Matthew S. Fritz and Houston F. Lester
Mediator variables are variables that lie between the cause and effect in a causal chain. In other words, mediator variables are the mechanisms through which change in one variable causes change in a subsequent variable. The single-mediator model is deceptively simple because it has only three variables: an antecedent, a mediator, and a consequent. Determining that a variable functions as a mediator is a difficult process, however, because causation can be inferred only when many strict assumptions are met, including, but not limited to, perfectly reliable measures, correct temporal design, and no omitted confounders. Since many of these assumptions are difficult to assess and rarely met in practice, the significance of a statistical test of mediation alone usually provides only weak evidence of mediation.
New methodological approaches are constantly being developed to circumvent these limitations. Specifically, new methods are being created for the following purposes: (1) to assess the impact of violating assumptions (e.g., sensitivity analyses) and (2) to make fewer assumptions and provide more flexible analysis techniques (e.g., Bayesian analysis or bootstrapping) that may be more robust to assumption violations. Despite these advances, the importance of the design of a study cannot be overstated. A statistical analysis, no matter how sophisticated, cannot redeem a study that measured the wrong variables or used an incorrect temporal design.
Matthew S. Fritz and Ann M. Arthur
Moderation occurs when the magnitude and/or direction of the relation between two variables depend on the value of a third variable called a moderator variable. Moderator variables are distinct from mediator variables, which are intermediate variables in a causal chain between two other variables, and confounder variables, which can cause two otherwise unrelated variables to be related. Determining whether a variable is a moderator of the relation between two other variables requires statistically testing an interaction term. When the interaction term contains two categorical variables, analysis of variance (ANOVA) or multiple regression may be used, though ANOVA is usually preferred. When the interaction term contains one or more continuous variables, multiple regression is used. Multiple moderators may be operating simultaneously, in which case higher-order interaction terms can be added to the model, though these higher-order terms may be challenging to probe and interpret. In addition, interaction effects are often small in size, meaning most studies may have inadequate statistical power to detect these effects.
When multilevel models are used to account for the nesting of individuals within clusters, moderation can be examined at the individual level, the cluster level, or across levels in what is termed a cross-level interaction. Within the structural equation modeling (SEM) framework, multiple group analyses are often used to test for moderation. Moderation in the context of mediation can be examined using a conditional process model, while moderation of the measurement of a latent variable can be examined by testing for factorial invariance. Challenges faced when testing for moderation include the need to test for treatment by demographic or context interactions, the need to account for excessive multicollinearity, and the need for care when testing models with multiple higher-order interactions terms.