# IVs and moderator variables correlate in three-way interaction - problematic?

#### jango

##### New Member
Hi everybody,

let's assume I hypothesize:
• H1: A direct effect of X1 on Y
• H2: A direct effect of X2 on Y
• H3: A two-way interaction between X1 and X2
• H4: A three-way interaction between X1, X2 and X3
• H5: A three-way interaction between X1, X2 and X4
and run the following OLS regressions to test H4 and H5:

H4
Y = a + b1X1 + b2X2 + b3X3 + b4X4 + b5X1X2 (two-way) + b6X1X3 + b7X2X3 + b8X1X2X3 (three-way X3)

H5
Y = a + b1X1 + b2X2 + b3X3 + b4X4 + b5X1X2 (two-way) + b6X1X4 + b7X2X4 + b8X1X2X4 (three-way X4)

However, descriptive statistics show that X1 and X2 (central IVs) correlate with X3 and X4 (moderator variable for the three-way interactions) as follows:
• Correlation between X1 and X4: r = .4 (p < .01) [possibly because X4 can lead to X1, which is not within the scope of my research model]
• Correlation between X2 and X3: r = -.17 (p < .01) [possibly because X3 can reduce X2, which is not within the scope of my research model]
• Correlation between X2 and X4: r = .10 (p < .1) [possibly because X4 can lead to X2, which is not within the scope of my research model]
n = 300 (multicollinearity is not a problem - VIFs are < 3)

I know that a correlation between an IV and a moderator variable is possible and "acceptable" in the case of a two-way interaction (see https://www.researchgate.net/post/Can_the_moderator_and_the_independent_variable_be_correlated). However, is there any reason these correlations can be problematic (empirically) in the case of a three-way interaction as described above? If yes, can I do something about it?

Thank you very much in advance.

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