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I've created a multiple regression predicting 1 DV from 4 IVs (all mean-centered) + 1 interaction term between two of the IVs. The interaction term is significant.

I'd like to get a nifty graph comparing the effect of one of the variables included in the interaction on the DV at particular values (say, $\pm1 SD$) of the other variable (i.e., the moderator).

I understand how to do this when I only have 3 IVs (predictor, moderator, and interaction), but how can I do this when I have 2 other IVs not involved in the interaction?

Let me know if additional info or exact numbers will help.

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  • $\begingroup$ Perhaps I need to regress my predicting variable onto the other two IVs (nuisance variables), and then conduct the simple slopes analysis as if the new corrected predicting variable, the moderating variable, and their interaction are the only IVs? I'm reticent to do this however, because it seems like the interaction between the moderating variable and the corrected predicting variable will be conceptually different than the original interaction. $\endgroup$
    – Spencer
    Commented Sep 17, 2012 at 17:53

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In general, multiple regression terms (predictor variables and their coefficients) are ceteris paribus. That is, they represent effects of variables when all else is held equal. The reason you have to go through this procedure (which I gather you understand perfectly fine), is because, for the terms included in the interaction, that's no longer true. Nonetheless, it remains true of the rest of the terms. Thus, you can simply ignore them when you are making a graph to just understand how the effects of the terms included in the interaction combine to influence the DV. Of course, you should be careful not to interpret the value displayed for the DV at a given point on those variables as the optimal prediction for an observation, you would need to take that observation's values for the other predictors into account for that.

On the other hand, if you just want to visualize your model in 3 or 4 dimensions, you could try a coplot.

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  • $\begingroup$ Thanks for the great response. So it sounds like you are saying that I can simply create a 2-dimensional plot of my predicting IV vs. my DV. Then I plot lines using only the intercept, predicting IV beta coefficient, and the fixed moderating variable (and its beta coefficient). This is still taking the nuisance IVs into account because I included them in the model when calculating those beta coefficients. The coplot is also an interesting idea, but unfortunately my data set is small enough that it wouldn't be very enlightening. Unless what I just parroted back is flawed, thanks so much! $\endgroup$
    – Spencer
    Commented Sep 17, 2012 at 19:43
  • $\begingroup$ I think you have it. When you make the plot you want to use all 3 betas together when plotting the functions. Also, I wouldn't say that you are still taking the nuisance variables into account (although I suppose it's a matter of interpretation), I would say that I'm ignoring them for the moment, because they don't influence the relationship pictured. $\endgroup$
    – gung - Reinstate Monica
    Commented Sep 17, 2012 at 19:57
  • $\begingroup$ Annnnd one last question: It would be more intuitive to look at the effects on the original data than the mean-centered data, but can I do that? Maybe the best way to do it is to standardize everything and visualize the effects that way. Its just not as intuitive to look at the +1 SD and -1 SD effects on the mean-centered data, ya know what I mean? $\endgroup$
    – Spencer
    Commented Sep 17, 2012 at 20:29
  • $\begingroup$ Your model exists in the transformed data world. However, if all you did was subtract the means, that's a linear transformation, so it should be possible to get back without disrupting anything. That also means that there isn't any real advantage either way, although it may be more intuitive for you for psychological reasons. $\endgroup$
    – gung - Reinstate Monica
    Commented Sep 17, 2012 at 20:41

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