# How to conduct a moderated multiple regression with two (or more) moderators?

I've been trying for a while to understand how to perform this type of analysis, but I can't seem to find any literature or even forum posts about it, so any help or guidance anybody can offer would be greatly appreciated.

Suppose I have five continuous predictors (X1-X5) and one continuous output (Y). I'd like to test whether the effects of X1-X5 on Y are moderated by two continuous variables (M1 and M2). Specifically, there is prior evidence to suggest that the effects of X1-X5 on Y will be stronger at higher levels of M1 and M2.

What is the correct way to analyse the data to test these predictions? Some options I've considered are:

1. A single long regression equation including all of the interaction terms (i.e. Y = β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6M1 + β7M2 + β8X1M1 + β9X1M2 + β10X2M1 + β11X2M2 + β12X3M1 + β13X3M2 + β14X4M1 + β15X4M2 + β16X5M1 + β17X5M2 + C + e)

2. Conducting separate multiple regression analyses for each moderator (i.e. Y = β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6M1 + β7X1M1 + β8X2M1 + β9X3M1 + β10X4M1 + β11X5M1 + C + e AND Y = β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6M2 + β7X1M2 + β8X2M2 + β9X3M2 + β10X4M2 + β11X5M2)

3. Converting the two moderators into a single polychotomous nominal moderator (e.g. splitting each moderator into 'High' and 'Low' and using these to create four groups: Low M1 Low M2; Low M1 High M2; High M1 Low M2; High M1 High M2).

Is anybody able to offer any guidance on which of these, if any, would be the correct approach? Any references to textbooks or webpages with more information would also be very welcome.

• I have the same question. How did you solve it? – Pien Aug 14 at 10:15
• Hi @Pien - unfortunately I didn't manage to solve it. You might like to try asking on a statistics subreddit (e.g. /r/AskStatistics, /r/Statistics), as these seem to have more active communities and don't remove questions so often. – mr0860 Aug 15 at 11:04