[R-sig-ME] lme4 random effects for repeated measures, unbalanced data

[Ben Bolker]

On 16-07-19 07:28 PM, Ann Marie Raymondi wrote:
> Hello Listers,
> 
> I have a vegetation data set that consists of 150 plots that were sampled
> 1-3 times over a three year period.  Plots are my unit of observation and
> they are unbalanced (since plots were sampled either once, twice, or three
> times).  I would like to use mixed-effects models in order to account for
> variation in both plots and sampling year and to keep my sample size large
> (instead of conducting my analysis within individual years). Here is an
> example of the grouping of my data:
> 
> Plot_ID       Plot     Year
> 2012_101   101     2012
> 2013_101   101     2013
> 2014_101   101     2014
> 2012_201   201     2012
> 2013_201   201     2013
> 2013_301   301     2013
> 
> My response variables are cover of vegetation functional groups and
> predictors include variables related to fire and treatment history.
> Additionally, I am not interested in how plots change over time per se, but
> rather, in aggregating sampling from all three years to increase my sample
> size and to account for the spatial/temporal correlation that arises from
> doing so.  It is my assumption that treating plot as a random effect
> (intercept only) accounts for variation that arises from potential spatial
> autocorrelation, but my main question is how to account for the repeated
> measures and if I need to account for the grouping of cells within sampling
> years:
> 
> Potential model:
> 
> model<-lmer(response~covariates + (1|Plot) + (1|Year).
> 
> However, I know that is not appropriate to use a random effect with only
> three levels, year in this case.  I'm hoping for recommendations on how to
> incorporate year as a random effect.  Is including (Year |  Plot)
>  recommended?  And if so, how might I interpret that effect, i.e., is it
> accounting for variation introduced by different sampling year or variation
> in plots over sampling year?

> Thank you in advance for any help/suggestions!
>

  Include Year as a fixed effect.  You could try to include (Year|Plot),
but it will overlap with the residual error (since each plot is measured
once per year), so it probably won't work (without some more fussing
around).  You'll probably get most of the signal by including Year as a
fixed effect.