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lme4factorialmixed-modelsnlme
Heder Braun
Heder Braun

Reputation: 21

Linear mixed model and factorial design with 3 levels

Four common bean trials were established in fields, one trial per year. We combined density, bean genotype, and fungicide to manage white mold with a factorial scheme. The experimental design was a randomized complete block with four replicates. Each trial was analyzed by a three-way ANOVA. The fixed factors were density, genotype, fungicide, and interactions. The random factor was block.

My intent is to treat each trial as a form of replication, then I would like to combine all trials together in a more concise analysis. We don’t want to draw conclusions between trials. We want to make conclusions of in general about our treatments.

I have used the complex model with fixed and random effects like this:

y ~ DENS:GEN:FUNG + (1 | trials) + (1 | trials:block)

I would be very grateful if someone could tell me if the model is appropriate for my search.

Upvotes: 2

Views: 405

Answers (1)

Robert Long
Robert Long

Reputation: 6867

The model:

y ~ DENS:GEN:FUNG + (1 | trials) + (1 | trials:block)

has the following features:

  1. A fixed effect for the 3-way interaction DENS:GEN:FUNG,

  2. Random intercepts for block varying within levels of trials

It is very rarely a good idea to fit a 3-way interaction as a fixed effect without the 2-way interactions and the main effects. See these for further discussion:

https://stats.stackexchange.com/questions/236113/are-lower-order-interactions-a-prequisite-for-three-way-interactions-in-regressi

https://stats.stackexchange.com/questions/27724/do-all-interactions-terms-need-their-individual-terms-in-regression-model

As for the random structure, then yes, based on the description, this seems to be appropriate, although you don't state how many trials there are - if this is very few then it may be better to fit trials as a fixed effect.

Upvotes: 1

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