Let's say we have a situation like this - we are predicting y with one continuous (cont) and 2 categorical predictors (A and B). A and B have only two levels - 1 and 0, and reference is 0

$y\sim cont+A+B$

$y=b_0+b_{A1}+b_{B1} + b_{A1:B1} + (b_{cont} + b_{cont:A1} + b_{cont:B1} + b_{cont:A1:B1})*cont $

and the results are following:enter image description here

If we calulate the results for each slope, we get
slope (A0, B0) = -.61
slope (A1, B0) = -.23 = cont + cont:A1
slope (A0, B1) = -.24 = cont + cont:B1
slope (A1, B1) = -.23 = cont + cont:A1 + cont:B1 + cont:A1:B1

Now, the problem is that I don't know how to interpret the 3-way interaction due to the non-significant cont:A1:B1 coefficient.

Do I interpret slope(A1, B1) just by setting cont:A1:B1 to zero?
So slope(A1,B1) = cont + cont:A1 + cont:B1 = .10

Or does that mean that slope(A1,B1) = slope(A1,B0) =-.23

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    $\begingroup$ Please consider completely getting rid of the 3-way interaction. $\endgroup$ – David Jun 3 '19 at 8:09

The significance of the effect doesn't change how you interpret the model. If you leave in the three way interaction, then you have to include it in any calculations of slope. If you take it out, then you have to run a new model and it will have different coefficients. But you can't set it to 0 in this model.

  • $\begingroup$ How come that it doesn not? For example, if the 3-way interaction in this example is significant then I would interpret that the regression line of y being regressed on cont has a slope of -.23 in case A =1, and B=1. If the interaction is not significant, then I the cont:A1:B1 would statistically not be different from 0, and the slope would then be .10, which in my case would make a big difference. Or am I missing something here? $\endgroup$ – User33268 Aug 28 '17 at 10:42
  • $\begingroup$ P.S. I never thought about excluding the interaction term, but if it is statistically not different from 0, than we take it to be 0 $\endgroup$ – User33268 Aug 28 '17 at 10:44
  • $\begingroup$ No, that's just not right. You have to either include it or exclude it. If you include it, you can't set it to 0. The other parameters are estimated including the interaction; they will change if you delete it. Statistical significance doesn't matter here. $\endgroup$ – Peter Flom - Reinstate Monica Aug 28 '17 at 10:54
  • $\begingroup$ Ok, then I misunderstood it. But can you explain me when the significance does matter? $\endgroup$ – User33268 Aug 28 '17 at 11:02
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    $\begingroup$ It matters when you are doing a hypothesis test. $\endgroup$ – Peter Flom - Reinstate Monica Aug 28 '17 at 11:03

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