Using Hayes’ Process macro to test models involving simple, parallel, and sequential mediation
In this presentation, I demonstrate how to use the Process macro to test for simple, parallel, and sequential mediation using Models 4 and 6.
A copy of this Powerpoint can be downloaded from the link under the video description. Please consider downloading it, as it goes into more detail than I can provide in a timely fashion in this video. Also, a link to the data is provided under the video description as well.
**All diagrams in this Powerpoint were drawn using the AMOS program. These are to illustrate the models being tested. Process does not produce diagrams of the type I include in this presentation.
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Simple, parallel, and multiple mediation using Process macro
Simple mediation model
Parallel mediation model (2 mediators)
Sequential mediation with two mediators
In this simple mediation model (as discussed by Baron & Kenny, 1986), we have paths ‘a’, ‘b’, and ‘c’ being estimated. The paths you see in this model (and any mediation model) are referred to as direct effects. In short, the model is specified such that the X has a direct effect on the mediator (M), with the mediator having a direct effect on the outcome (Y). X is also presumed to have a direct effect on Y. Mediation is evidenced when there is evidence that the indirect effect of X on Y flows through mediator (M). The indirect effect in this model is computed as the product of paths ‘a’ and ‘b’: IE=a*b.
So in mediation models, effects are described in terms of direct effects (represented with the single- headed arrows) and indirect effects (which are the products of paths that trace from one variable to another via one or more mediators).
Finally, we can speak of the total effect of X on Y. It is simply the sum of all direct and indirect effects from X to Y. So, in this simple model, the total effect of X on Y is: DE + IE = c + a*b
Note: Conventionally path c is referred to as ‘c-prime’
(as it is a partial regression slope). However,
throughout this Powerpoint, I will be naming the path as ‘c’ with the understanding that it is not reflecting a zero-order relationship, but rather that it is a partial regression slope. This will come in handy later in more complex mediation models.
In the context of mediation analysis, the classic “independent” and “dependent” variable designations break down. This is because mediating variables take on the roles of both independent and dependent variable.
Instead of referring to variables as “independent” and “dependent”, we will refer to variables within mediation models as either being “exogenous” or “endogenous” (Kline, 2016). Exogenous variables are those that are not predicted by any others within a system of variables. As such, these variables do not have arrows drawn to them. Endogenous variables are those that are predicted by others within a system. These variables have arrows pointed at them. Because endogenous variables are predicted by others within the system, they have prediction error associated with them (see model on the right using SEM diagramming).
Baron & Kenny (1986) conceptual model SEM model with error terms included
Using OLS regression, the path coefficients in this mediation model can be broken down into two regression models: (a) a simple regression with X predicting the mediator; (b) multiple regression with both X and the mediator predicting Y.
For our examples, we will be using a dataset containing continuous measures of student
achievement, performance goals, mastery goals, interest, and anxiety. We also have a dummy coded variable reflecting gender identification (coded 0=identified male, 1=identified female).
This dataset can be downloaded from:
https://drive.google.com/open?id=1SRKpaJMQ-LkhM0DCbtFeBoRGS2akgTy0
Example 1: We are testing whether the effect of mastery goals on student
achievement is mediated by interest. This is an example of a simple mediational model.
Set Model to 4
The indirect and total effects in the model are tested using bootstrap samples. The default setting for confidence intervals is 95%. You can change this and the number of bootstrap samples.
Although we are not doing so in this example, it is possible to include
additional covariates in your mediation models.
Under options, you can click on Effect size & request Standardized coefficients, etc.
We see that in the first (simple) regression, mastery goals is a significant (positive)
predictor of interest (b=.7701, s.e.=.0858, p<.001). This coefficient reflects the direct effect of mastery on interest within the path model. [Notice that the standardized path coefficient is also provided, which is .6073.]
We see that in the second regression, both mastery goals (b=.3613, s.e.=.0768, p<.001) and interest
(b=.2106, s.e.=.0606, p=.0007) are significant, positive predictors of achievement. These coefficients reflect the direct effects of both interest and mastery goals on achievement within the path model.
[The standardized path coefficients for this portion of the model are .3967 and .2932 for mastery and interest, respectively.]
The unstandardized indirect effect (.1622) of interest is calculated as the product of paths a (.7701) and b (.2106) from the previous regression models.
This indirect effect is tested using bootstrap standard errors and confidence intervals.
The null hypothesis is that the population indirect effect is zero, whereas the alternative is that the population indirect effect is non-zero. So if zero falls between the lower and upper bound of the
confidence interval (again, the default is 95%), then you maintain the null. If zero falls outside of the interval, then you reject the null.
Here, we reject the null.
Note: If you are following along with this presentation with the data provided, the bootstrap standard errors and confidence intervals may not be exactly the same as you see here. This is due to the resampling process.
Nevertheless, the values should be close.
This is the total effect of X on Y, computed as DE + IE
= .3613 + .1622 = .5325. Because zero (the null) does not fall between the lower and upper bound of the 95% confidence interval, we infer that total effect of mastery goals on achievement is significantly
different from zero.
