Hello Astere Bararyenya,

You can check this post:

http://www.science.smith.edu/~jcrouser/SDS293/labs/lab12-r.html

Hope it helps!

Dear Eliana,

Thank you so much for the post. Let me try, although adding other therms is confusing me. It is clear for the polynomial term.

I think the way you can do this is to use the contrast function in the emmeans package. Basically, you would formulate the mixed effects model using lme or lmer, and then set up the contrasts you want to test, and then call the contrast function.

There's not a perfectly representative example here: https://rcompanion.org/rcompanion/h_01.html ,with the caveat that I wrote it. Also, you can change the lsmeans package to emmeans, and the lsmeans function to emmeans. I haven't tested all this for polynomial contrasts, but I think it should all give you what you want.

A description of how to set up the contrasts can be found here: https://www.ndsu.edu/faculty/horsley/Polycnst.pdf

EDIT: Just to be clear, you formulate the model and conduct the anova, and then evaluate the polynomial contrasts almost as if it were a post-hoc test. The factor that goes in to the polynomial contrasts is a factor.

Thank so much Salvatore for the explanation and scripts. For understanding, I would like to fit a model to test the effect of genotype by harvest time^3 by location by season. Also include a random effect model replication within location and season. Factors become a bit more

Genotype is like a crop variety for those who are not in agriculture fields