How to Compare Different Treatment Levels to Control in Linear Mixed-Effects Model? I've run a human subjects study where participants answer a series of questions with a decision aid. In addition to the decision aid I have different "improvements" to the decision aid that further aim to improve performance. I want to see if using the "improvements" improve performance. To analyze the results I created the following linear mixed-effects model in R (lme4):
correct ~ round + baseaid + imp1:imp2 + (1 | participant)
both imp1 and imp2 are types of a treatment and have two levels, and overlap completely with baseaid.
I want to check if any of imp1 or imp2 are better than just baseaid.
The most straightforward way to do this is to do a treatment vs. control emmeans(). BUT since this compares the treatments to each other and adjusts the p-values, none of the effects are significant. Instead, I can just compare the "maximum" treatment of baseaid == 1 && imp1 == 1 && imp2 == 1 to baseaid == 1 && imp1 == 0 && imp2 == 0 which is significant.
Instead, is there a way to combine imp1 and imp2 together and compare them to the baseline instead of comparing the maximal treatment to the baseline?
 A: The technical answer
What needs to be done is first to list the EMMs:
EMM = emmeans(model, ~ baseaid*imp1*imp2)
EMM

Then determine which two you want to compare. Then construct a contrast that compares those two means. I think it is
contrast(EMM, list(mycon = c(0, -1, 0, 0, 0, 0, 0, 1)))

The above is based on my speculation that each factor has levels (0,1) in that order, in which case the order of the EMMS will be (0,0,0), (1,0,0), (0,1,0), (1,1,0), (0,0,1), (1,0,1), (0,1,1), (1,1,1); so from the question, we want to compare (1,1,1) with (1,0,0), i.e. the 8th and 2nd ones.
It is also easily possible to compare each treatment with control. I gather that the control is the factor combination (1,0,0). So to compare each other combination with the second one, do
contrast(EMM, "trt.vs.ctrl", ref = 2, adjust = "mvt")

It seems like perhaps combination (0,0,0) is meaningless, in which case use
contrast(EMM, "trt.vs.ctrl", ref = 2, exclude = 1, adjust = "mvt")

The "mvt" adjustment that I suggest is the Studentized maximum modulus, which is essentially the same as the Dunnett adjustment when it is a family of treatment-vs.-control comparisons with balanced data.
The honest statistical answer
The wording of the question suggests that the desired contrast was chosen by identifying the smallest P value from among the 28 pairwise comparisons originally obtained. Accordingly, all 28 tests have already been performed, and the adjusted P value obtained originally for that particular comparison is the correct P value to be used in reporting. Pretending not to have looked at all those results is dishonest.
If you really are concerned only with the comparisons with control, then I think it is OK to use one of the trt.vs.ctrl methods above, with the "mvt" adjustment. That is exactly the correct adjustment (if the model assumptions hold) for the maximum comparison with control.
