[R-sig-ME] Presenting results of a mixed model containing factors

[Sarah Dryhurst]

I am running a mixed effects model using the following code:

m1<- lmer(DV~TMT*TMT2+(1|Block/TMT1),verbose=T)

An example dataset is here: http://pastebin.com/bHug5kTt

The two explanatory variables are both factors with two levels
(treatment and control).  Treatment 2 is split within Treatment 1
which is in turn within block.

The model output I get is as follows (sorry for the formatting!)


Linear mixed model fit by REML

Formula: Richness ~ NT * WT + (1 | Block/WT)
   Data: rich2013
           AIC     BIC    logLik    deviance   REMLdev
           93.04  101.3  -39.52    81.87        79.04

Random effects:
 Groups   Name        Variance   Std.Dev.
 WT:Block (Intercept) 3.3667e+00 1.8348e+00
 Block    (Intercept) 8.2334e-19 9.0738e-10
 Residual             6.1667e-01 7.8528e-01
Number of obs: 24, groups: WT:Block, 12; Block, 6


Fixed effects:
                 Estimate   Std. Error        t value
(Intercept)  12.0000     0.8148          14.728
NTNX         -0.5000     0.4534           -1.103
WTS          -3.6667     1.1523           -3.182
NTNX:WTS  3.3333     0.6412            5.199


Correlation of Fixed Effects:
                 (Intr)      NTNX     WTS
NTNX          -0.278
WTS           -0.707   0.197
NTNX:WTS  0.197    -0.707  -0.278



I have a few questions - i'm sorry if this is not the right place to
ask them (they are quite simple!):

In interpreting this model, am I correct in thinking that the output I
get tells me the effect of one level of each factor compared with the
other level of that factor, and also the effect of the interaction in
terms of the effect of one combination of treatments compared to
another combination of treatments?

My main concern lies in how to report this model in a paper or thesis.
 It seems to be common practice to the "main effect" of each factor in
a model (and perhaps the main effect of an interaction?), and then to
discuss the difference between factor levels later.  Is this correct?

If the above is correct, in an lm, I would simple use
summary.aov(model) to give me the summary of the main effects of each
explanatory factor and the interaction and report these, along with
their test statistic and p value (subjective, I know).  However I do
not know how to do this in lme4, or indeed if this is even a correct
approach.

Specifically then, I am wondering:
a) Is the extraction of these "main effects" possible in lme4 and if
so, how is it done?
b) How best to present the results of the two treatments...
c) How best to present the results of the interaction between the two
treatments at all levels of this interaction (so for all combinations
of factor levels that make up the 2x2 factorial experiment).

I have struggled to find much information relating to how to present
such models online...

Many thanks in advance!

Sarah