Interaction between two factors as Random effects in mixed model in R

Question

I would like to know how to write random effects of two interacting factors. For example, I have 6 species which were planted in 48 plots and replicated in two blocks. There are in total 48 combinations (all possible 1, 2, 3, 5, and 6 species combinations ) for the 6 species.

By design, combinations are actually nested within diversity: the combinations are the correct replicates for each diversity level; hence the effect of diversity should be tested against the (random) variation among combinations within diversity levels.Since, diversity or species richness is a continuous variable I can't consider combinations are nested within diversity.

I would like to make the interaction between block and combination as random effect. I am not sure how to write in properly in mixed models in R. Thanks

This may be a better question for Cross Validated: https://stats.stackexchange.com — jdobres, Mar 03 '22 at 16:57
yes. 48 plots in each block. there are two blocks. thanks for the answer. — Tanvir Shovon, Mar 03 '22 at 20:47
Possible cross-site duplicate: [Interactions between random effects](https://stats.stackexchange.com/questions/96600/interactions-between-random-effects). — Ian Campbell, Mar 04 '22 at 01:36
@jdobres Please consider having a look at this Meta Q&A: [Migrate or close low- or medium-quality questions?](https://meta.stackoverflow.com/questions/416232/migrate-or-close-low-or-medium-quality-questions) — Ian Campbell, Mar 04 '22 at 01:40

score 1 · Answer 1 · answered Mar 03 '22 at 19:58

In the standard R mixed model notation (going back to Doug Bates's nlme package), treating the interaction between block and combination as a random effect would be (1|block:combination), i.e. the baseline (intercept) value of your response variable varies according to a Gaussian distribution across {block × combination} values.

This should work for most mixed-model packages in R: nlme, lme4, brms, GLMMadaptive ...

Interaction between two factors as Random effects in mixed model in R

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