Consider the following regression model:

Y= α0 + α1 X + α2 MO + α3 (X*MO) + ε 

Y= Dependent variable

X=Independent variable

MO=Moderating variable

Now, If the moderating variable consists of, for example, three elements (A, B, C), which of the following expression is correct, and why? Please indicate your sources. Thank you.

I.Y=a0 +a1X+a2 A+a3B+a4C+ [a5 X*A+a6 X*B+ a7 X*C] + ε 

II. Y=a0+a1X+a2A+a3B+a4C+ [a5X*A+a6 X*B+ a7 X*C +a8X*AB+a9 X*AC+a10 X*BC] + ε 

III. Others -please specify.