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I have two factors that are fully crossed, the levels of the factor are each coded 0 and 1. I am running a regression testing for one main effect and one interaction. The following is my logistic regression formula:

m1=glmer(y~1+A+A:B+(1|Participants)+(1|Word),data=data, family = "binomial")

I am wondering if this is acceptable (only testing for one main effect and an interaction), and also why I am getting two interaction terms in my output:

Fixed effects:
        Estimate Std. Error z value Pr(>|z|)   
(Intercept) -0.18740    0.21600  -0.868  0.38561   
A1           0.74546    0.28399   2.625  0.00867 **
A0:B1        0.01537    0.28244   0.054  0.95662   
A1:B1        0.15884    0.28650   0.554  0.57929   
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  • 2
    $\begingroup$ Please migrate it to CV. $\endgroup$ – user227710 Jul 3 '15 at 0:17
  • $\begingroup$ Is there some reason why you are not including the main effect of B in your model? It's generally best to include main effects of variables for which you are examining interactions. $\endgroup$ – EdM Jul 3 '15 at 15:22
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There are 4 possible states for the interaction of A and B. That is

  1. A0:B0, and not shown as it is absorbed into the intercept term for the regression.
  2. A1 (implicitly A1:B0).
  3. A0:B1.
  4. A1:B1.

Each of these states affects the response in a different way.

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