# Understanding the connection between binomial (logit link) and emmeans output

I ran a binomial model with a logit link in R. I am trying to understand the coefficient relation to the logit scale output provided by the emmeans package in R. Idled is the reference level for "manip" and included in the intercept. Slcarea, mean_vd.x, and mean_mfvd.x are continuous and numerical.

Call:  glm(formula = KILL ~ manip + slcarea + mean_vd.x + mean_mfvd.x,
family = binomial(link = logit), data = sbm)

Coefficients:
(Intercept)  manipburnplus      manipdisk   manipharvest       manipmow        slcarea      mean_vd.x    mean_mfvd.x
0.226982       1.593982       0.415085       1.356314       0.036138       0.682750      -0.015690      -0.007954


Here is the emmeans output on the logit scale:

> confint(emmeans(fm_sbm_KILL_veg,"manip"),level = .85)
manip    emmean    SE  df asymp.LCL asymp.UCL
idle     -0.836 0.296 Inf   -1.2624   -0.4105
burnplus  0.758 0.469 Inf    0.0828    1.4323
disk     -0.421 0.244 Inf   -0.7729   -0.0698
harvest   0.520 0.707 Inf   -0.4985    1.5383
mow      -0.800 0.753 Inf   -1.8847    0.2841

Results are given on the logit (not the response) scale.
Confidence level used: 0.85


and emmeans on the response level (probability):

> confint(emmeans(fm_sbm_KILL_veg,"manip"),level = .85,type="response")
manip     prob     SE  df asymp.LCL asymp.UCL
idle     0.302 0.0624 Inf     0.221     0.399
burnplus 0.681 0.1019 Inf     0.521     0.807
disk     0.396 0.0584 Inf     0.316     0.483
harvest  0.627 0.1654 Inf     0.378     0.823
mow      0.310 0.1611 Inf     0.132     0.571

Confidence level used: 0.85
Intervals are back-transformed from the logit scale


I understand the emmeans logit to emmeans response relationship (inverse logit) but not the coefficient to logit scale output. Can someone help me understand this connection? More specifically, how would I calculate the idle level (-0.836) from the intercept coefficient (0.226982)?

As Russ suggested.

> emmeans(fm_sbm_KILL_veg,"manip",level=.85)@linfct
(Intercept) manipburnplus manipdisk manipharvest manipmow       slcarea mean_vd.x mean_mfvd.x
[1,]           1             0         0            0        0 -1.266326e-17  51.33096    32.43631
[2,]           1             1         0            0        0 -1.266326e-17  51.33096    32.43631
[3,]           1             0         1            0        0 -1.266326e-17  51.33096    32.43631
[4,]           1             0         0            1        0 -1.266326e-17  51.33096    32.43631
[5,]           1             0         0            0        1 -1.266326e-17  51.33096    32.43631


EMM = emmeans(...)