Fitting a model on continuous response variable using lme4 package in R? Factorial or Nested design?

Question

I am trying to find the effect of plant traits on water infiltration and did some analysis using lme4 with the help of 2 statisticians, both of them suggest different models to check it. I can't decide who I can believe. Also my statistical background is very poor especially with the R. Please let me know which one is correct, or if none of them correct, please nominate the correct one.

Here my data descriptions:

1. Design or nesting of the study
   • There are 3 Regions (North, Mid and South)
   • Within each region we selected 2 different plant communities, but the communities are consistent across 3 regions
   • For each community we got 3 different habitat quality like poor, mid and good
   • For each habitat quality we selected 2 replicate sites

So, 3 regions x 2 communities x 3 condition or quality x 2 replicate sites = Totally 36 sites.

2. Each site there are 4 different plant types like tree, shrub etc and we called it Microsites. We did 3 replicate measurements of infiltration for each microsite. So within a site 4 microsites x 3 replicated measurements = totally 12 measurements per site. The measurement is infiltration.

   • infiltration (continuous response variable)

3. we want to see the effect of following factors that we recorded

   • height (numerical)
   • canopy shape (categorical)
   • stem width (continuous)

The model suggested by Statistician 1: He says it is nested,

D1$SSI10rnd <-round(D1$SSI10, digits = 0)
mod4 <-glmer(SSI10rnd ~ Height + Shape + Community*CondClass*Microsite + 
(1|Region/Community/CondClass/CCRep/Microsite), data=D1, family=poisson)

The model suggested by Statistician 2: As she says our design is factorial, also she highlighted the response variable is continuous

mod_full=lmer(log(SSI10) ~ Region * Community * CondClass * Microsite + 
height + shape + width + (1|SiteNumber), data=D1)

*ps: CondClass referring the habitat condition levels

Do you think the site is only random effect for my design? Also, I am not sure how i can distinguish random and fixed effects.

Answer 1

As you describe your situation, the second model appears to match it best. If all combinations of Region, Community, CondClass, and Microsite are crossed factorially but each Site is specific to a particular Community, then that model captures the factorial part of the design while allowing Sites to be random effects with different intercepts, and includes your main effects of height, shape and width.

When I see a difference of opinion, though, I start to wonder about subtleties. For example, does a "poor" ConditionClass really mean the same thing for each combination of Region, Community, and Microsite? If not, then some additional nesting structure might be called for. Perhaps that is the type of issue that Statistician 1 considered while Statistician 2 didn't. Also it seems strange that a statistician would treat a truly continuous variable as Poisson. We don't see any of your data here, but might there be something in them that recommendeds a discrete Poisson handling of your infiltration values? It's also possible that your description of the design was understood differently by the two statisticians.

You might consider asking this question of each of the statisticians, asking for reasons why one model was chosen over the other. Their abilities to explain their rationales should help clarify who understands your problem best and may help you better understand the best way to model your design as you re-explain it to them.