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contrasts(data_all$condition_f) = contr.helmert(3)

model_vector <- glmer(cbind(normCor,normIncor) ~ condition_f*sorting_f*time_f + rescaled_VM + rescaled_L + (1+condition_f+time_f+sorting_f|id) + (1+time_f|word_id), data = data_all, family = binomial(link = 'logit'), glmerControl(optimizer="bobyqa", optCtrl=list(maxfun=2e5))) 
summary(model_vector)

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: cbind(normCor, normIncor) ~ condition_f * sorting_f * time_f +      rescaled_VM + rescaled_L + (1 + condition_f + time_f + sorting_f |      id) + (1 + time_f | word_id)
   Data: data_all
Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e+05))

     AIC      BIC   logLik deviance df.resid 
 35224.6  35450.3 -17580.3  35160.6     8509 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-13.5117  -1.1089  -0.1801   1.0330   8.2894 

Random effects:
 Groups  Name            Variance Std.Dev. Corr                   
 word_id (Intercept)     0.72186  0.8496                          
         time_fretention 0.22858  0.4781   -0.75                  
 id      (Intercept)     1.68692  1.2988                          
         condition_f1    0.02358  0.1536   -0.11                  
         condition_f2    0.01460  0.1208    0.16  0.01            
         time_fretention 0.91416  0.9561   -0.68 -0.03  0.08      
         sorting_fsorted 0.83799  0.9154   -0.46  0.11 -0.37  0.13
Number of obs: 8541, groups:  word_id, 73; id, 59

Fixed effects:
                                              Estimate Std. Error z value Pr(>|z|)    
(Intercept)                                   0.206778   0.254561   0.812  0.41663    
condition_f1                                 -0.070279   0.127098  -0.553  0.58030    
condition_f2                                 -0.006019   0.075334  -0.080  0.93632    
sorting_fsorted                               0.448982   0.326037   1.377  0.16848    
time_fretention                              -1.174478   0.183483  -6.401 1.54e-10 ***
rescaled_VM                                  -0.008824   0.131198  -0.067  0.94637    
rescaled_L                                    0.255718   0.142523   1.794  0.07278 .  
condition_f1:sorting_fsorted                  0.168045   0.053817   3.123  0.00179 ** 
condition_f2:sorting_fsorted                  0.099171   0.038233   2.594  0.00949 ** 
condition_f1:time_fretention                  0.146651   0.077239   1.899  0.05761 .  
condition_f2:time_fretention                 -0.035498   0.045058  -0.788  0.43080    
sorting_fsorted:time_fretention              -0.066772   0.253215  -0.264  0.79201    
condition_f1:sorting_fsorted:time_fretention -0.110543   0.050520  -2.188  0.02866 *  
condition_f2:sorting_fsorted:time_fretention -0.082406   0.030258  -2.723  0.00646 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Anova(model_vector, test = "Chi")

helmert.emmc <- function(levs, ...) {
    M <- as.data.frame(contr.helmert(levs))
    names(M) <- paste(levs[-1],"vs earlier")
    attr(M, "desc") <- "Helmert contrasts"
    M
}
model_vector_emmeans <- emmeans(model_vector, ~condition_f|sorting_f)
contrast(model_vector_emmeans, "helmert")

sorting_f = shuffled:
 contrast                    estimate    SE  df z.ratio p.value
 Somewhat similar vs earlier   0.0743 0.213 Inf   0.350  0.7267
 Dissimilar vs earlier         0.0621 0.366 Inf   0.170  0.8651

sorting_f = sorted:
 contrast                    estimate    SE  df z.ratio p.value
 Somewhat similar vs earlier   0.0132 0.214 Inf   0.061  0.9510
 Dissimilar vs earlier        -0.4501 0.368 Inf  -1.224  0.2210

model_vector_emmeans <- emmeans(model_vector, ~condition_f*sorting_f)
contrast(model_vector_emmeans, "helmert")

contrast                             estimate    SE  df z.ratio p.value
 Somewhat similar shuffled vs earlier   0.0743 0.213 Inf   0.350  0.7267
 Dissimilar shuffled vs earlier         0.0621 0.366 Inf   0.170  0.8651
 Very similar sorted vs earlier         1.4521 0.863 Inf   1.682  0.0925
 Somewhat similar sorted vs earlier     1.5047 0.968 Inf   1.554  0.1201
 Dissimilar sorted vs earlier           0.3466 1.089 Inf   0.318  0.7502

Hence, my question is: how can I calculate accurate significance values for Helmert contrasts using the R glmer function, using Anova, emmeans or some other means? Thanks a lot in advance!

contrasts(data_all$condition_f) = contr.helmert(3)

model_vector <- glmer(cbind(normCor, normIncor) ~ 
    condition_f*sorting_f*time_f + rescaled_VM + rescaled_L + 
    (1+condition_f + time_f + sorting_f|id) + (1+time_f|word_id), 
    data = data_all, family = binomial(link = 'logit'), 
    glmerControl(optimizer="bobyqa", optCtrl=list(maxfun=2e5))) 
summary(model_vector)

