I have
1408 leaf-level observations, which works out to 64 leaves per species,
 32 trees per species, and  at least 10 trees in two different light
environments
(*I've included model structure below for your reference). Across all
species, I would like to determine how much variation in leaf traits is
attributable to
 a) species ('SPP'), b) light environment ('proxy'), c) location
('TRANSECT'), and d),Tree ('"FieldTag").  I have fitted an unconditional
model using nlme:
 x<-lme(log(LMA)~1,random=~1|SPP/proxy/TRANSECT/FieldTag,data=example)

 From the above model,  I can extract variance components using VarCorr.
However, I am not sure how to calculate confidence intervals for variance
(' intervals'  provides 95% intervals but for standard deviation). More
importantly, I think there is a strong argument for using SPP and proxy as
fixed effects , but I am unsure how to calculate variance for both fixed
and random effects (as well as their confidence intervals).

Secondly, I would like to be able to do the same as above for each species,
i.e. estimate their variance across light environments, as well as within
them.  Ideally, I would use a simplified version of the model above:
 species_y<-lme(log(LMA)~1,random=
~1|proxy/TRANSECT/FieldTag,data=example_sppx).  Ideally, I would like to be
able to
relate the variation of each species to the global estimate of variation
for all species from the previous model (e.g: var_sppx/var_allspecies), but
I'm not sure how statistically kosher this would be.

To make my questions more explicit, I've summarized them below:

1) How can I extract variance components for a mixed effects model with
both fixed effects and nested random effects?

2) How can I estimate confidence intervals for variance of fixed and random
effects?

3) In order to calculate confidence intervals properly for variance (or
parameter estimates), would bootstrapping be a reasonable approach, or
would using a MCMC sample be preferable?

I apologize for the basic nature of these questions, and would really
appreciate to hear any thoughts or suggestions about what direction to take
with
this analysis.

Cheers,

Dylan


Classes ‘nmGroupedData’, ‘groupedData’ and 'data.frame':	1408 obs. of
16 variables:
 $ SPP        : Factor w/ 22 levels "ALCHCO","AMAICO",..: 1 1 1 1 1 1
1 1 1 1 ...
 $ ID         : Factor w/ 1408 levels "ALCHCO1_1","ALCHCO1_2",..: 1 2
3 4 5 6 7 8 9 10 ...
 $ FieldTag   : Factor w/ 704 levels "ALCHCO1","ALCHCO10",..: 1 1 2 2
3 3 4 4 5 5 ...
 $ SITE       : Factor w/ 28 levels "8","9","11","12",..: 13 13 18 18
18 18 18 18 19 19 ...
 $ TRANSECT   : Factor w/ 39 levels "16","17","21",..: 21 21 27 27 27
27 27 27 28 28 ...
 $ LEAF       : Factor w/ 4 levels "1","2","3","4": 1 2 1 2 1 2 1 2 1 2 ...
 $ CE         : Factor w/ 3 levels "2","3","4": 2 2 2 2 1 1 2 2 2 2 ...
 $ SLA        : num  15.3 16.8 15.1 15.7 17.2 ...
 $ LMDC       : num  0.396 0.38 0.373 0.389 0.326 ...
 $ Leaf_area_m: num  0.00603 0.00444 0.00487 0.00343 0.00294 ...
 $ Leaf_Size_m: num  0.00613 0.00451 0.00495 0.0035 0.00298 ...
 $ LMA        : num  65.4 59.6 66.4 63.7 58 ...
 $ SPL        : num  114 139 159 145 177 ...
 $ SPP_CE     : Factor w/ 53 levels "ALCHCO _ 2","ALCHCO _ 3",..: 2 2
2 2 1 1 2 2 2 2 ...
 $ proxy      : Factor w/ 2 levels "0","1": 2 2 2 2 1 1 2 2 2 2 ...
 $ proxy_CE   : Factor w/ 44 levels "ALCHCO _ 0","ALCHCO _ 1",..: 2 2
2 2 1 1 2 2 2 2 ...
 - attr(*, "formula")=Class 'formula' length 3 log(LMA) ~ proxy_CE | FieldTag/ID
  .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv>
 - attr(*, "formulaList")=List of 2
  ..$ FieldTag:Class 'formula' length 2 ~FieldTag
  .. .. ..- attr(*, ".Environment")=<environment: 0x0000000005b67cf8>
  ..$ ID      :Class 'formula' length 2 ~ID
  .. .. ..- attr(*, ".Environment")=<environment: 0x0000000005b65a28>
 - attr(*, "order.groups")=List of 2
  ..$ FieldTag: logi FALSE
  ..$ ID      : logi FALSE
 - attr(*, "FUN")=function (x)

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