Mediational models are concerned with explaining the mechanism by which an independent variable exerts its influence on a dependent variable. For example, it has been shown that among young women body dissatisfaction has a negative relationship with exercise behaviour. Thus the greater the dissatisfaction, the less exercise is engaged in. An obvious question to ask is "what explains this negative relationship?". In other words, what is the mechanism by which greater dissatisfaction leads to less exercise, or what mediates the relationship?

A number of variables could be hypothesised as mediators in this case. One obvious candidate is social physique anxiety (SPA). SPA represents concerns about having one's body negatively evaluated by others. It would seem reasonable to hypothesise that higher levels of dissatisfaction with one's body would lead one to have greater social physique anxiety, which in turn would lead one to be less likely to exercise because of fears about how others in exercise settings would evaluate one's body.

Mediated relationships can be represented graphically as follows:

In above example, the independent variable (IV) is body dissatisfaction, the mediating variable (MV) is social physique anxiety and the dependent variable (DV) is exercise.

Testing for mediation

This lesson explains informal procedures for testing for mediation, as described by Barron and Kenny (1986) as well as a more formal procedure that gives a fuller test of the extent to which the effect of the IV exerts an indirect effect on the DV through the MV, known as the Sobel Test.

Testing for mediation involves establishing four conditions:

1.
The IV is significantly related to the DV (path c).
2.
The IV is significantly related to the MV (path a).
3.
The MV is significantly related to the DV (path b).
4.
When controlling for the effects of the MV on the DV, the effect of the IV on the DV (path c) is no longer significant.

These conditions are tested by performing three separate regression analyses:

Analysis One

First, the DV is regressed on the IV (path c). The standardised regression coefficient (beta) is examined to determine the size and direction of the relationship and whether it is significant. Note that as this is a simple regression (only one IV) the beta is the same as the bivariate correlation between the two variables. If this relationship is not significant, there can be no mediation as there is no relationship to mediate!

Analysis Two

Second, the MV is regressed on the IV (path a) and the beta examined for its size, direction and significance. Again, this is just the same as the bivariate correlation. If this relationship is not significant, then the hypothesised MV cannot be a mediator.

Analysis Three

Finally a hierarchical regression analysis is performed in two steps.

At Step One the DV is regressed on the MV (path b). At Step Two the DV is regressed on the IV again (path c).

The beta for path b at Step One is examined to determine the strength, direction and significance of the relationship between the MV and the DV. If this is not significant, then again there can be no mediation by that hypothesised MV.

The beta for path c at Step Two is now examined. If the hypothesised MV is indeed a mediator, then the significant relationship between the IV and the DV established in the first analysis should no longer be significant. That is, when controlling for the effects of the MV on the DV (by entering it first into the analysis), the effects of the IV are no longer significant.

 

In order to illustrate how to implement these procedures in SPSS, I will use some data collected from the SSHES Research Methods I class. These data are concerned with the extent to which students' self-regulation for studying research methods is controlled (i.e. they only do it because they have to rather than because it is personally important to them) influences their exam performance. Specifically, I hypothesise that being more controlled in one's regulation will be negatively related to exam performance and that this relationship is mediated by intrinsic motivation for studying research methods:

 

 

The data were collected longitudinally, with controlled regulation measured at week five in the course, intrinsic motivation at the end and exam performance several weeks later.

Analysis One

Open the data file in SPSS, click on Analyze/Regression/Linear:

 

 

Now transfer the DV to the Dependent: box and the IV to the Independent(s): box using the arrow buttons and click on OK:

 

 

Tables 1.1 - 1.3 show the results of this first regression analysis:

Table 1.1

 

This table shows the multiple R (.159), which in this case is the same as the bivariate correlation between the variables, as there is only one predictor. The R Square shows that only 2.5% of the variance in exam performance is predicted by controlled regulation.

Table 1.2

Although only a small amount of variance is explained in exam performance by controlled regulation, this table shows that the relationship (the R) is significant (F = 6.753, p = .01).

Table 1.3

This table shows the regression coefficients. As there is only one predictor, the Beta (-.159) and its significance are the same as the R and its significance shown in Tables 1.1 and 1.2. However, we can now see that the direction of the relationship is negative: as predicted, the more controlled the regulation, the lower the exam score. The results of this analysis show that the first condition for mediation has been met; the IV is significantly related to the DV (path c).