The c_ps is the partially standardized total effect. It is computed as the total effect/sy, where sy is the standard deviation for Y.
The standard deviation for the Y variable is 1.274432. So, the partially standardized total effect is: .5235/ 1.274432 = .4108.
The c’_ps is the partially standardized direct effect. It is
computed as the direct effect/Sy. Given the abovementioned standard deviation for Y, the partially standardized direct effect is: .3613/ 1.274432 = .2835.
For more details, see Hayes (2018, p. 134-135).
The c_cs is the completely standardized total effect. It is
computed as c_ps * Sx, where Sx is the standard deviation for X (in this case, mastery goals).
The standard deviation for the X (mastery) variable is 1.399233.
So, the completely standardized total effect is: .4108* 1.399233
= .5748.
The c’_cs is the completely standardized direct effect. It is
computed as c’_ps * Sx, where Sx is the standard deviation for X.
The completely standardized direct effect is: .2835* 1.399233 = . 3967.
For more details, see Hayes (2018, p. 134-135).
The partially standardized indirect effect is computed the
unstandardized indirect effect divided by the standard deviation for Y: i.e., ab/ Sy. The standard deviation for Y is (again) 1.274432.
As such, the partially standardized indirect effect is: .1622/
1.274432 = .127.
For more details, see Hayes (2018, p. 134-135).
The standardized indirect effect is computed as the product of the standardized paths ‘a’ and ‘b’:
IE=.6073*.2932=.178. We see this effect is significant, as 0 does not fall between the lower and upper
bound of the confidence interval.
Note: This effect is also computed by multiplying the partially standardized indirect effect by the standard deviation for X.
Example 2: We are testing whether the effect of mastery goals on student
achievement is mediated by both interest and anxiety. This is an example of a parallel mediational model.
As before, mastery goals is a significant (positive) predictor of interest (b=.7701, s.e.=.0858, p<.001). This coefficient reflects the direct effect of mastery on interest within the path model. [Notice that the
standardized path coefficient is also provided, which is .6073.]
Mastery goals is a significant negative predictor of anxiety (b=-.3992, s.e.=.0949, p<.001). The standardized regression
coefficient for this path is -.3371.
Mastery goals is a significant positive predictor of achievement (b=.3449, s.e.=.0801, p<.001), as is interest (b=.2109, s.e.=.0607, p=.0007). Anxiety, however, is not a significant predictor of achievement (b=-.0404, s.e.=.0549, p=.4627).
These are unstandardized indirect effects. The unstandardized indirect effect of mastery on achieve via the first mediator (interest) was .1625 and was statistically significant (given 0 does not fall within the confidence interval). The
unstandardized indirect effect of mastery on achieve via the second mediator (anxiety) was .0161, but was not statistically significant as 0 falls between -.0301 and .0698). Both of these effects are referred to as specific indirect effects.
The total indirect effect is the sum of the two specific indirect effects; and this can also be tested. The total indirect effect is . 1625+.0161 = .1786. The total indirect effect is statistically significant as 0 falls outside the confidence interval.
The remaining output is interpreted in the same fashion as that with Example 1.
Example 3: We are testing whether the effect of mastery goals on student
achievement is mediated by both interest and anxiety. It includes serial mediation as the effect of mastery goals on anxiety flows through interest and then anxiety, where the effect of interest on achievement itself is mediated by anxiety.
To perform sequential (serial) mediation, you will need Model Number 6.
Also include the mediators in the Mediator(s) M box in the order in which they are supposed to appear in the model. Because interest
(M1) is antecedent to anxiety (M2), it is entered first.
Indirect effect 1 (.1625) is computed as: path a * path e Indirect effect 2 (.0164) is computed as: path d * path c
Indirect effect 3 (-.0003) is computed as: path a * path b * path c The total indirect effect is computed as: Ind1+Ind2+Ind3 = .1786.
Example 4: Here we are building on Example 3 by adding in a covariate (performance goals).
In our previous model, we only had mastery as a predictor of interest. Here, performance goals is added as a predictor to control for its effects from the relationship between mastery and interest.
In our previous model, we only had mastery and interest as predictors of anxiety. Performance goals is added to this portion of the model as a predictor to control for its effect on the relationships between mastery and interest and anxiety.
In our previous model, we only had mastery, interest, and anxiety as predictors of achieve. Performance goals is added to this portion of the model as a predictor to control for its effect on the relationships between the
aforementioned predictors and achieve.
(Remaining output is not shown. However, it is interpreted the same way as in previous examples, with controls for Performance goals.)
References
Baron, R.M., Kenny, D.A. (1986). The mediator-moderator distinction in social psychological research:
Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, 1173-1182. [Downloaded July 7 from https://www.sesp.org/files/The%20Moderator-Baron.pdf ]
Hayes, A.F. (2018). Introduction to mediation, moderation, and conditional process analysis: A regression- based approach. New York: The Guilford Press.
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