# Interpreting random effect variance in glmer

I’m revising a paper on pollination, where the data are binomially distributed (fruit matures or does not). So I used glmer with one random effect (individual plant) and one fixed effect (treatment). A reviewer wants to know whether plant had an effect on fruit set — but I’m having trouble interpreting the glmer results.

I’ve read around the web and it seems there can be issues with directly comparing glm and glmer models, so I’m not doing that. I figured the most straightforward way to answer the question would be to compare the random effect variance (1.449, below) to the total variance, or the variance explained by treatment. But how do I calculate these other variances? They don’t seem to be included in the output below. I read something about residual variances not being included for binomial glmer — how do I interpret the relative importance of the random effect?

> summary(exclusionM_stem)
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: binomial  ( logit )
Formula: cbind(Fruit_1, Fruit_0) ~ Treatment + (1 | PlantID)

AIC      BIC   logLik deviance df.resid
125.9    131.5    -59.0    117.9       26

Scaled residuals:
Min      1Q  Median      3Q     Max
-2.0793 -0.8021 -0.0603  0.6544  1.9216

Random effects:
Groups  Name        Variance Std.Dev.
PlantID (Intercept) 1.449    1.204
Number of obs: 30, groups:  PlantID, 10

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)  -0.5480     0.4623  -1.185   0.2359
TreatmentD   -1.1838     0.3811  -3.106   0.0019 **
TreatmentN   -0.3555     0.3313  -1.073   0.2832
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
(Intr) TrtmnD
TreatmentD -0.338
TreatmentN -0.399  0.509


However, if your reviewer isn’t hung up on statistical details and would be satisfied with a more heuristic explanation of “importance”, you could point out that the estimated among-plant standard deviation is 1.20, very close to the magnitude of the largest treatment effect (-1.18); this means that the plants vary quite a bit, relative to the magnitude of the treatment effects (e.g., the 95% range of the plant effects is approximately $4\sigma$, from $-1.96 \sigma$ to $+1.96\sigma$).