# Interpretation interaction term in glmer()

#### mmercker

##### Member
Hi,

I am using the glmer() function from the package lme4 for a mixed logistic regression model. Here, the formula is Y ~ X + Z + X:Z, where Y is the binomial outcome, X is a categorical predictor with 3 levels (X1, X2, X3, where X1 is the baseline), and Z is a continuous predictor.

In the summary plot, however, I find effect sizes, standard error and p-values for

intercept
X
Y
X1:Y
X2:Y
X3:Y

I am a little bit confused since the baseline-interaction term appears also in the summary?! In other functions from other packages this is not the case. So how can I interpret these interaction terms in glmer()?

Thanks!

#### hlsmith

##### Less is more. Stay pure. Stay poor.
So this is not a mixed model (multilevel)?

Not a regular R user, so I will provide general statements.

When you test an interaction you need to make sure the main effects for the terms in the interaction are still in the model. Though, some times it seems difficult to interpret the interaction term when you have a categorical variable with multiple groups. So I will look for the Type III effect, which some times provides a general estimate that I can examine for significance.

Another option is to create an estimate statement for each unique group, so you calculate the predicted probability for each combo, X1*Z, X2*Z, and X3*Z and slap confidence intervals on these. I will usually adjust the alpha in the confidence intervals to account for the number of groups (e.g., a Bonferroni approach so estimate +/- ((0.05*3) * SE)). You can contrast these terms using a test or also very beneficial - graph them to see probability changes based on the interaction.

Not sure if this gets at your question or not?

#### mmercker

##### Member
Hi,

actually you are right, the real model is more complicated and is indeed a multilevel model, especially a GLMM: Data are nested within individuals. However, if I use other (multilevel) packages in R but the similar model, I find only X2:Z and X3:Z in the summary, and in this case the interpretation is easy: E.g. nonzero interaction X2:Z means that the slope of Y depending on Z differs between X1 (the baseline) and X2. However, I do still not grasp why X1:Z appears in the glmer summary. What does this term measure/represent? And how can I interpret the other two interaction terms?

Thanks

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Can you post the output to help us see what you are referencing?

#### mmercker

##### Member
Thank you hlsmith, by looking over my code I found the mistake. Your first suggestion/feeling was right: The main effect for the terms in the interaction was not in the model, that was the reason for the odd outcome. Thanks for the helpful discussion.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Great. Good luck now explaining cross-level interactions. The idea makes sense, but it seems complexing as well. What, spellcheck says "complexing" isn't a word. Hmm.