Moderator variables are particularly useful in experimental psychology to explore whether a specific treatment always has the same effect or if differential effects appear when another condition, context, or type of participant is introduced. This is one reason why contextual variables and demographic variables, such as age, gender, ethnicity, socioeconomic status, and education, are some of the mostly commonly examined moderator variables in psychology. Moderator variables are extremely important to psychologists because they provide a more detailed explanation of the specific circumstances under which an observed association between two variables holds and whether this association is the same for different contexts or groups of people. Note that moderating variables are not necessarily assumed to directly cause the outcome to change, only to be associated with change in the strength and/or the direction of the association between the predictor and the outcome. Keeping the temperature constant, if the bread made with whole-wheat flour took longer to finish baking than the bread made with white flour, then the type of flour would be a moderator variable, because the relation between temperature and cooking time differs depending on the type of flour that was used.
But consider a baker making two different types of bread dough, one with regular white flour and the other with whole-wheat flour. In general, the higher the temperature of the oven (independent variable), the faster the bread will finish baking (dependent variable). That is, the magnitude and even the direction of the relation between one variable, usually referred to as a predictor or independent variable, and a second variable, often called an outcome or dependent variable, depends on the value of the moderator variable. When the strength of the association between two variables is conditional on the value of a third variable, this third variable is called a moderator variable. 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. 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.
Within the structural equation modeling (SEM) framework, multiple group analyses are often used to test for moderation. 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. In addition, interaction effects are often small in size, meaning most studies may have inadequate statistical power to detect these effects. 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. When the interaction term contains one or more continuous variables, multiple regression is used. When the interaction term contains two categorical variables, analysis of variance (ANOVA) or multiple regression may be used, though ANOVA is usually preferred. Determining whether a variable is a moderator of the relation between two other variables requires statistically testing an interaction term. 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. 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.