R help - Mar 2012 - two lmer questions - formula with related variables and output interpretation

Hello,
I have been attempting to set up a lme and have looked at numerous posts
including 'R's lmer cheat-sheet' as well as reading a number of
papers and
other resources including R help, but I am still a little confused on how to
write my model (I thought I had it).

I have asked a number of questions on different forums; most of which have
been resolved.

My main concern right now is whether my model is correct. I studied broods
of precocial chicks and watched each chick every other day for five minutes
if possible. As chicks on the same day are completely non-independent the
mean was found for each brood for each day. Variables that were recorded
were the behaviours during that time and the habitats used.

There were seven broods. Three at one site and four at the other site. Only
one site had a brood that consistently used mudflats rather than oceanfront
habitats. As none of the data within a brood is truly independent, along
with the very small number of broods, it became impossible to use
conventional statistics to test the hypotheses and so it was suggested that
mixed-effects models would be the best option as it would not only allow for
all data to be used with a random effect of Brood ID to negate the
pseudo-replication but also let me look at partial use of mudflats in one of
the other broods that only used it periodically.

So, for this part of the analysis I would like to see which factors affect
the amount of time feeding. I set up a global model with ten fixed variables
plus (1|Brood). Site, tide.h.l, tide.inc.out, MF.vs.OF, Human Disturbance
Rate (HDr), Human Disturbance proportion of time(HDp), non-Human Disturbance
(two variables as for Human Disturbance) and Age and mean.foraging.rate. As
so:

gm1<-lmer(Feeding~Site+tide.level+MF.vs.OF+HDr+HDp+NHDr+NHDp+Age+mean.for.rate+(1|Brood),
data=AllBrood, REML=TRUE)

I wished to put all the factors together to explore which ones really did
influence the time spent feeding and used 'dredge' command to run all
possible combinations and then averaged the models with an AICc Delta<2. I
was expecting that the proportion of time being disturbed (HDp and NHDp)
would be the most relevant as by default the greater time in other
behaviours the less time for feeding. However, MF.vs.OF had a larger effect
than HDp and NHDp but this may be because MF observations did not experience
HDp at all so this may push the effect of this habitat. Surprisingly
non-human disturbance rates rather than time had a greater effect (but these
are quite even among habitats.

The results of the model.avg are as follows:
 Estimate Std. Error z value Pr(>|z|)    
(Intercept)   102.7190     5.5300  18.575  < 2e-16 ***
HDr            -1.5495     0.3451   4.490 7.11e-06 ***
MF.vs.OF2      -7.6780     3.7507   2.047  0.04065 *  
NHDp           -0.5145     0.2909   1.769  0.07695 .  
NHDr           -1.4164     0.4663   3.037  0.00239 ** 
Site2           6.1477     2.7400   2.244  0.02485 *  
tide.h.l2      -7.2546     2.6914   2.695  0.00703 ** 
tide.inc.out2  -5.8486     2.6187   2.233  0.02553 *  
HDp            -0.3773     0.2732   1.381  0.16731    
mean.for.rate  -0.3966     0.3220   1.232  0.21807    
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 

Full model-averaged coefficients (with shrinkage): 
 (Intercept)        HDr  MF.vs.OF2       NHDp       NHDr      Site2 
tide.h.l2 tide.inc.out2        HDp
  102.718962  -1.549499  -5.734171  -0.239550  -1.416373   5.336532 
-7.254627     -5.848553  -0.044795
 mean.for.rate
     -0.081734

Relative variable importance:
  (Intercept)           Age           HDp           HDr mean.for.rate     
MF.vs.OF          NHDp          NHDr 
         1.00          0.00          0.12          1.00          0.21         
0.75          0.47          1.00 
         Site      tide.h.l  tide.inc.out 
         0.87          1.00          1.00 

I was wondering whether there would be a better way to formulate the model
to allow for this effect, or could I just keep it as is and just infer that
it may be partly affected by the amount of disturbance within these habitats
but as it has a greater effect that other factors are at play which would
then lead me onto the next model which is going to explore observations that
do not include disturbance which would allow me to tease the natural factors
affecting feeding behaviour? I was going to run this second model with site
still as a fixed effect and then run it with (1|Site) to remove site effect
(if one is found).

I would prefer to keep it simple as I really want to use a lme, but don't
have the understanding for more complex interactions.

I has also asked a question, which is yet to be answered on stats stack
exchange, in regards to the output of the model.avg.  as follows:

I have seen the Estimates described as the effect of the variable and this
is discussed in results sections as an important value to report (in regards
to the size of them and their direction (+ve/-ve). (the paper I was reading
was stating that those with the bigger or smaller numbers had the greatest
effect (even quoting that one was 48% lower than the other) However if this
is what is reported and discussed, why would the relative variable
importance vary in relation to the estimate? It seems that this should also
be looked at but am not sure how the z and p values are calculated from a
model.

Therefore I would like to know which is more important when trying to
discuss the findings. I admit that my knowledge is limited, but I would like
to grasp this in simple terms if I could.

As an additional note, the paper I am referring to also has a table showing
the Estimates and the 95%CI. The title of the table however says
"Model-averaged parameter estimates and relative importance values for
variables affecting adult piping plover foraging rates in New
Jersey,2007?2009." which does not seem to fit with what was actually shown,
unless the RIV are inferred somehow from the CIs

The link can be found here: 

It would allow you to look at the results and what I am talking about, but
at the same time, if someone would be able to look at that question too I
would appreciate it.

Thank you all in advance.

Rachel

P.S. I know that some may wonder why I am running models if I don't know the
ins and outs, but I really do understand what they represent, I just don't
understand the intricacies between variables and if Estimates or relative
variable importance is more important as the study that is similar to mine
only used the former and I expected them to be correlated


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I realised that I removed the link to the question but forgot to remove the
text regarding it. Sorry. I am not sure if I am supposed to link to other
forums, but I can add the links as needed (as the format is clearer).

I actually have one more question though in regards to which data to use.
If it is better to just report the estimates and CIs then should I use those
with shrinkage instead, and if so, does anyone know how I can get the CIs
for these rather than just the regular CIs. I apologise if I am asking too
many questions within one post.

Rachel

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