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I'm trying to interpret a significant three-way interaction. Basically, I've used hierarchical regression to analyse my data, and I have come up with a significant three-way interaction.

My DV is continuous. My 3 IVs are continuous, categorical (2 levels), and another categorical (3 levels). My sample size is 194.

I know that I can do up graphs to eyeball the interactions, but I need a statistical method in order to figure out whether or not a slope is significant. I'm aware of Jeremy Dawson's template to figure out significant slope differences, but they only work for 3 continuous variables. Is there a method I can use to do this?

I've also had a read through the UCLA's SPSS guide to interpreting three-way interactions. Would this be the way to go?

Thanks in advance for any help you can provide.

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I am a little confused by your question, since you say that you have already found a significant 3 way interaction and then say you want to find whether slope differences are significant, but I think you want to see which of the levels are different in terms of their slopes, is that right?

I don't know SPSS, but in SAS you can request particular tests of different hypotheses. In SAS you can do this with EFFECT statements. You can also do this inside a LSMEANS statement.

But I would shy away from these statements; first, they usually have low power (unless all your variables are perfectly measured and perfectly reliable). Second, significance just isn't that significant. Effect size is more important. Third, the graphs say more (especially in interaction interpretation) than any p-value could.

To quote my favorite professor in grad school "When an article is full of significance tests, the authors are p-ing all over the research".

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  • $\begingroup$ I think you want to see which of the levels are different in terms of their slopes, is that right? Yep, that was what I mean. I have actually never used SAS before. But I'll see if I can find the SPSS equivalent for those functions you mentioned. $\endgroup$ – soupy Jun 20 '11 at 14:51
  • $\begingroup$ LSMEANS is SAS lingo for marginal means. onbiostatistics.blogspot.com/2009/04/… $\endgroup$ – Thomas Levine Jun 21 '11 at 0:57
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my first answer :-)

Short answer: You should look at Kristopher Preacher's website. He has set up an Rweb-Server for computing "Simple intercepts, simple slopes, and regions of significance in MLR 3-way interactions", which not only gives you the results you need, but also generates R code that you can toy with.

Additional comment: Psychologists generally love this stuff. It gives you "The Region of Significance", that is "the specific values of w and z at which the regression of y on x moves from non-significance to significance." (quoting Preacher) for continuous and/or dichotomous predictors. Look at his online material for more explanation.

With regard to categorical vs. continuous predictors: On the websites mentioned you generally test whether the association of predictor1 with dependendent is different at different levels of predictor2. In the 3-way case, you test whether this 2-way interaction is different at different levels of predictor3. With continuous predictors, [Aiken & West][1] suggest a "simple slopes test" by comparing the slope of predictor1 at 1SD above mean with 1SD below mean of predictor2. For your three-category predictor, just use two dummy variables.

[1] Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Newbury Park, London, Sage.

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  • $\begingroup$ Thanks Wolf, that link really helps. I'll take some time to slowly read and digest that. :) $\endgroup$ – soupy Jun 22 '11 at 11:32
  • $\begingroup$ That applet was promising until I realised that the conditional values for the moderators are only limited to two levels... Thanks anyway, at least it's a start! $\endgroup$ – soupy Jun 22 '11 at 12:47

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