[R-sig-ME] model specification for continuous environmental vars

[Hans Ekbrand]

On Thu, Dec 12, 2013 at 01:39:04PM -0500, Tim Howard wrote:
> List members - 
> I am learning a lot, quickly, but still have a way to go. I would 
> greatly appreciate some help with model specification in glmer.
> I can't find a good example that parallels what I've got.
> 
> My dataset consists of spatially-balanced random samples of rare 
> plants within alpine summits. There were two sampling bouts (yr1 and yr2)
> with yr2 collected 6 years after yr1. A new set of random plots were 
> collected at each bout (e.g. new estimate of the population, not repeated 
> measures). I would like to test the difference in plant density from yr1 to yr2, overall. 
>  
> These are count data with many zeros, fitting a negative binomial distribution.
>  
> This is what confuses me:  I ALSO have environmental information 
> that influences density, such as elevation, solar radiation, slope (and more)
> I would like to include these variables in the model, but I am not 
> exactly sure how. Based on my reading, this is what I think I have:
>  
> block random effects: summit
> continuous random effects: elev, solrad, slope
> fixed effect: time (=samp)
> individual random effects to deal with overdisperson: plotID
>  
> I have over 350 plots for each sample bout, spread among 17 summits.
>  
> Given this I think my model is:
>  
> mod <- glmer(count ~ samp + (1|summit) + (1|elev) + (1|solrad) + (1|slope) + (1|pltID), 
>        data=dat, family="poisson")
>  
> My primary questions: 
> Is this the appropriate way to handle these environmental variables?

>From my limited understanding of these issues, I'd say elev, solrad
and slope should be fixed effects - the are universal in the sense
that they are defined for every (imaginable) case.

If they vary within each summit, you could - in addition to having
them as fixed terms - also include them as random slope terms:
(elev|summit) + (solrad|summit) + (slope|summit), if you want to
explain (some of) the variance between summits.

Since you do not have repeated measures of pltID, you can not include
a random term for pltID - there is no variance within each value of
pltID.

I would model like this 

mod <- glmer(count ~ samp + (1|summit) + elev + solrad + slope, data=dat, family="poisson")

And possibly try (but I don't think you have enough data for this)

mod <- glmer(count ~ samp + (1|summit) + elev + solrad + slope + (elev|summit) + (solrad|summit) + (slope|summit), data=dat, family="poisson")