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I want to see whether there is an interaction effect between "session" and "structure" on participants’ accuracy.

For this I run a glmer model:

model <- glmer(Accuracy ~ session * structure + (1|subj)+(1|item), 
               dataframe, family = 'binomial')

With these factors: (1) session={session1, sesison2, session3}; structure={native, non-native}

I got this as an output:

Fixed effects:
                                Estimate Std. Error z value Pr(>|z|)  

(Intercept)                     -0.08201    0.12683  -0.647  0.51789   
session2                         0.06282    0.11419   0.550  0.58222   
session3                         0.14083    0.11313   1.245  0.21320   
session4                         0.35178    0.11369   3.094  0.00197 **

structurenon_native              0.08284    0.17685   0.468  0.63949  

session2:structurenon_native     0.07159    0.16015   0.447  0.65486   
session3:structurenon_native    -0.01698    0.15869  -0.107  0.91480   

From this output, I understand how to interpret the results for one factor only. For example, it is clear to me that session 2 is compared to session 1, just as session 3 is compared to session 1. And non-native structure is compared to a native structure.

However, I am absolutely confused what interaction effects are compared to? For example, is an interaction of “session2:structurenon_native” compared to “session1:structurenon_native” or “session1:structurenative”. Actually, I tried to interpret it both ways, but my interpretations do not make sense.

Could anybody please help me how to understand what the reference level is for interactions in glmer?

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  • $\begingroup$ Just a request to leave this open as it applies to much more than GLMER. $\endgroup$
    – Peter Flom
    Aug 30, 2018 at 11:31

1 Answer 1

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The "compared to" analogy breaks down a bit with interactions. If you only had main effects, your first interpretation of those main effects would be correct. But once you add an interaction, it gets more complex.

The main effects apply when the other variables in the interaction are 0.

So, e.g the session 2 main effect:

session2 0.06282 0.11419 0.550 0.58222

Compares session 2 to session 1 when structure is native. To compare session 2 to session 1 when structure is nonnative, you have to add the interaction to the session 2 main effect.

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    $\begingroup$ Peter Flom, thank you! I discovered there were several posts related to my question. That all makes sense now. $\endgroup$
    – Tasha
    Aug 30, 2018 at 19:54

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