path analysis

n. Path analysis is a multilevel strategy for analysis of complex interrelationships among variables of interest. There are a variety of specific statistical strategies that researchers use to conduct path analysis. One basic objective of path analysis is to uncover mediated relationships, that is to say, relationships between variables that are accounted for or explained by intermediary variables. In a sense, a mediated relationship between two variables is one that “passes through” a third variable. Mediated relationships exist when a significant proportion of a demonstrated overlap between two variables is accounted for by a mutual relationship with a third variable.

It is important to distinguish between mediation and a similar-sounding term with a very different meaning: moderation. Critics have pointed out instances where researchers have mistakenly used these two terms interchangeably. Mediation, one of the central aspects of path analysis, is about channeling relationships between other variables. Moderation is synonymous with interaction, which occurs when the influence of one variable upon another variable varies, depending on the value of a third variable. For example, an interaction would exist if a hypothetical relationship between viewing violent pornography and aggressive behavior depended on the sex of the participant in the following way: for males, there is a relationship between viewing violent porn and subsequent aggressive behavior, and for females there is no relationship between violent porn and aggression.

Mediation can be quite complex; the simplest version of it exists in the abstract as follows: Mediation exists when a relationship between variable A and variable C is channeled through variable B in the following way: A is related to B, B is related to C, and the relationship between A and C is significantly reduced when variable B is added to the statistical model.

Here is a more concrete hypothetical example of mediation: There is a relationship established between university class attendance (A) and scores on the final exam of the course (C). Closer examination of this relationship shows that (1) attendance is associated with higher scores on periodic measures of understanding of course content (B), (2) understanding of course content is associated with final exam scores, and (3) the relationship between attendance and final exam scores is significantly reduced when understanding of course content is added to the model.

Relationships between variables, which are often referred to as path coefficients in path analysis, are presented in a few different ways. Path coefficients generally range from −1 to 1, similarly to correlation coefficients (often path analysis is conducted using multiple regression analysis, and the path coefficients are standardized beta weights). Researchers refer to the detailed analysis of path coefficients as decomposition of effects. There are three basic ways in which path coefficients are measured: total effects, direct effects, and indirect effects. The total effect is the overall relationship between one variable and another, variables A and C from the hypothetical example. That total effect can be decomposed into direct and indirect components.

The direct effect is the amount of the total relationship between A and C that is remaining or “left over” when the complete model is present, that is, when variable B enters the model in the hypothetical example. In order for mediation to be potentially present, the total effect will be reduced when the mediator variables are added to the model, resulting in a smaller direct effect compared to the total effect. The difference between the total effect and the direct effect is the indirect effect. The indirect effect is the portion of the relationship that is potentially mediated. In summary, total effect = direct effect + indirect effect.

In order for mediation to exist, most researchers require not only the presence of indirect effects, but also significant direct relationships between the primary variables and the mediator variables. To return to the abstract example, in order for mediation to exist, the total effect between A and C must be larger than the direct effect when B is added to the model (the difference between the total effect and the direct effect between A and C is called the indirect effect). In addition, for mediation to exist, A must have a significant relationship with B, and B must have a significant relationship with C.

To return to the concrete example, then, assume that the total effect path coefficient between class attendance (A) and final exam scores (C) is .65. When understanding of course content is added to the model, the direct effect path coefficient between attendance and final exam scores is .15. Therefore, the indirect effect path coefficient is .50 (total effect .65 minus direct effect .15 equals .50). In addition, there is a significant path of .53 between attendance and understanding of content, and also a path between understanding and final exam scores, .38. Because there is a significant indirect effect of .50 between attendance and final exam scores, and because there are direct relationships both between attendance and understanding and between understanding and final exam scores, we can conclude from our path analysis that the relationship between attendance and final exam scores is mediated by understanding of course content.

Path analysis can be conducted in a variety of ways, involving a variety of different types of variables and testing a variety of different types of hypotheses and/or research objectives. Sometimes path analysis will be used to test a theoretical model that results directly from prior research findings, and at other times it will be used as an exploratory tool based on a few basic a priori expectations about relationships among variables.

One of the advantages of path analysis is that it allows researchers to map complex interrelationships among variables. As psychological science progresses, there are corresponding increases to the complexity of psychological research models. Path analysis allows researchers to test complex interrelationships among varieties of variables in such a way that research begins more closely to approximate the very complex circumstances that exist in the real world. Many researchers believe that more complex research designs, which involve many variables and many interrelationships among those variables, are a necessary-but-difficult challenge for psychological researchers because only complex research has the potential to approximate the real world realistically. – MWP