[R-sig-ME] Can we analyse combined split plot experiment using lmer()?

[Peter Claussen]

Rabin,

Was each combination of year and location and independent experiment? That is, were the main crops seeded independently, for each year and location, or were plantings on exactly the same day, with the same equipment, and using the same varieities?  Was the timing of in-season tillage the same for all locations or years? Were cover crops seeded at exactly the same stages, with the same seed sources and equipment?

Those are things that contribute to experimental error in the split-plot blocking structure. So, for a first pass, I would pool location and year as environment, and compare
lmer (biomass ~ environment*crop*tillage*cover+(1 | rep/crop/tillage), data=data)
lmer (biomass ~ environment*crop*tillage*cover+(environment | rep/crop/tillage), data=data)

The first model assumes homogeneity of experimental error across experiments, the second allows for independent errors, I think. 

If there are interactions between environments and treatments, then you may need to decompose the environments into years and location, and we can in theory assume some correlation among years and among locations, but you don’t really have enough samples to explore that in detail

Cheers,

> On Sep 12, 2019, at 10:48 PM, Rabin KC <kc000001 using umn.edu> wrote:
> 
> Hello community,
> 
> A few days ago, I posted about using lmer() to analyze a split split-plot
> design.
> The research design is as such:
> 
> I am interested in the response variable biomass of cover crops. I have the
> main plots as crops (corn and soybean). The subplot is tillage, which is
> randomized within the crops and has 3 levels (conventional-till, no-till,
> and strip-till). Within tillage(subplot), 3 cover crop strategies are
> randomly assigned (AR, ARCC, ARCCFR). Therefore 1 rep (block) has 18
> treatments. The whole experiment is replicated 4 times, therefore, total
> experimental units equal to 72 units.
> 
> The experiment is conducted in 2 locations for 2 years, therefore total
> units equal to 288.
> 
> Now the model (as suggested by Peter Claussen in our community) for the
> experiment conducted each year and location is :
> 
> model <- lmer (biomass ~ crop*tillage*cover+(1|rep/crop/tillage),
> data=data)
> 
> The random-effects seem to be the split-plot error terms in the above model.
> 
> My question now is:
> 
> Now when I combine each year and location, how should I model this
> experiment. I am thinking about the following model:
> 
> model.all <- lmer (biomass ~location*
> crop*tillage*cover+(1|year/rep/crop/tillage), data=data)
> 
> Where location is a fixed effect and year is a random effect.
> 
> Does this above model actually work? Or should it be like follows:
> 
> model.all.1<- lmer (biomass ~ crop*tillage*cover+(1|year)+
> (1|rep/crop/tillage), data=data)
> 
> Also, I would be very grateful if someone would advise me if the
> assumptions of normality and constant variances apply for these lmer models?
> 
> Thank you,
> Rabin
> 
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