Estimating Means and Confidence Intervals using lme4

Question

I am running a mixed model logistic regression in R using lme4::glmer(). It is a model with four categorical variables. Each variable is effects coded (-1, 1). There are random effects for both participant and stimulus (coded as "actor"). I have reproduced the output below.

Generalized linear mixed model fit by maximum likelihood 
(Laplace Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: correctDummy ~ raceEffect * infoEffect * objectEffect * groupEffect +  
    (object | participant) + (object | actor)
   Data: df
Control: glmerControl(optimizer = "bobyqa")

     AIC      BIC   logLik deviance df.resid 
 38532.9  38722.4 -19244.4  38488.9    40778 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-6.5155  0.2361  0.3815  0.5268  2.8158 

Random effects:
 Groups      Name        Variance Std.Dev. Corr 
 participant (Intercept) 0.3320   0.5762        
             objectnogun 0.3584   0.5986   -0.22
 actor       (Intercept) 0.2709   0.5204        
             objectnogun 0.4135   0.6430   -0.65
Number of obs: 40800, groups:  participant, 153; actor, 40

Fixed effects:
                                                 Estimate Std. Error z value Pr(>|z|)    
(Intercept)                                     1.5311984  0.0829808  18.452  < 2e-16 ***
raceEffect                                     -0.0225314  0.0655927  -0.344 0.731218    
infoEffect                                      0.0005097  0.0188336   0.027 0.978410    
objectEffect                                   -0.0497586  0.0604082  -0.824 0.410107    
groupEffect                                     0.2048575  0.0540882   3.787 0.000152 ***
raceEffect:infoEffect                           0.0004164  0.0188259   0.022 0.982353    
raceEffect:objectEffect                         0.0218374  0.0542910   0.402 0.687515    
infoEffect:objectEffect                         0.1939512  0.0188332  10.298  < 2e-16 ***
raceEffect:groupEffect                         -0.0022580  0.0187905  -0.120 0.904351    
infoEffect:groupEffect                         -0.0135822  0.0188172  -0.722 0.470418    
objectEffect:groupEffect                        0.0141459  0.0322551   0.439 0.660978    
raceEffect:infoEffect:objectEffect             -0.0192888  0.0188261  -1.025 0.305562    
raceEffect:infoEffect:groupEffect              -0.0157074  0.0188125  -0.835 0.403748    
raceEffect:objectEffect:groupEffect             0.0150685  0.0187907   0.802 0.422605    
infoEffect:objectEffect:groupEffect            -0.0253699  0.0188176  -1.348 0.177593    
raceEffect:infoEffect:objectEffect:groupEffect -0.0113857  0.0188127  -0.605 0.545037    

I would like to know how to calculate the model predicted means and 95% CI for certain conditions. For example, I would like to calculate the predicted means and 95% CI for each of the two groups for the main effect of "groupEffect". I would also like to calculate the predicted means and 95% CI for each of the four groups involved in the "infoEffect:objectEffect" interaction.

To be clear, I am not looking to calculate 95% CI around the effects themselves (which I can calculate via bootstrapping with lme4::bootMer() or using lme4::confint()). I want to calculate the predicted means (i.e., the proportion of times the first group responds correctly; the proportion of times the second group responds correctly) and 95% CI.

I thought the lsmeans() package might be able to do what I am looking for but I have not had success with it. It seems like many of the packages out there that do something like this are geared towards models that work with continuous variables, not binary ones.