Many researchers want to examine whether one variable mediates the association between two variables (see Shrout & Bolger, 2002). They might, for instance, want to ascertain whether stress mediates the relationships between workload and dishonesty. That is, they might predict that workload promotes stress, which in turn tends to provoke dishonesty.

Other researchers often need to examine whether one variable moderates the association between two variables (James & Brett, 1984). They might, for instance, want to examine whether feelings of engagement moderate the relationship between workload and dishonesty.

To illustrate, workload might be positively related to dishonesty when individuals do not feel engaged in their tasks. However, workload might not be related to dishonesty when individuals feel engaged in their tasks. Engagement, thus, moderates or changes the relationship between workload and dishonesty

In some circumstances, however, researchers might want to examine both mediation and moderation in the same model. According to Baron and Kenny (1986), some researchers examine a model called mediated moderation. In this instance, two variables interact with each other to affect a mediator, which in turn influences another variable.

As an example, workload and engagement might interact with each other to affect stress, and stress might in turn influence dishonesty. In other words, the relationship between one variable, like workload, and a mediator, like stress, is moderated by another variable, like engagement.

Alternatively, using the definitions of Baron and Kenny (1986), researchers might want to examine a model called moderated mediation. In this instance, a variable moderates the relationship between an independent variable and a mediator or between a mediator and a dependent variable.

As an example, the researcher might still want to examine the proposition that stress mediates the association between workload and dishonesty. In addition, engagement might moderate the relationship between workload and stress. Alternatively, engagement might moderate the relationship between stress and dishonesty.

This article presents some of the techniques that can be used to examine such models. This article, however, does assume basic knowledge of moderated regression.

A variety of approaches have been developed to assess mediation and moderation in combination (for a review, see Edwards & Lambert, 2007). One technique, utilized about 23% of the time when mediation and moderation are examined in the same study (Edwards & Lambert, 2007), is called the piecemeal approach. This approach involves analyzing moderation and mediation separately, but then deriving a joint conclusion. To illustrate, suppose the researcher wants to assess the proposition that workload and engagement might interact with each other to affect stress, and stress might in turn influence dishonesty-a form of mediated moderation. To examine this model, the researcher could:

- Conduct moderated regression to examine whether the association between workload and dishonesty is moderated by engagement. In this instance, dishonesty is the dependent variable, whereas workload, engagement, and the product of workload and engagement are the independent variables.
- Next, a procedure to examine mediation is applied, often using the phases stipulated by Baron and Kenny (1986). In particular, researchers might examine whether stress mediates the relationship between workload and dishonesty-disregarding engagement from this process. That is, they would conduct several analyses to show that workload is related to dishonesty, workload is related to stress, stress is related to dishonesty after controlling workload, but workload is not related to dishonesty after controlling stress (for updated procedures, see Kenny, Kashy, & Bolger, 1998).

This procedure presents two difficulties, however (Edwards & Lambert, 2007). First, this process does not distinguish between several possibilities. Perhaps, for example, engagement might moderate the relationship between workload and stress. Alternatively, engagement might moderate the relationship between stress and dishonesty. Indeed, engagement might only moderate the direct relationship between workload and dishonesty.

Second, the phases stipulated by Baron and Kenny (1986) have often been criticized. The first phase-establishing the relationship between workload and distress, for example, might not be successful if suppressors are present (see Collins, Graham, & Flaherty, 1998& MacKinnon, Krull, & Lockwood, 2000).

The subgroup approach is utilized approximately 31% of the time when mediation and moderation are examined in the same study (Edwards & Lambert, 2007). In this instance, researchers examine the mediation model at several levels of the moderator.

To demonstrate, consider again the researchers who want to assess whether stress mediates the relationship between workload and dishonesty and to ascertain whether engagement moderates any of these associations. Conceivably, the researcher could:

- Divide participants into, for example, three groups, depending on their level of the moderator. For example, the three groups could be low, medium, and high levels of engagement.
- Researchers could examine the mediation for each of these three groups separately.
- To illustrate, researchers could apply the Baron and Kenny (1986) protocol to the participants with low engagement& they might conduct several analyses to show that workload is related to dishonesty, workload is related to stress, stress is related to dishonesty after controlling workload, but workload is not related to dishonesty after controlling stress (for updated procedures, see Kenny, Kashy, & Bolger, 1998).
- Next, they could apply the same protocol to participants with moderate engagement
- Finally, they could apply the same protocol to participants with high engagement
- Suppose some of these relationships are significant for some, but not all, levels of engagement, the researcher could conclude the moderator affected the mediated effects.
This methodology also presents some consequential difficulties. First, none of these phases of the approach directly assess whether mediation differs across levels of the moderator. To illustrate, suppose mediation is established at each level of engagement. This finding does not necessarily imply these associations-such as the relationship between stress and dishonesty-is i dependent of engagement. Perhaps, the relationship is less pronounced, but nevertheless significant, when engagement is low.

Likewise, suppose stress is related to dishonesty only when the level of engagement is high. This finding, however, does not definitely imply that level of engagement moderates the relationship between stress and dishonesty. The B value might be .4 and significant when level of engagement is high and .39 and non-significant when level of engagement is low-the difference between these B values being negligible.

Second, the moderator, if a numerical variable, needs to be classified into categories. This process reduces power and can generate biased B values (Maxwell & Delaney, 1993& Stone-Romero & Anderson, 1994). The reduced power also increases the likelihood the independent variable is not significantly related to the dependent variable after controlling the mediator-one of the criteria to establish mediation.

