Interpretation of moderational effect

[Paul Olz]

Hello,

while looking at the results of my final models, I am confused about the interpretation of three numbers:

Dependent variable		(1)	(2)	(3)	(4)
Y		Model 1	Model 2	Model 3	Model 4
Independent variables
X1			...	...	...
X2			...	....	....
X3			....	....	....
Interaction effect
	M1			0.16**	-2.74**
				(0.12)	(1.11)
	X1 # M1				0.05**
					(0.07)
Control variables
...		...	....	...

The fist model just focusses on the controls, the second adds the IV, the third just adds the M1 as a normal variable and model 4 looks at the moderation effect. How can the change from 0.19 to -2.92 be interpreted?

Thank you very much in advance!!!

[Clyde Schechter]

"M1" means two different things in models 3 and 4.

You don't say anything about the nature of these variables, but for purposes of explanation, I will assume that M1 is a 0/1 variable. In Model 3, the coefficient for M1 represents the expected difference in the outcome variable between M1 = 1 and M1 = 0. In words, it is the marginal effect of M1 on the outcome.

However, in model 4, because you have an interaction, there is no such thing as the marginal effect of M1. Rather, there are many marginal effects of M1, depending on the value of X1. In this model, the coefficient of M1 has a different meaning: it is the expected difference in the outcome variable between M1 = 1 and M1 = 0 when X1 = 0. (It is possible that X1 is never actually 0 in the real world, in which case the coefficient of M1 really has no meaning. It is only there as an ingredient in the calculation of the marginal effect of M1 for actual values of X1.)

Since the coefficient of M1 represents two different things in these models, no explanation is needed for the difference between those values. There is no real reason to expect them to be similar in any way.

[Paul Olz]

Thank you very much!!!