I’m confused about how to correctly code comparisons between specific factor levels when interactions are involved.
There is a good description of how to run comparisons with the hypothesis
function here without interations, where you simply add the levels of interest to the intercept.
In this conversation, @paul.buerkner describes how to do this when an interaction is involved, by adding both the interactions and main effects to the intercept. But when I try and apply this to my example I get strange results. I must have interpreted Paul’s example incorrectly, and am not doing this correctly. Here is my example:
My model is a multilevel proportional binomial model of seedling survival, with a set of predictors that includes a couple of interactions. This is the model output:
Family: binomial
Links: mu = logit
Formula: seedling.count  trials(seedling.count.old) ~ Fertiliser + Shelter + Grass2 + mo(pasture.cover) + light.st + (1  Block) + Shelter:mo(pasture.cover) + Shelter:Grass2
Data: d2 (Number of observations: 281)
Samples: 4 chains, each with iter = 6000; warmup = 3000; thin = 1;
total postwarmup samples = 12000
GroupLevel Effects:
~Block (Number of levels: 20)
Estimate Est.Error l95% CI u95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 2.29 0.53 1.48 3.52 1.00 3033 5253
PopulationLevel Effects:
Estimate Est.Error l95% CI u95% CI Rhat Bulk_ESS Tail_ESS
Intercept 4.14 0.97 6.11 2.25 1.00 3111 5605
FertiliserF_2 0.25 0.15 0.55 0.04 1.00 17872 9622
ShelterS_2 1.76 0.72 0.38 3.18 1.00 4992 7110
Grass2G_1b 0.15 0.38 0.90 0.58 1.00 10311 9896
Grass2G_2a 0.08 0.59 1.27 1.06 1.00 9308 8573
Grass2G_2b 0.37 0.63 1.64 0.83 1.00 8163 8270
Grass2G_3a 0.26 0.61 0.97 1.45 1.00 9432 8791
Grass2G_3b 0.26 0.64 1.02 1.49 1.00 10170 8649
light.st 0.45 0.10 0.26 0.64 1.00 16633 9492
ShelterS_2:Grass2G_1b 0.77 0.55 0.32 1.86 1.00 8568 8489
ShelterS_2:Grass2G_2a 1.24 0.64 0.00 2.52 1.00 8634 8774
ShelterS_2:Grass2G_2b 0.67 0.65 0.60 1.96 1.00 7991 8489
ShelterS_2:Grass2G_3a 1.46 0.65 0.20 2.73 1.00 8973 9042
ShelterS_2:Grass2G_3b 0.65 0.68 0.67 1.99 1.00 9366 9585
mopasture.cover 0.11 0.14 0.17 0.38 1.00 4939 7238
mopasture.cover:ShelterS_2 0.44 0.13 0.70 0.18 1.00 4893 6971
Simplex Parameters:
Estimate Est.Error l95% CI u95% CI Rhat Bulk_ESS Tail_ESS
mopasture.cover1[1] 0.22 0.17 0.01 0.60 1.00 9145 6511
mopasture.cover1[2] 0.16 0.14 0.00 0.51 1.00 13373 6151
mopasture.cover1[3] 0.15 0.13 0.00 0.47 1.00 13097 6842
mopasture.cover1[4] 0.17 0.14 0.01 0.51 1.00 13337 6790
mopasture.cover1[5] 0.16 0.14 0.00 0.51 1.00 13833 7836
mopasture.cover1[6] 0.15 0.13 0.00 0.48 1.00 12070 8217
mopasture.cover:ShelterS_21[1] 0.06 0.06 0.00 0.21 1.00 12720 6682
mopasture.cover:ShelterS_21[2] 0.09 0.07 0.00 0.27 1.00 11174 5866
mopasture.cover:ShelterS_21[3] 0.17 0.10 0.01 0.39 1.00 8816 5009
mopasture.cover:ShelterS_21[4] 0.17 0.11 0.01 0.43 1.00 10516 5837
mopasture.cover:ShelterS_21[5] 0.29 0.16 0.02 0.61 1.00 8361 6314
mopasture.cover:ShelterS_21[6] 0.23 0.11 0.03 0.47 1.00 12202 6691
Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
In interested in examining various contrasts of the Shelter:Grass2 interaction.
 Shelter has two levels: S_1 (reference), S_2
 Grass2 has 6 levels: G_1a (reference), G_1b, G_2a, G_2b, G_3a, G_3b
Here is the conditional_effects
plot for the Shelter:Grass2 interaction:
For the purposes of this example, these are the comparisons I want to make:

 Compare G_3a and G_3b (pink and dark blue) within Shelter treatment S_2

 Compare S_1 and S_2 within Grass2 treatment G_3b (pink)
Here is the code I’ve used for Comparison 1 and the output. The estimate is negative, which indicates that the G_3b treatment has lower seedling survival than the G_3a treatment (and this matches what is seen in the conditional effects plot) :
hypothesis(seedling2_R5_a, "Intercept + ShelterS_2:Grass2G_3b + ShelterS_2 + Grass2G_3b = Intercept + ShelterS_2:Grass2G_3a + ShelterS_2 + Grass2G_3a")
Hypothesis Tests for class b:
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
1 (Intercept+Shelte... = 0 0.81 0.61 2.04 0.32 NA NA
Comparison 2, however, gives a positive estimate, indicating that survival is higher for S_2 than S_1. But the conditional effects plot shows the opposite.
hypothesis(seedling2_R5_a, "Intercept + ShelterS_2:Grass2G_3b + ShelterS_2 + Grass2G_3b = Intercept + Grass2G_3b")
Hypothesis Tests for class b:
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
1 (Intercept+Shelte... = 0 2.41 0.78 0.94 4.02 NA NA *
Please could I have some help understanding what has gone wrong with my comparisons, and how I can code them correctly.
Thanks very much
 Operating System: Windows
 brms Version: 2.15.0