Ecological model

Dear Dr. Benjamin Bolker,
This is Mitra. I am following your wonderful GitHub page and your papers.
I attended and fully enjoyed your great presentation on the Ecological
Forecasting webinar series, on Nov 1st, 2021. Actually, I am the one who
asked tons of questions (my apologies for that).

To cut the story short, I am writing to request your direction for choosing
the correct model for my data set (I appreciate you have a busy schedule
and I apologize for adding extra work to it). I am working on soil biotic
abiotic data set, which all transformed. The data I am dealing with was
collected from hilly experimental farmland (ith strip-split plot layout).

I have considered slope position*Tillage*Rotation*Fertilizer levels as the
fixed factors while the random effects are replications and replication:
rotation  (1 | rep) + (1 | rep: rotation) (explanation for choosing the
fixed and random effects -> Slope position was considered as a fixed factor
since each transect was representative of different soils in our hilly
field. The amount of residue returned to each plot was dependent upon the
biomass that accrued from the previous cropping season, which could provoke
the inter-individual differences in our rotation subplots. Besides we were
interested in both between-group effects of rotation and pure rotation
impact).

I tested collinearity, homogeneity of residuals and etc everything looks
fine, then I have also tested various models with different nested random
factors to find the best fit for my data (AIC, effect size), (the linear
mixed effect models were fitted by RMEL)

Sorry for the long description I thought it's necessary to begin with an
introduction, *my question is which of these models, considering the AIC
and my explanation can be the adequate model for my data set?*

*I highly appreciate your answer and your time*
Best regards
Mitra

Models:



lmeModel1: pH ~ slope * Till * Rotation * Fert + (1 | rep) + (1 |
rep:Rotation)

lmeModel2: pH ~ slope * Till * Rotation * Fert + (1 | rep) + (1 |
rep:Rotation:Fertilizer)



lmeModel3: MW.N ~ slope * Till * Rotation * Fert + (1 | rep) + (1 |
rep:Till:Rotation:Fertilizer)

npar

AIC

BIC

logLik

deviance

Chisq

Df

Pr(>Chisq)



lmeModel1

27

272.4301

341.0991

-109.215

218.4301



lmeModel1

27

288.7502

357.4210

-117.383

234.7501

0

0





lmeModel3

27

290.3459

359.0148

-118.173

236.3459

0

0