MANOVA with $n$ variables, I would like to do pairwise comparisons between $k$ levels for one of the variables.
What is the suitable method to adopt for this while adjusting $\alpha$ for the $k(k-1)$ multiple comparisons?
Hotelling$T^2$ tests along with
Bonferronicorrection or FDR/pFDR appropriate? FDR/pFDR q values would be preferable as the $\beta$ value is important here.
Any suggestions for
Rpackages to do the same? (Particularly for MANOVA post-hoc multiple comparisons}
How to test the null hypothesis $H_0^j:|\mu_1^j-\mu_2^j|\ge\delta$ instead of $H_0^j:\mu_1^j=\mu_2^j$ as in an equivalence test for the multiple comparisons?
Based on the answer and further comment by rvl, I was able to explore and come up with the following.
library(lsmeans) # Use the `oranges` dataset in `lsmeans` package. # multivariate linear model oranges.mlm <- lm(cbind(sales1,sales2) ~ price1 + price2 + day + store, data = oranges) # Get the least square means oranges.Vlsm <- lsmeans(oranges.mlm, "store") # Multiple comparisons with fdr p value adjustment test(contrast(oranges.Vlsm, "pairwise"), side = "=", adjust = "fdr") # With threshold spcified test(contrast(oranges.Vlsm, "pairwise"), side = "=", adjust = "fdr", delta = 0.25)