### Moderated causal steps approach

Most of the remaining 53% of studies that examine both mediation and moderation utilize a variant of the causal steps approach (Edwards & Lambert, 2007)-a method that was promulgated by Baron and Kenny (1986& see also Muller, Judd, & Yzerbyt, 2005). Again, to illustrate this approach, suppose the researcher wants to assess the proposition that workload and engagement might interact with each other to affect stress, and stress might in turn influence dishonesty-a form of mediated moderation. To examine this model, the researcher could:

- First, show the relationship between workload and dishonesty-that is, the association between the dependent and independent variable-is moderated by engagement. That is, conduct moderated regression. In this instance, dishonesty is the dependent variable, whereas workload, engagement, and the product of workload and engagement are the independent variables.
- Second, show the relationship between workload and stress-that is, the association between the dependent variable and mediator-is moderated by engagement. That is, conduct moderated regression again. In this instance, however, stress is the dependent variable, whereas workload, engagement, and the product of workload and engagement are the independent variables.
- Third, repeat the first step, except control the mediator-in this instance, stress. Mediation is established if stress is related to dishonesty, but the interaction between workload and engagement is no longer significant.

Edwards and Lambert (2007) do highlight some subtle problems with this technique. Most of these problems apply to the causal steps approach even when moderators are not examined. Nevertheless, Edwards and Lambert (2007), in their justification of an alternative technique, also argue the causal steps approach might overlook nonlinearities that are formed if a variable moderates both the association between the independent variable and mediator as well as between the mediator and dependent variable. In addition, this technique does not ascertain whether the moderator affects the indirect effect, the direct effect, or both.

### General path analytic framework

Edwards and Lambert (2007) develop another approach to override the problems with previous protocols. This technique, however is more complex-and demands more mathematical knowledge. Readers should examine this paper carefully before they apply the approach.

To simplify this approach, Edwards and Lambert (2007) do provide some sample SPSS syntax, however. The researcher needs to:

- Center all variables, by subtracting the mean from each value
- Substitute dv, iv, mediator, and moderator for the relevant variable names
- Create the relevant product terms as needed for each regression below, by using the transpose menu and the compute option
- Execute the syntax
An example of this syntax is presented below. The first regression relates the independent variable and the moderator to the mediator. The second regression examines whether the association between the mediator and dependent variable is moderated by another variable, after controlling the independent variable. Many other equations, as specified by Edwards and Lambert (2007), also need to be examined, however.

REGRESSION

/DEPENDENT med

/METHOD = ENTER iv mod iv*mod.

REGRESSION

/DEPENDENT dv

/METHOD = ENTER iv med mod med*mod.

- Then, adjust the following syntax to estimate standard errors.
- The numbers in the model program command are the B values generated at each step, where X relates to the iv and Z relates to the moderator

SET RNG=MT MTINDEX=54321

MODEL PROGRAM a05= .04 aX5= .81 aZ5=-.05 aXZ5=-.14 .

COMPUTE PRED = a05 + aX5*iv + aZ5*mod + aXZ5*iv*mod

CNLR med

/OUTFILE=ivmod05. SAV

/BOOTSTRAP=1000 /

SET RNG=MT MTINDEX=54321.

MODEL PROGRAM b020=-.03 bX20= .28 bM20= .31 bZ20= .06 bXZ20=-.13 bMZ20=-.01.

COMPUTE PRED = b020 + bX20*iv+ bM20*med + bZ20*mod + bXZ20*iv*mod + bMZ20*med*mod

CNLR dv

/OUTFILE=ivmod20. SAV

/BOOTSTRAP=1000.

Other regression equations can also be examined, such as:

- DEPENDENT = dv. INDEPENDENT = iv mod iv*mod.
- DEPENDENT = dv. INDEPENDENT = iv mod.

Aiken, L. S., & West, S. G. (1991). ** Multiple regression: Testing and interpreting interactions**. Thousand Oaks, CA:Sage.

Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. **Journal of Personality and Social Psychology**, 5, 1173-1182.

Collins, L. M., G raham, J. W., & Flaherty, B. P. (1998). An alternative framework for defining mediation. ** Multivariate Behavioral Research**, 33, 295-312.

Edwards, J., & Lambert, L. S. (2007). Methods for integrating moderation and mediation: a general analytical framework using moderated path analysis. ** Psychological Methods**, 12, 1-22.

James, L. R., & Brett, J. M. (1984). Mediators, moderators, and tests for mediation. **Journal of Applied Psychology**, 69, 307-321.

Kenny, D. A., K ashy, D. A., & Bolger, N. (1998). Data analysis in social psychology. In D. T. Gilbert & S. T. Fiske (Eds.), The handbook of social psychology(4th ed., Vol. 1, pp. 233-265). New York:McGraw-Hill.

MacKinnon, D. P., K rull, J. L., & Lockwood, C. M. (2000). Equivalence of the mediation, confounding, and suppression effect. ** Prevention Science**, 1, 173-181.

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Muller, D., Judd, C. M., & Yzerbyt, V. Y. (2005). When moderation is mediated and mediation is moderated. **Journal of Personality and Social Psychology**, 89, 852-863

Shrout, P. E., & Bolger, N. (2002). Mediation in experimental and nonexperimental studies: New procedures and recommendations. ** Psychological Methods**, 7, 422-445.

Stolzenberg, R. (1980). The measurement and decomposition of causal effects in nonlinear and nonadditive models. In K. Schuessler (Ed.), Sociological methodology(pp. 459-488). San Francisco:Jossey-Bass.

Stone-Romero, E. F., & Anderson, L. E. (1994). Relative power of moderated multiple regression and the comparison of subgroup correlation coefficients for detecting moderating effects. **Journal of Applied Psychology**, 79, 354-359.

Tate, R. L. (1998). Effect decomposition in interaction and nonlinear models. In R. E. Schumacker & G. A. Marcoulides (Eds.), Interaction and nonlinear effects in structural equation modeling(pp. 167-181). Mahwah, NJ:Erlbaum.

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