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial  ( logit )
 Formula: cbind(normCor, normIncor) ~ condition_f * sorting_f * time_f   
  +      rescaled_VM + rescaled_L + (1 + condition_f + time_f + 
  sorting_f |      id) + (1 + time_f | word_id)
   Data: data_all
Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e+05))

     AIC      BIC   logLik deviance df.resid 
 35224.6  35450.3 -17580.3  35160.6     8509 

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-13.5117  -1.1089  -0.1801   1.0330   8.2894 

Random effects:
 Groups  Name            Variance Std.Dev. Corr                   
 word_id (Intercept)     0.72186  0.8496                          
         time_fretention 0.22858  0.4781   -0.75                  
 id      (Intercept)     1.68692  1.2988                          
         condition_f1    0.02358  0.1536   -0.11                  
         condition_f2    0.01460  0.1208    0.16  0.01            
         time_fretention 0.91416  0.9561   -0.68 -0.03  0.08      
         sorting_fsorted 0.83799  0.9154   -0.46  0.11 -0.37  0.13
Number of obs: 8541, groups:  word_id, 73; id, 59

Fixed effects:
                                              Estimate Std. Error z value Pr(>|z|)    
(Intercept)                                   0.206778   0.254561   0.812  0.41663    
condition_f1                                 -0.070279   0.127098  -0.553  0.58030    
condition_f2                                 -0.006019   0.075334  -0.080  0.93632    
sorting_fsorted                               0.448982   0.326037   1.377  0.16848    
time_fretention                              -1.174478   0.183483  -6.401 1.54e-10 ***
rescaled_VM                                  -0.008824   0.131198  -0.067  0.94637    
rescaled_L                                    0.255718   0.142523   1.794  0.07278 .  
condition_f1:sorting_fsorted                  0.168045   0.053817   3.123  0.00179 ** 
condition_f2:sorting_fsorted                  0.099171   0.038233   2.594  0.00949 ** 
condition_f1:time_fretention                  0.146651   0.077239   1.899  0.05761 .  
condition_f2:time_fretention                 -0.035498   0.045058  -0.788  0.43080    
sorting_fsorted:time_fretention              -0.066772   0.253215  -0.264  0.79201    
condition_f1:sorting_fsorted:time_fretention -0.110543   0.050520  -2.188  0.02866 *  
condition_f2:sorting_fsorted:time_fretention -0.082406   0.030258  -2.723  0.00646 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Anova(model_vector, test = "Chi")

helmert.emmc <- function(levs, ...) {
    M <- as.data.frame(contr.helmert(levs))
    names(M) <- paste(levs[-1],"vs earlier")
    attr(M, "desc") <- "Helmert contrasts"
    M
}
model_vector_emmeans <- emmeans(model_vector, ~condition_f|sorting_f)
contrast(model_vector_emmeans, "helmert")

sorting_f = shuffled:
 contrast                    estimate    SE  df z.ratio p.value
 Somewhat similar vs earlier   0.0743 0.213 Inf   0.350  0.7267
 Dissimilar vs earlier         0.0621 0.366 Inf   0.170  0.8651

sorting_f = sorted:
 contrast                    estimate    SE  df z.ratio p.value
 Somewhat similar vs earlier   0.0132 0.214 Inf   0.061  0.9510
 Dissimilar vs earlier        -0.4501 0.368 Inf  -1.224  0.2210

model_vector_emmeans <- emmeans(model_vector, ~condition_f*sorting_f)
contrast(model_vector_emmeans, "helmert")

contrast                             estimate    SE  df z.ratio p.value
 Somewhat similar shuffled vs earlier   0.0743 0.213 Inf   0.350  0.7267
 Dissimilar shuffled vs earlier         0.0621 0.366 Inf   0.170  0.8651
 Very similar sorted vs earlier         1.4521 0.863 Inf   1.682  0.0925
 Somewhat similar sorted vs earlier     1.5047 0.968 Inf   1.554  0.1201
 Dissimilar sorted vs earlier           0.3466 1.089 Inf   0.318  0.7502

Hence, my question is: how can I calculate accurate significance values for Helmert contrasts using the R glmer function, using Anova, emmeans or some other means?

model_vector_emmeans <- emmeans(model_vector_emmeans, ~condition_f*sorting_f)
contrast(model_vector_emmeans, "helmert")

model_vector_emmeans <- emmeans(model_vector, ~condition_f*sorting_f)
contrast(model_vector_emmeans, "helmert")

contrast(model_vector_emmeans, "helmert")

Gives me five levels, of which I am not sure where they come from, I think from creating the interaction (2 * 3 levels) and doing Helmert, also not what I intended to do:

model_vector_emmeans <- emmeans(model_vector_emmeans, ~condition_f*sorting_f)
contrast(model_vector_emmeans, "helmert")

Gives me five levels, of which I am not sure where they come from, I think from creating the interaction (2 * 3 levels) then applying the contrast (resulting in n-1 = 5 levels), also not what I intended to do: