Hi Ben,

Thank you for the prompt response.  I actually have Zuur et al. 2009 in
front of me and in Chapter 5, 'Mixed Effects Modelling for Nest Data', they
first settle the issue of random effects and then deal with the fixed
effects in a step-1 fashion.  However, when reading 'Natural Selection and
Genetic Variation for Reproductive Reaction Norms in a Wild Bird
Population' by Brommer et al. 2005, it appears on page 1364, column 2, that
they first selected the fixed effects structure and then decide the random
effect structure.  It's unbelievable how little consensus there is in many
different areas of mixed models and thus for me, leads to a lot of
uncertainty.  This is why I am so appreciative of your responses.

As far as estimating the population intercept and slope, you mentioned that
this can be difficult, but said 'You could check out the 'lsmeans' package.
 Alternatively, if you set sum-to-zero contrasts for everything
(options(contrasts=contr.sum)) the intercept should represent the
(unweighted) mean'.  I am not familiar with either option and after
checking the .pdf for 'lsmeans', I really don't understand it much at all.
For the second option, I did a google search for how to implement this into
my model and can't quite figure it out.  Am I just adding
'(options(contrasts=contr.sum)) into my model specification or is this done
after the model has been run?  Does this deliver the population slope as
well?  There is a figure in Zuur et al. 2009 on page 108 of Chapter 5 that
shows the overall population response, along with each beach response.  I
suppose this is what I am looking for in the end.

Thank you again for your help.

Jacob


On Wed, Aug 28, 2013 at 2:02 PM, Ben Bolker <bbolker@gmail.com> wrote:

>
>
>  [cc'ing back to r-sig-mixed-models]
>
> -------- Original Message --------
> Subject:        Re: [R-sig-ME] Help with Interpretation of LMER
> Output--Correctly Formatted Post (I Hope)
> Date:   Wed, 28 Aug 2013 10:51:16 -0400
> From:   AvianResearchDivision <segerfan83@gmail.com>
> To:     Ben Bolker <bbolker@gmail.com>
>
>
>
> Hi Ben,
>
> Thank you for the response.  I apologize for not getting back to you
> earlier, but I have been stuck in the field the last few days.  I will
> check out the book you have recommended.  Also, I am using lmerTest to
> get p-values.  In the meantime, can you answer two more minor questions?
>
> 1.  In your response, you mentioned that the intercept and Environ were
> NT1's values.  If this is the case, how do I obtain the overall
> population average response?
>
>    The definition is a bit tricky -- it really depends how you
> want to define the average.  For a balanced, nested, linear model
> the answer is unambiguous, but beyond that there are a lot of
> decisions to make.  You could check out the lsmeans
> package.  Alternatively, if you set sum-to-zero contrasts for
> everything (options(contrasts=contr.sum)) the intercept should represent
> the (unweighted) mean.
>
>
> 2.  I've done a lot of reading about linear mixed models over the last
> couple of months, but I can't find anything definitive about how you go
> about the model selection in terms of fixed effects first or random
> effects first.  What would you recommend?  If I select the fixed effects
> first by LRTs, would I just use lm, instead of lmer in the model?  Also,
> If I am interested in an individuals response to a fluctuating predictor
> variable (plasticity), as well as the population response, should I
> always keep random slopes in the final model and just report that a LRT
> for slopes was either significant or not?
>
>    This is a big can of worms.  I don't remember what the GLMM FAQ
> <http://glmm.wikidot.com/faq> says.  I believe Zuur et al recommend
> selecting fixed effects first.  If model selection is necessary I
> think I'd recommend starting with the random effects (as shown in
> the Banta et al. _Arabidopsis_ example that can be found in the
> 'worked examples' section of the glmm.wikidot.com site).  I would
> lean towards your final suggestion (err on the side of retaining
> all sensible RE in the models, whether they are significant or not,
> as long as they can be estimated reasonably reliably from the data).
> However, I don't think this is a settled question.
>
> Thank you for your help again.  I do appreciate the fact that you took
> the time to carefully answer each prior question.
>
> Jacob
>
>

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