# interpret interaction effect in linear mixed model with dummy-coded categorical predictors with lmer

I've looked through quite a few websites and threads here, but I find the interpretation of interaction effects in linear mixed models with categorical factors quite tricky and would be glad if someone who is more experienced than me can assure me that I am on the right track. Specifically, I would like to make sure whether I can draw conclusions straight from the beta values or whether I need any post-hoc tests.

I conducted a linear mixed model using lmer in R which looks like this:

lmer(hitRate ~ intervallBetweenTests * group * condition + (1 | Name), data = df)


The factors intervallBetweenTests (short vs. long) and group (A vs. B) are dummy-coded and between-subject-factors, condition (1 vs. 2) is a within-subject-factor. Name refers to the individual subject-code.

I've got this result:

                                              Estimate                Pr(>|t|)
intercept                                    3.50449   <0.0000000000000002***
intervallBetweenTestsLong                   -2.56790           0.000000563***
groupB                                      -0.24303               0.24565
condition2                                  -0.26121               0.18678
intervallBetweenTestsLong:groupB             0.76563               0.03234*
intervallBetweenTestsLong:condition2         0.45790               0.04451*
groupB:condition2                            0.21247               0.13654
intervallBetweenTestsLong:groupB:condition2 -0.30631               0.14532


I would interpret it this way: hitRate decreases from short to long intervallBetweenTests by -2.5679 (main effect intervallBetweenTests). This decrease from short to long timeBetweenTesting is 0.76563 lower for groupB than groupA (intervallBetweenTests:group) and 0.45790 lower for condition 2 than condition 1 (intervallBetweenTests:condition). So, can I conclude from these results that group B shows a significantly lower decrease in hit rate from short to long intervall between tests than group A? Or are any post-hoc tests necessary for such a statement?

I would say that no post-hoc tests are needed since one advantage of regression models (compared to ANOVAs) is that the direction of (interaction-)effects is indicated by the sign of the (beta) estimate.

here you need to add "for group A and condition 1". The point here is that the (main) effect for variable that is interacted with another variable, is that it is conditional on the other variable being at zero (or it's reference level in the case of the categoical variable). The same logic applies to the estimate for group (conditional on intervallBetweenTests short and condition 1$$`$$.