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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.

  1. 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)
  2. 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.

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    $\begingroup$ There's a lot of information within 'Design or nesting' that will need more explanation if you are to get useful feedback here. To put it another way: you are asking us to choose between the opinions of two statisticians while providing us (presumably) with much less information than they had while forming those opinions. $\endgroup$
    – mkt
    Jul 4 '16 at 11:40
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    $\begingroup$ This isn't really coding related; flagging to move to CV $\endgroup$
    – Alex W
    Jul 5 '16 at 20:33
  • $\begingroup$ The response is not Poisson so at least that part of model 1 is wrong and with so few levels of each nesting factor it may make sense to specify 5 levels of nesting. You need to provide much more information about the design of your study. $\endgroup$ Jul 6 '16 at 9:33
  • $\begingroup$ Please clarify the physical relations among the variables you list under "design or nesting." That's needed to determine the nesting vs factorial structure. For example, do different regions have different sites? Are individual microsites specific to particular sites? What exactly is meant by "communities" in your study? A diagram of some sort would be very helpful. $\endgroup$
    – EdM
    Jul 6 '16 at 11:16
  • $\begingroup$ Thank you all for the comments. I have just edited to clarify the design of my study. Hope everything you want to know is in here. Please have a look once. Thanks in advance. $\endgroup$
    – Vandka
    Jul 7 '16 at 3:02
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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.

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