What is a moderator variable?
This alters the effect the independent variable has on the dependent variable.
This does not impact the independent variable.
What does a multiplicative interaction model look like?
A multiplicative interaction model is used with regressions involving moderating variables, which has the independent variables AND a multiplicative interaction:
y = b0 + (b1 x X) + (b2 x Z) + (b3 x XZ) + e
Multiplicative Interaction: (b3 x XZ)
What is a conditional hypothesis?
A relationship between two (or more) variables depends on the value of one (or more) other variables.
e.g. An increase in ‘x’ is associated with an increase in ‘y’ when condition ‘z’ is met, but not when ‘z’ is absent.
e.g. The positive impact of information and communication technology use, ‘x’, on productivity, ‘y’, will be higher in firms with higher employee empowerment, ‘z’.
How do you form a regression for a conditional hypothesis?
- Include interaction terms if the hypothesis is conditional:
First identify –> Which variable is the moderator variable in this instance? - Include all constitutive terms
i. Include each of the elements that constitute the interaction term:
ii. If you have the interaction xz, always include x and z too as predictors. - Interpret ‘the effect’ correctly
i. To interpret correctly, estimate the marginal effect of ‘x’ on ‘y’ for different values of ‘z’. - Meaningful marginal effects- to find the marginal effect of ‘x’ on ‘y’, it is the partial derivative of ‘y’ with respect to ‘x’: dy/dy (with the rounded ‘d’)
i. Without involving the moderator, we can only tell whether ‘x’ has a significant effect on ‘y’ when ‘z’ = 0.
What is mediation?
- This is where the impact of x on y is transmitted by another variable (w).
- This is where w = mediator
- The effect runs (partly or completely) via a third variable w.
What is the difference between a moderator with a dummy variable vs with a continuous variable:
The same multiplicative interaction occurs:
Y = b0 + b1(x) + b2(D) + b3(xD) + e
* However, dummy variables vary based on the 2 categories (D = 1 & D=0).
* Whereas for a continuous variable, the effect of x on y varies for every value of z.
Example below:
Marginal effect of x (dummy variable):
dy/dx = b1 + b3(D =1)
= -1.833 -1.881 = -3.714
dy/dx = b1 + b3(D = 0)
= -1.833
The negative effect of x on y is higher for D=1
Marginal effect of x (continuous variable):
dy/dx = b1 + b3(z) = -4.133 + 2.166(z)
The effect of x on y varies for every value of z.
When answering questions asking for the direct and indirect effects, what do you mention?
- Sign (positive / negative)
- Size (coefficient)
- Significance (p-value)
