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I am trying to perform post-hoc tests on a linear mixed-effect model with a significant three-way interaction, whereby two of the two-way interactions are significant. There are two 2-level factors and one continious variable in the three way interaction, plus two covariates and a random intercept. The first factor is time, with two timepoints. The model looks like this:

lmer(DV ~ Fact1_Time * Fact2_Condition * Cont1 + Age + Sex + (1|ID), data) 

I have attempted to run post-hoc tests using the emmeans function, but the results seem wrong. How would I perform post hoc tests on significant two way interactions between Fact1_Time * Fact2_Condition and Fact2_Condition * Cont1? Any help would be appreciated.

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    $\begingroup$ Your question doesn't indicate what "seemed wrong" about what you attempted, or indeed about what you tried to do. I'd suggest looking at vignette("interactions") which gives several examples. Typically, with interactions of factors you may want to use 'by' variables or perhaps compute interaction contrasts. With a factor and a covariate, the 'emtrends` function may be used to estimate slopes,then you can use pairs() to compare them. $\endgroup$ – Russ Lenth Aug 8 '20 at 18:57
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Regression analyses do not require post-hoc tests per se. This is mostly an ANOVA thing where you start with the model F-test and then follow up with post-hoc tests for effects of specific factors. In regression, you still have a model F-test, and then you interpret your Beta coefficients. All beta coefficients alone should be sufficient to understand interactions in regression. Though, three way interactions can be a lot to get ones head around. Often the suggested approach for interpreting/reporting interactions in regression is to show them visually, and the Beta coefficients are sufficient information to show all the potential differences.

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