Measuring Interaction With Dummy Variable

[harintabima]

Hi!

Can anyone help me interpret a model using dummy (0,1) variable as moderating effect?I am using gender (male=1, female=0) as moderator. I interpret the output like this: the calculation results (for example: path significances) with multiplication by the moderator means the calculation result for male (male=1, female=0), and the ones without the multiplication means the result for female. Am I right?please, correct me.

Thank you very much.

Regards,
Surya.

[Diogenes]

Hi,


Y = Dependent variable (endogenous)
X = Independent or predictor
Z = Moderator (gender in your case)

Y = a + b1 *X + b2 * Z + b3 * XZ

If X = 0 ==> Y = a + b2 *Z then b2 is the contribuition of the moderator Z to the constant "a"

dY/dX = b1 + b3 * Z then b3 is the contribuition of the moderator Z to the slope of the preditor X.

Actually, this is not 100% correct, because the multiplicative term (XZ) is collinear with the predictor X, then the interpretation in these cases (analysis of moderation) is always a problem.

For more details see:
CARTE, Traci A.; RUSSEL, Craig J. In pursuit of moderation: nine common errors and their solutions. MIS Quarterly. v.27, n.3, 2003. p. 479-501.

I hope this help.

Bido

[Diogenes]

Actually, in your case (dummy moderator) it is simplier then I had explained above.
Interpretation is a problem if moderator is a continuous variable (colliearity – like I have explained), but with dummy.

Let´s try a example:

Y = Dependent variable (endogenous)
X = Independent or predictor
Z = Moderator (male = 0 female = 1)

Y = 5 + 0,4 *X + 0,3 * Z + 0,1 * XZ (unstandardized)

For male (Z = 0) --> Y = 5 + 0,4 * X ( constant = 5 and slope = 0,4 --> reference model )

For female ( Z = 1) --> Y = 5,3 + 0,5 X

Two equations or models.

I hope this help.

Bido