Moderator variables in hierarchical regression analysis

[DLDRVH4]

I have read the Frazier, Tix, & Barron, 2004 article and found it very helpful. However, I now have a few additional questions:
- First, I want to make sure I understand centering- This is literally subtracting the sample mean of each variable from the individual data points?
- Second, my moderator variable has 2 scales (a femininity and a masculinity scale). In creating interaction variables, do I multiply each scale by each IV? If I have 3 IVs and a moderator with 2 scales, this makes 6 interaction terms, correct? Does this mean I need to have a sample size of at least 5 x 12 (1 covariate, 3 IVs, 2 moderators, and 6 interaction terms)?
Thanks.

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[Ollie123]

In this case, you are correct about how you go about centering, though there are other ways to do it so don't assume "centering" always means to the sample mean (e.g. with multiple measurements, data can be centered to either the sample mean or a within-individual mean).

As for the rest, do you mean you have 3 IVs or, one IV with 3 levels? If the former, how many levels does each IV have (if any are categorical - in which case don't forget to dummy code)? If the former, you will have many more than 6 interactions if you want to look at all possibilities.

Separate subscales are essentially treated as two different variables in this analysis...though be careful in how you approach this since they are potentially highly correlated so you may need to account for that.

I don't know where the 5 x 12 came from, but power analysis for interaction effects can be beastly and I'd need a lot more information than you gave to have any idea if its enough...though I'll hazard a guess that even 60 people is probably not anywhere near enough for this type of analysis.

 

[DLDRVH4]

I have three continuous IVs (predictor variables) and, from what you say above, 2 moderator variables (2 scales of one instrument) which will be highly correlated I'm sure. Can I do anything to prevent this correlation from being a problem? I have centered the predictor and moderator variables.

OK. One other question. I am thinking about eliminating one of the scales so that I just have one moderator. Would I need to create more than 3 interactions (the moderator variable multiplied by each of the IVs)?

 

[ClinicalTrainee]

If you want to look for moderation with all three predictors, then yes you will need three interaction terms.

I should also note that when you center the variables, try to make sure you filter out people with missing data on any of the variables in the model. Regression throws out any cases that have missing data, so if you center the variables without taking this into account first, your centered variables will not truly be centered (mean = 0.0000) when you run the analysis.

 

[QClinician]

It provides a true 0, making beta values more interpretable

 

[JockNerd]

It provides a true 0, making beta values more interpretable

Not really; this is just an consequential thing. The purpose of centering is to orthogonalize interaction terms. If you don't do it your interaction terms are multicollinear with the parent variables and the whole analysis tanks.

I still prefer to regress the main effects out of the interaction; mucking about with distributions scales always seemed weird to me. Plus if you need to do transformations or something everything is weirded up if you center.

 

[DLDRVH4]

Thank you all. What about standardizing instead of centering?