Mediating Variable Research Paper

1. The Mediated Effect

When quantified, the mediating variable effect is known as the mediated or indirect effect. It is called the indirect effect because it represents an effect of X on Y that is transmitted indirectly through the mediating variable. If some, but not all, of the effect of X on Y is transmitted through M, the effect is partially mediated because a direct effect of X on Y exists even after adjustment for the mediator.

The mediating variable effect differs from other ‘third-variable’ effects used to understand the relationship between two variables. For a moderator or interaction variable, the effect of X on Y differs for different values of the moderator variable, but a moderator does not transmit the effect of X on Y like the mediating variable. A confounding variable, when included in the investigation of the association between X and Y, changes the association between X and Y. A confounder changes the association between X and Y because it is related to both X and Y but not because it is in a causal sequence relating X to Y. Although the conceptual distinction between a confounder and a mediator is clear, it can be difficult to differentiate between them with actual data. The underlying causal sequence is the important aspect of the mediating variable.

2. Examples

Because the mediating variable elaborates the relationship between two variables by explaining why or how an effect occurs, it is of considerable importance in many fields. One of the first applications of the mediating variable was in psychological theories that learning processes, such as habit strength, explained the association of stimulus and response (Hull 1943). Later, a distinction was made between hypothetical mediating constructs representing processes or entities not directly observed and intervening variables which were observed measures of these hypothetical constructs (MacCorquodale and Meehl 1948). Duncan (1966) established the use of mediating variables in sociology when he applied path analysis techniques developed earlier by Sewall Wright (1934) to examine causal mediating relations among variables. One of the first sociological examples was that father’s socioeconomic status causes the mediating variable, child’s educational achievement, which causes child’s socioeconomic status. The effect of father’s socioeconomic status on child’s socioeconomic status was not entirely mediated by child’s educational achievement, so a direct effect between father’s and child’s socioeconomic status was also included in the model. Decomposition of effects into direct and indirect effects is a common focus of sociological research, whereas identifying mediating variables that entirely explain an effect is more common in psychological research.

A new application of the mediating variable is in chronic disease research (Schatzkin et al. 1990). Prospective studies examining the effects of etiological factors or prevention strategies on chronic disease require lengthy follow-up measurements because of the low frequency of occurrence and the slow development of the disease. As a result, researchers attempt to identify mediating variables on the causal pathway relating risk factors to disease. The mediating variables are called intermediate or surrogate endpoints. Using colon cancer as an example, the proliferation of epithelial cells in the large bowel occurs before colon cancer and is causally related to colon cancer. A study targeting cell proliferation rather than colon cancer requires less time and fewer subjects.

Mediating variables are critical in the development and application of prevention programs. Here the prevention program is designed to change mediating variables hypothesized to be causally related to the dependent variable. It is assumed that the prevention program causes change in the mediating variable which in turn causes change in the dependent variable. Programs to prevent coronary heart disease target behaviors such as diet and smoking and biological factors such as cholesterol level and blood pressure. Social influences-based drug prevention programs are designed to increase skills to resist drug offers and engender norms less tolerant of drug use. Treatment programs for substance abuse target mediators such as communication skills and social support to prevent a relapse to drug abuse.

Theories of health behavior and observed empirical relationships guide the selection of mediating variables for prevention programs. A prevention program based on established theory regarding mediating variables may be more likely to change the outcome measure and the results provide a test of the theoretical basis of the prevention program. Competing theories of the onset of drug abuse, for example, may suggest alternative mediators that can be tested in an experimental design. Prevention programs will also cost less and will have greater benefits if effective and ineffective mediating processes are identified.

Mediating variables in prevention serve a different purpose than other applications of mediating variable methodology. In the prevention case, mediating variables are selected before the study and are fundamental to the prevention program because of their causal relationship to the dependent variable. In most other applications, the purpose of the mediating variable is to identify the processes that generated an effect, after the effect has been found.

3. Tests of the Mediated Effect

The parameter estimates and standard errors from the following three equations provide the information for tests of the mediated effect (MacKinnon and Dwyer 1993):

                                           Y = τX + ε₁                             (1)

                                           M = αX + ε₂                          (2)

                                            Y = τ´X + βM + ε₃                (3)

where Y is the dependent variable, X is the independent variable, M is the mediating variable, τ codes the relationship between the independent variable and the dependent variable, τ´ is the coefficient relating the independent variable to the dependent variable adjusted for the effects of the mediating variable, α is the coefficient relating the independent variable to the mediating variable, β is the coefficient relating the mediating variable to the dependent variable adjusted for the independent variable, and ε₁ , ε₂ , and ε₃ code unexplained variability. The intercepts are not included to simplify the presentation. There are two estimators of the mediated effect, αβ and τ–τ´ , which are algebraically equivalent in ordinary regression but not in other analyses such as multilevel and logistic regression.

There are three major types of tests of the mediated effect that use the information in the above regression models: (a) causal step tests, (b) difference in coefficients tests, and (c) product of coefficients tests. Methods to assess mediation based on causal steps entail tests of the different logical relationships among the three variables involved that must be true for a variable to be a mediator. The following sequence of causal steps described in Baron and Kenny (1986) is the most widely used method to assess mediation. (a) The independent variable (X) must affect the dependent variable (Y), τ in Equation (1). (b) The independent variable (X) must affect the mediator (M), α in Equation (2). (c) The mediator must affect the dependent variable (Y) when the independent variable (X) is controlled, β in Equation (3). The conceptual links between each necessary causal relationship and the statistical tests are clear in the causal step method. However, the causal step method has no direct estimate of the mediated effect and standard error to construct confidence limits. The first requirement, a significant relationship between the independent and dependent variable, excludes models where mediation exists but the relationship between the independent variable and the dependent variable is not significant.

