Glmer result interpretation of mixed effects and intercept

I am having trouble interpreting my mixed-model results. I am a biologist and not really good at statistics yet. I have done a mixed-model using binomial family, as the dataset I am working on is proportional.

I want to know if the proportion of diseased larvae is affected by the element type (C, H, W), the distance (D1, D2, D4), and by the combined effect.

Looking at the result from the mixed model and comparing them with mean values for the groups, it does not make sense to me how element H:distanceD4 can have a significant effect, as the highest mean is for actually for elementW:distanceD4. The mean values for combined effects:

How can I interpret the results and is there a possibility for me to have values for element C D1, element C D2, and element C D4, as I understand they are under the intercept.

Would really like a simple explanation how to interpret mixed-model results.

 proov<-glmer(cbind (diseases.larvae, no_dis) ~ element+distance+element*distance + (1|LS),
+              family=binomial,
+              data=P15)
>
> summary(proov)
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: binomial  ( logit )
Formula: cbind(diseases.larvae, no_dis) ~ element + distance +
element * distance + (1 | LS)
Data: PB15_Fu

AIC      BIC   logLik deviance df.resid
206.3    230.6    -93.2    186.3       74

Scaled residuals:
Min      1Q  Median      3Q     Max
-3.0145 -0.5601  0.3253  0.5598  1.5617

Random effects:
Groups Name        Variance Std.Dev.
LS     (Intercept) 2.132    1.46
Number of obs: 84, groups:  LS, 18

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)                      1.3553     0.6709   2.020   0.0434 *
element H                       -1.4098     1.0178  -1.385   0.1660
element W                       -0.4458     1.1251  -0.396   0.6919
distanceD2                      -0.1957     0.3667  -0.534   0.5935
distanceD4                      -0.3088     0.4490  -0.688   0.4917
element H:distanceD2             0.6214     0.6906   0.900   0.3683
element W:distanceD2             1.2881     1.2617   1.021   0.3073
element H:distanceD4             1.9899     0.7930   2.510   0.0121 *
element W:distanceD4             1.9567     1.5574   1.256   0.2090
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


• It may be helpful to provide some exploratory plots like scatterplots or boxplots to show what you mean by the results not being sensible. Jan 3, 2023 at 14:06
• you get the individual contrasts (and also the logistic regression equivalent of estimated marginal means) by using the emmeans package: library(emmeans) and then em<-emmeans(proov, specs=pairwise ~ element:distance. Jan 3, 2023 at 16:18
• To add this is not so much a mixed model issue, but an interaction interpretation issue. Interpreting categorical interactions in a regression model is kind of complex. Here are some sources: stats.stackexchange.com/questions/536015/… , data.library.virginia.edu/understanding-2-way-interactions, and theanalysisfactor.com/… Jan 3, 2023 at 16:24
• thank you, I added a barplot. Just asking, if I am moving to the right direction, is that estimates show if it positive or negative effect, and if it has a strong or weak effect on intercept, in my case element C?
– Sisi
Jan 3, 2023 at 19:21
• differences between groups are relevant for the interpretation and mean values are just reflecting magnitude! Feb 24, 2023 at 0:54