Understanding and analysing split split design using lmer()

Dear Rabin,

The mail list has stripped your csv file. Send small files as txt. Or put
the data somewhere online and send the link.

You want to use a random intercept to model the effect of an experimental
unit which is not captured by your fixed effects. E.g. for each combination
of replicate, crop and tillage you have 3 types of cover. So you want a
"tillage" level random intercept to model this. You can do this by
assigning a unique id to each combination of replicate (4), crop (2) and
tillage (3) = 36 subplot. So number your subplots for 1 to 36. With such
unique ids you don't have to worry about (partially) nested or (partially)
crossed effects. See
https://www.muscardinus.be/2017/07/lme4-random-effects/

You can do the same thing at the crop level: unique combinations of
replicate (4) and crop (2) = 8 combinations. The problem is that for a
descend estimate of the random effect variance, you need a lot of levels (>
200) see https://www.muscardinus.be/2018/09/number-random-effect-levels/.
If you only want to use random intercept to correct for dependencies within
the data, then you can get a way with a smaller number (>10). In your case,
you have too few replicates to take the replicate and replicate/crop plot
effect into account. So I recommend that you only take the subplots
(replicate/crop/tillage) into account. Note that this effect will take up
any effect at a higher level (replicate/crop) when you don't model that
effect.

I'd go for lmer(biomass~crop*tillage*cover+ (1|subplot),data=data)

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx at inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be


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Op ma 9 sep. 2019 om 20:36 schreef Rabin KC <kc000001 at umn.edu>:

Hello R mixed models community,

I am trying to fit a model for a split- split-plot design using lmer. I
know how to do this with aov and ssp.plot function in agricolae, but I
need
to use lmer in this case.

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(sub plot), 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.

Data arranged in a csv file is attached in this email.

Now the analysis part:

I know how to do this using aov/ ssp.plot( agricolae). The code is as
follows:

model<-with(data,ssp.plot(rep,crop,tillage,cover,biomass)).
Same thing with aov:


model1<aov(cover_coverage~rep+crop*tillage*cover+Error(rep/crop/tillage),data=data)

For my  analysis using lmer, and lme,  I have the following code:

model2<-lmer(biomass~crop*tillage*cover+ (1|rep),data=data)

model3<-lme(fixed=biomass~crop*tillage*cover, data=data, random=~1|rep)

Now my confusion and questions are:
1. I have used crop, tillage, and cover as fixed effects. And only the rep
(block) as random. Is the random effect properly assigned for this design?

2. I have read a lot about crossed and nested design. Crawley and Oehlert
give particular examples about it, but I have trouble understanding if
this
design has nested factors or crossed factors.

I would be very relieved to receive feedback with the matter in hand.

Looking forward, and thank  you  a lot,

Sincerely,
Rabin