Analysis Two

Now you perform exactly the same analysis but with the MV as the dependent variable (in this example, intrinsic motivation, labelled INTMOT)

Tables 2.1 - 2.3 show the results of this second regression analysis:

Table 2.1

This shows that controlled regulation explains 4.9% of the variance in intrinsic motivation.

Table 2.2

This shows that the relationship between controlled regulation and intrinsic motivation is significant (F = 7.524, p = .007).

Table 2.3

The beta shows that the relationship between controlled regulation and intrinsic motivation is negative: the more controlled the regulation the less intrinsically motivated the student is, as predicted. The analysis shows that the second condition for mediation has been satsified (path a: the IV and MV are significantly related).

Analysis Three

Now you perform the final, hierarchical regression analysis. Open the regression dialogue box and transfer the DV to the Dependent: box and the MV to the Independent(s): box:

 

 

Now click the Next button and transfer the IV to the Independent(s): box:

 

 

You have now set up the two steps in the hierarchical analysis. The MV is entered at block one and the IV at block two. Now click on Statistics and check the R squared change box:

 

 

Click Continue and then OK to run the analysis.

Tables 3.1 - 3.3 show the results of the third analysis:

Table 3.1

 

This shows the two steps in the analysis. At step one, intrinsic motivation explains 4.9% of the variance in exam performance (R square = .049). At step two, controlled regulation does not add significantly to the variance explained (R square change = .005, p = .394).

Table 3.2

This shows that the variance explained by intrinsic motivation is significant (F = 7.201, p = .008).

Table 3.3

The regression coefficients at step two (along with the results in Tables 3.1 and 3.2) show that intrinsic motivation is significantly (and positively) related to exam performance, thus meeting the third condition for mediation (path b: the MV is significantly related to the DV). The beta for controlled regulation (path c), which was significant in the first analysis, is now no longer significant when controlling for the effects of the MV, intrinsic motivation. Thus the final condition for demonstrating mediation has also been met.

Reporting the results

The results of a mediated regression analysis can be reported in a table like this:

It is also useful to present a graphic showing the regression coefficients, with the coefficients for the effect of the IV on the DV in both analysis one and analysis three, with the latter in parentheses:

 

 

Full versus partial mediation

If the effect of the IV on the DV becomes non-significant at the final step in the analysis, full mediation is demonstrated. That is, all of the effects are mediated by the MV. In many cases this might not be a reasonable expectation. There might be several mechanisms by which the IV exerts its influence on the DV, or it might have direct as well as indirect effects. If the regression coefficient is substantially reduced at the final step, but remains significant, we can say that there is partial mediation. That is, part of the effect of the IV is mediated by the MV but other parts are either direct or mediated by other variables not included in the model.

Indirect effects and the Sobel Test

The above procedures provide tests of the conditions necessary to demonstrate mediation. However, they do not indicate the size of the indirect effect, nor whether or not the indirect effect of the IV through the MV is significant.

The size of the indirect effect is calculated as the product of the direct effects of the IV on the MV and the MV on the DV. In the above example, then, the indirect effect is -.222 * .205 = -.045.

The Sobel Test tests whether the indirect effect of the IV on the DV through the MV is significantly greater than zero. The test requires the unstandardised regression coefficients for paths a and b and their standard errors, which are obtained when running the second and third regression analyses. You can access further details and an easy to use online interactive calculator for the Sobel Test from Kristopher Preacher's site at the University of North Carolina by clicking here. A Sobel test performed on the example in this lesson shows that the indirect effect of controlled regulation on exam performance through intrinsic motivation is significant (p < .05).

Note that the Sobel test lacks power for detecting significant indirect effects with small samples and/or small effect sizes. Kristopher Preacher's site also provides instructions and macros for performing an alternative, bootstrapping method of testing for mediation which is recomended for smaller samples. The macro also provides results for the Baron and Kenny approach in one easy step. A further macro is provided for simultaneous testing of models with multiple mediators.

 

References

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, 51, 1173-1182.