Regression Data

Hayes’ Process Macro: Model 4

Model 4 is commonly referred to as the Simple Mediation Model.

The goal of a Simple Mediation Model analyses: to establish the extent to which the predictor variables (X) influences an outcome variable (Y) through one or more mediator variables (Mi).

If a researcher’s goal is to test how X exerts its effect on Y, they may postulate a model in which one or more intervening variables (M) is located between X and Y.

Mediators (Mi): Mediators are conceptualized as the mechanism through which X influences Y.

In a Simple Mediation Model with only one mediator (M1), 2 paths are added to the existing XY analysis, the a & b paths. [XMY]

( ai ) the path from X to M; the relationship between the predictor and the mediator

( bi ) the path from M to Y; the relationship between the mediator and the outcome

( c’ ) the direct effect [X to Y], the relationship between X-Y without mediation.

Main ideal: in a simple mediation model you are looking at whether variation in X is associated with variation in M, which in turn is associated with variation in Y. Assessing mediators allows for assessment of the mechanisms that contribute to an association.

A Simple Mediation Model examines how the effect of X on Y is partitioned into 2 paths: (1) the direct effect; X-Y (2) the indirect effect; X-M-Y.

The mediator = the intervening variable, it answers how X influences Y.

Main Idea: Example using Social Media

Previous research suggests that excessive social media use (X) may reduce life satisfaction (Y). This has been the focus of a lot of research; however, there are A LOT of explanations for how social media use influences well-being. As such, assessing the relationship between social media use (X) and life satisfaction (Y), without considering the mechanisms that potentially mediate this association, adds little to the existing research.

Mediation analysis can provide added information about the mechanisms that influence this association. For example, a researcher may say that social media leads to social isolation/loneliness. This may lead to the following hypotheses: The relationship between Social Media (X) and Life Satisfaction (Y) may have something to do with Social media’s relationship with Loneliness (M); therefore, it is hypothesized that Loneliness may be a mechanism by which Social Media exerts its influence on Life Satisfaction.

Social Media Example: How does social media influence life satisfaction? Possible through its relationship with loneliness.

In order to support this hypothesized model, you would want to find that the X is associated with M & that the M is associated with Y; however, the MAIN goal/hypothesis would be to find evidence of a significant Indirect Effect.

Whereas the direct effect ( c’ ) is the relationship between X-Y, the indirect effect is evidence that the mediator (e.g., loneliness) mediates the relationship between X-Y.

Example Hypotheses:

Hypotheses 1: Social media use will be significantly associated with Loneliness (a path)

Hypotheses 2: Loneliness will be associated with Life Satisfaction (b path)

Hypotheses 3: Loneliness (M1) will significantly negatively mediate the indirect effect of social media use (X) on life satisfaction (Y).

You could have a hypotheses about the direct effect; however, typically the focus is on the indirect pathway.

The process of assessing a mediation model is related to the Causal Steps. That is, you want to know the individual paths (a path, b path, c’ path) before you assess the Indirect Effect (the primary focus). You want to piece all the information together to interpret the results.

1) the effect of X on M

(?) does variation in X cause variation in M

2) the effect of M on Y

(?) does variation in M cause variation in Y

3) the effect of X on Y through M.

(?) does variation in X cause variation in Y as a product of the X-M & M-Y variation.

Estimation of the Direct, Indirect, and Total Effects of X.

In OLS regression (as used in Hayes Process Macro), an effect tells us about the association between variables. If X has a positive direct effect on Y, it tells us that higher levels of X should be associated with higher levels of Y. However, in the Social Media example, the effect of M on Y should be negative; as such, we would expect higher levels of Loneliness to be associated with lower levels of Life Satisfaction.

The indirect effect is the product of the a & b paths exemplified in the figure above. That is, if the effect of X on M = .05 and the effect of M on Y = 1.3 [ .05 x 1.3] then the indirect effect of X on Y through M = 0.65.

*Included below is an example of a SPSS output of a Simple Mediation Model, using Hayes’ Process Macro [using social media example].

