• Mediation occurs when one variable (X) is related to another variable (Y) through a third variable (Z).
• Typically, the goal of a mediation analysis is to better understand the causal relation between X and Y.
• Does X predict Y only because X predicts Z and Z predicts Y? Or does X also have some direct effect on Y that has nothing to do with Z?

Example: Research aim to understand the effects of using a chosen name on life-satisfaction for this population.

• Initial literature review suggests youth who use a chosen name have higher levels of life-satisfaction.
• You want to know- Why would using a chosen name lead to more satisfied with life?
• Interviews with trans youth suggest that those who use a chosen name report feeling more connections.

• New hypothesis: Interpersonal connectedness is a mediating variable in the relation between chosen name use and life-satisfaction.

Alternative Expressions:

• The relation (or path) between chosen name use and life-satisfaction is mediated by interpersonal connectedness
• Chosen name use has an indirect effect on life-satisfaction through feelings of interpersonal connectedness
• Chosen name use causes increased feelings of connectedness, which in turn cause higher levels of life satisfaction

• Indirect effects are effects of one variable on another that take place through another variable.
• Direct effects describe causal paths that are not mediated or moderated.
• Sometimes a predictor variable has both a direct and indirect effect on an outcome (i.e. some of the total effect of X on Y is direct, and some is indirect).

• If the only way X affects Y is through Z, the effect of X on Y is fully mediated.
• However, if after accounting for Z there is still some direct effect of X on Y, then Z is only a partial mediator, or the effect of X on Y is partially mediated.

• Mediation analysis can be implemented as a series of regression analyses.
• Requires multiple regressions because there are mutiple outcomes per person, e.g. X predicts Z, then Z predicts Y.
• Path analysis is a general framework for conducting a system of regressions. If that system of regressions includes a mediating relationship, then it can be called a mediation analysis.

• Mediation analysis can also be performed in a latent variable framework.
• If all or any of X, Y, and Z are latent variables, the model is a structural equation model (SEM).
• The theory of mediation analysis doesn't change

I think mediation is often best understood by looking at variable diagrams. Let's take a look at a couple:

Path Models

• Chosen name use predicts connectedness which in turn predicts life-satisfaction, denoted by paths a and b, respectively.
• Path c' (pronounced "c-prime") represents direct effect of chosen name use on life-satisfaction after including or "controlling for" the mediator.
• The bottom diagram shows an unmediated model of chosen name use predicting life-satisfaction through a single direct effect

• Often the purpose of mediation analysis is to observe the difference between c and c'.
• If c is statistically significant but c' is not, then we may determine that the effect of chosen name use on life-satisfaction is fully mediated by interpersonal connectedness.
• If c' is statistically significant even with the inclusion of the mediating variable, then the effect is only partially mediated.
• The total effect c is equivalent to a*b + c', where a**b* (typically just called ab) refers to the indirect effect.