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

[Rabin KC]

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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