Mediation, Confounding and Interaction

In multi-variate analysis we should distinguish between direct, indirect and combine effect of variables. By Including a variable to our model we can uncover the direct effect of continuous variables, and the difference between the effects two categorical variables on the dependent variable.

Yet very often, we are required to consider more complex structure of effect(s). First we should take into consideration a possibility of confounding; where a variable that was not included in our model is significantly affects one (or more) of our independent variable(s) and the dependent variable. As nicely defined by Hernán and Robins, (2013:83) “[c]onfounding is the bias that arises when the treatment and the outcome share a common cause.”

This should be distinguish from a situation of mediation – where a variable function as a mediator between one (or more) independent variable and our dependent variable. Put differently, the independent variable affects the dependent variable through the mediator. We should distinguish between a full mediation and a partial mediation.

A full mediation is identified in a situation where the following conditions are fulfilled:
1. the mediator has significant effects on the independent variable and the dependent variable. More recent research states that this condition is not essential, but indirect effect can be also identified when only the second condition is fulfil, but here we should rule out the possibility of a suppressor variable (Rucker et al. 2011).
2. when the mediator variable is not included in the model, the independent variable has significant effect on the dependent variable, but as soon as the mediator variable is introduced to the model this effect between the independent variable and dependent variable disappeared. A partial mediation is established when the effect of the independent variable weaken but not disappeared as soon as the mediator variable variable is included in the model.

Last but not least is the situation of interaction effect – when “the differing effect of one independent variable on the dependent variable, depending on the particular level of another independent variable” (Cozby, 1997; p. 314)

Here we should differentiate between three scenarios. One is of a combine effect of two continuous independent variables (and for this reason this effect can be detect by multiplying the two continuous variables and including all the three variable – the two independent variable and the new interaction variable). To avoid a problem of multicollinearity, instead of using the original values of the independent variable, we can centre the independent variable (IV mean – IV original value).

Second is of interaction between a dichotomous variable and a continuous independent variable or another dichotomous variable . Here we will suspect of a different effect of (one of) the dichotomous variable in a way that one group (or category) of the dichotomous variable (e.g. in case of dichotomous variable of sex, female) is significantly related to the other independent variable, while the other group (or category) is not.

There are two ways of detecting this sort of interaction. 1. We could split the file along the dichotomous variable and perform the analysis for both groups separately. This will allow us to identify the effects for each group separately, but we could not estimate if this interaction is statistical significant. 2. Multiplying the dichotomous variable with the the other continuous variable (or categorical variable, as is done in log-linear analysis).

Third is of interaction between two categorical variables. Here we will have to multiply each dummy variable(s) that represents the categorical variable with each of the dummy variable(s) that represent(s) the other categorical variable. Each of this multiplication variable will indicates us the effect of the combined two categories (one from each categorical variable).


Further reading:

Cozby P (1997) Methods in Behavior Research. London: Mayfield Publishing Co.

Miguel A. Hernán, James M. Robins (2013) Causal Inference

Rucker Derek D., Preacher Kristopher J., Tormala Zakary L. and Petty Richard E. (2011) Mediation Analysis in Social Psychology: Current Practices and New Recommendations, Social and Personality Psychology Compass 5/6 : 359–371.


Happy Analysing!

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