I have a factor X with three levels and a continuous covariate Z.
To predict the continuous variable Y, I have the model
model<-lm(Y ~ X*poly(Z,2,raw=TRUE))
I know that the emmeans package in R has the function emtrends() to estimate the pairwise difference between factor level slopes and does a p-value adjustment.
emtrends(model, pairwise ~ X, var = "Z")
however this works when Z is a linear term. Here I have a quadratic term. I guess this means I have to look at pairwise differences at pre specified values of Z? and get something like the local "slope" trend?
Is this possible to do with emmeans? How would I need to do the p-adjustment, does it scale with the number of grid points? -so when the number of grid values where I do the comparison increases, bonferroni will become too conservative?
Also how would I do the pairwise comparison of the mean (prediction) at different grid values with emmeans (or is this the same regardless of using poly() as this relies only on model predicitons)?
thanks.