# Interpretation of binomial GLMM with interaction fitted with glmer

I have a glmer model from the R package lme4 with a binomial distribution and I was wondering whether I am interpreting the model output correctly. In my model I have a response variable correctness (incorrect, correct) -> so (0, 1). Predictors are: condition (0, 1) and treatment (0, 1).

My model looks like this:  model<- glmer(correct~ treatment + condition + treatment :condition + (1|id) + (1|item), family= binomial)

My model output:

 summary(model)

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept)             2.94373    0.23510  12.521  < 2e-16 ***
treatment1              0.09146    0.31465   0.291    0.771
cond1                  -0.95974    0.23691  -4.051  5.1e-05 ***
cond1:treatment1       -0.13183    0.32034  -0.412    0.681


My interpretation is:

• cond1 : The chance of answering correctly decreases significantly by -0.95974 when comparing condition 0 to condition 1 (p < .001).

• cond1:treatment1: When comparing condition 0 to condition 1 the decrease of chance by -0.13183 of answering correctly decreases not signficantly more for the treatment group as for the non treatment group (p = .681).

Is my interpretation correct? Also, would you report more than p values and estimates?

The chance of answering correctly decreases significantly by -0.95974 when comparing condition 0 to condition 1 (p < .001)

It's Logit(p) rather than p, that decreases significantly by -0.95974 when comparing condition 0 to condition 1, with p being the chance of answering correctly, and:

$$Logit(p) = ln(p/(1-p))$$

cond1:treatment1: When comparing condition 0 to condition 1 the decrease of chance by -0.13183 of answering correctly decreases not signficantly more for the treatment group as for the non treatment group (p = .681).

I would say that logit(p) when condition 1 is associated with treatment 1 is not significantly different than when condition 1 is associated with treatment 0.

Also you should consider fitting the model without the interaction then without the treatment variable according to these p-values.

• Thanks for your answer. Logit(p) is exp(coef...) in R, right? Jun 17, 2020 at 12:54
• What I meant is that with a binomial regression, your model is actually logit(p) ~ aX + b (with X a explanatory variable, a and b coefficients). So p ~ exp(aX + b) / (1 + exp(aX + b)) Jun 17, 2020 at 13:10