The second method to test for mediation compares the relationship between the independent variable and the dependent variable before and after adjustment for the mediator. The method tests whether a third variable, here a mediator, significantly changes the relationship between two variables. The difference in the regression coefficients (τ–τ´ ) described above is an example of this approach. Formulas for the standard error of τ–τ´ can be applied to construct confidence limits for the mediated effect (Clogg et al. 1992). A drawback of the change in coefficient method is that it is conceptually more similar to a confounding variable than a mediating variable.

The third method to test the significance of the mediated effect is based on the product of coefficients which is more consistent with the causal sequence in mediation. The estimator of the mediated effect is αβ, the product of regression coefficients α and β. The most commonly used standard error is the first-order Taylor series solution for the product of two random variables derived by Sobel (1982) using the multivariate delta method, where σα and σβ are the standard errors of a and b, respectively:

                                      σαβ = √ (α²σ²β + β² σ²α)                       (4)

The matrix formulas for the computation of this standard error are included in most covariance structure analysis software programs. Confidence limits for the mediated effect can be calculated using the standard error in Eqn. (4), and the result is then compared to a standard normal distribution to test for significance. The mediated effect divided by its standard error, αβ σαβ, does not always follow a normal distribution, however.

The product of coefficients methods provide an estimate of the mediated effect and the standard error of the mediated effect. In addition, the underlying model is a mediation model where the mediated effect is the product of coefficients hypothesized to measure causal relationships. For an independent variable coding experimental assignment, the α parameter tests whether the manipulation successfully changed the mediating variable it was designed to change and the β parameter tests whether the mediating variable is related to the dependent variable, as suggested by theory.

3.1 Causal Analysis of Mediating Variables

Methods based on the regression approach described above have been criticized based on causal analysis of the relationships among variables. For example, if X, M, and Y are measured simultaneously, there are other models (e.g., X is the mediator of the M to Y relationship or M and Y both cause X ) that would explain the data equally well and it is not possible to distinguish these alternatives without more information (Spirtes et al. 1993).

The case where X represents random assignment to conditions improves causal interpretation of mediating variables (Holland 1988, Robins and Greenland 1992). Holland applied Rubin’s (1974) causal model to a design where students are randomized to one of two groups, either to a group receiving motivation to study or to a control group that did not receive motivation. The mediating process is that assignment to the motivation group affects the number of hours studied which affects test performance. Under some assumptions, the typical regression coefficient for the group effect on test score, τ, and the group effect on number of hours studied, α, are valid estimators of the true causal effect, primarily because of the randomization of units to treatment. The relationship between the mediating variable of the number of hours studied and test score is more problematic (e.g., Y may cause M) and the regression coefficient β is not an accurate estimator of the causal effect because this relationship is correlational, not the result of random assignment. The estimator τ is also not an accurate causal estimator of the direct effect. The missing information for the causal effects is whether the relationship between the number of hours studied and test score would have been different for subjects in the treatment group if they had instead participated in the control group. Recent applications of this causal approach investigate exposure to treatment as the mediating variable. For example Angrist et al. (1996) investigated the effect of Vietnam war service on health with random selection in the draft as the independent variable, serving in Vietnam as the mediating variable, and health as the dependent variable.

4. More Complicated Mediation Models

The single mediator model described above is easily expanded to include a chain of mediating variables. In fact, most mediating variables are actually part of a longer theoretical mediational chain (Cook and Campbell 1979). For example, it is possible to measure each of the four constructs in a theoretical chain from exposure to a prevention program, to comprehension of the program, to short-term attitude change, to change in social norms, to change in the dependent variable. Typically, researchers measure an overall social norms mediator rather than all mediators in the chain, even though a more detailed chain is theorized.

The single mediator methods can be extended for multiple mediators and multiple outcomes with correspondingly more mediated effects (Bollen 1987). Multiple mediator models are justified because most independent variables have effects through multiple mediating processes. The true causal relationships are difficult to disentangle in this model because of the number of alternative relationships among variables. One solution to the problems inherent in the causal interpretation of multiple as well as single mediator models is to view the identification of mediating variables as a sustained research effort requiring a variety of experimental and nonexperimental approaches to identify mediating variables. The analysis of multiple mediators in one study informs the design of randomized experiments to contrast alternative mediating variables leading to refined understanding of mediating processes (West and Aiken

1997). Meta-analytical studies provide information about the consistency of mediating variable effects across many situations (Cook et al. 1992). Furthermore, the identification of mediating variables requires examination of additional sources including ethnographic, historical, and clinical information (Cronbach 1982).

5. Future Directions

Mediating variables will continue to play a major role in the social and behavioral sciences because of the need to understand how and why variables are related. In particular, the practical and theoretical benefits of mediating variables in prevention research should guide the development of effective prevention programs. Investigators will endeavor to find the information needed for the application of Rubin’s causal model and related approaches to mediating variable models. Accurate point and interval estimators of mediated effects will continue to be developed for various statistical methods including categorical and longitudinal models. In addition to statistical approaches, sustained study of mediating variables will include information from a variety of sources including history, journalism, and clinical experience.

Such comprehensive efforts are necessary to determine if a variable is truly intermediate in the causal sequence between two other variables.

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