What to look at in the output:

1. ( coeff): the effect, the sign (+ or -)

2. ( LLCI & ULCI): the confidence interval. This, in combination with the p-value (significance; p >.05) will tell you if the effect is significant or not. First look at the LLCI, then look at the ULCI, if the two numbers do not cross 0 than your effect is significant. For example, if the LLCI = .3143 and the ULCI = .6986 the effect is significant because both are positive and do not cross zero.

1st: it will go over the Model of M; the effect of X on M (a path)

The Model of M

If you look at the Model Summary, you can see the p-value = .077. As the significance level is typically >.05, the model of M is not significant as .077 is greater than .05. More evidence of this can be seen in the stats presented to the right of SocHours (the label for social media) under ‘Model’.

· The variables under “model” are being assessed for their relationship to the ‘OUTCOME VARIABLE’ presented above [SocHours ULS8].

· The effect ( b coeff) = .040; however, the LLCI = -.004 and the ULCI = .083. As such, the effect is not significant as the CI’s include zero.

· Therefore, the a-path was not supported.

2nd: the Model of Y; the effect of X on Y (C’ path) & the effect of M on Y (b path).

If you look under Model Summary, the Model of Y is significant at the p = .05 level (p < .05), evidence for this appears below.

If you look at the stat statements for Social Media [the effect of X on Y], b = -.012 (the effect); however, the LLCI & ULCI includes zero, so the direct effect of Social media (X) on Life Satisfaction (Y) is not significant.

In contrast, if you look at the effect of the mediator, Loneliness (ULS8), it has a significant negative effect [b = -1.501, LLCI = -1.845, ULCI = -1.157]. As the confidence intervals do not include zero and both are negative, we can conclude that the mediator (Loneliness) has a significant negative effect on Life satisfaction (Y). Therefore, evidence has been found for the b-path.

3rd: the Indirect Effects [mediation].

The indirect effect of X on Y through M: Is X’s effect on Y transmitted through M? [ The XMY causal chain] .

Under ‘Direct effect of X on Y’ we see again that the direct effect (c’ path) of Social Media (X) on Life Satisfaction (Y) was not significant.

Under ‘Indirect effect of X on Y’ we see that the indirect effect of Social Media (X) on Life Satisfaction (Y) through Loneliness was significant [ b =-.059, LLCI = -.047, ULCI = -.003.

As such, X does not affect Y directly; however, X affects Y indirectly through M. This supports the idea the loneliness may be the mechanism by which X transmits a significant effect on Y.

*Below is a statistical figure of the social media model and a statistical write up of these results.

Model Results: dotted lines = non-significant; full lines represent significant effect

Results write-up:

Individual pathways.

A model was proposed in which loneliness would mediate the relationship between social media use and life satisfaction. Hayes’ Process Macro (2018) produced regression coefficients, p values, and confidence intervals for each of the regressions included in the simple mediation model. In contrast to what was hypothesized (hypothesis 1), social media use was not found to have a significant effect on loneliness ( b = .040, SE = .022, CI = [-.004 to .083]); however, consistent with what was hypothesized (hypothesis 2), Loneliness was found to transmit a significant negative effect on life satisfaction ( b = -1.501, SE = .175, CI = [-1.845 to -1.157]).

In terms of the direct effect, findings indicated that social media did not have a significant direct effect on life satisfaction ( b = -.012, SE = .076, CI = [-.161 to .137]); as such, findings suggest that social media, on its own, does not influence life satisfaction.

Mediation.

Lastly, findings provided support for hypothesis 3, that social media use would have a significant negative indirect effect on life satisfaction through loneliness ( b = -.059, SE = .106, CI = [-.047 to -.003]); that is, findings suggest that loneliness significantly mediates the association. Though both the initial direct relationship between social media use and life satisfaction and the effect of social media on loneliness were both found to not be significant, findings provided support for the full indirect effect of the mediation model. As such, results provide support that the effect of social media on life satisfaction may be partially explained by the mediating influence of loneliness.