# Mediating relationship example for references

### Guidelines for the Investigation of Mediating Variables in Business Research

References. 1. The moderator-mediator variable distinction in social Required sample size to detect the mediated effect. References The effect of X on Y may be mediated by a process or mediating variable M, and the variable X may still affect Y. The . One example of inconsistent mediation is the relationship between stress and mood as mediated by coping. The moderator-mediator variable distinction in social the study of mediators and moderators: Examples from the child-clinical and.

The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, Work stress and alcohol effects: A test of stress-induced drinking. Journal of Health and Social Behavior, 31, Moving beyond the keg party: A daily process study of college student drinking motivations.

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Psychology of Addictive Behaviors, 19, A theoretical discussion of the structure, causes and consequences of affective experiences at work. Other third variables[ edit ] 1 Confounding: Another model that is often tested is one in which competing variables in the model are alternative potential mediators or an unmeasured cause of the dependent variable. An additional variable in a causal model may obscure or confound the relationship between the independent and dependent variables.

### Statistical analysis for identifying mediating variables in public health dentistry interventions

Potential confounders are variables that may have a causal impact on both the independent variable and dependent variable. They include common sources of measurement error as discussed above as well as other influences shared by both the independent and dependent variables. In experimental studies, there is a special concern about aspects of the experimental manipulation or setting that may account for study effects, rather than the motivating theoretical factor.

Any of these problems may produce spurious relationships between the independent and dependent variables as measured. Ignoring a confounding variable may bias empirical estimates of the causal effect of the independent variable. A suppressor variable increases the predictive validity of another variable when included in a regression equation.

Suppression can occur when a single causal variable is related to an outcome variable through two separate mediator variables, and when one of those mediated effects is positive and one is negative.

**8.6: Pass by Value vs. Pass by Reference - Processing Tutorial**

In such a case, each mediator variable suppresses or conceals the effect that is carried through the other mediator variable. For example, higher intelligence scores a causal variable, A may cause an increase in error detection a mediator variable, B which in turn may cause a decrease in errors made at work on an assembly line an outcome variable, X ; at the same time, intelligence could also cause an increase in boredom Cwhich in turn may cause an increase in errors X.

Thus, in one causal path intelligence decreases errors, and in the other it increases them. When neither mediator is included in the analysis, intelligence appears to have no effect or a weak effect on errors. However, when boredom is controlled intelligence will appear to decrease errors, and when error detection is controlled intelligence will appear to increase errors. If intelligence could be increased while only boredom was held constant, errors would decrease; if intelligence could be increased while holding only error detection constant, errors would increase.

In general, the omission of suppressors or confounders will lead to either an underestimation or an overestimation of the effect of A on X, thereby either reducing or artificially inflating the magnitude of a relationship between two variables. Other important third variables are moderators. Moderators are variables that can make the relationship between two variables either stronger or weaker. A moderating relationship can be thought of as an interaction.

It occurs when the relationship between variables A and B depends on the level of C. See moderation for further discussion.

Moderated mediation[ edit ] Mediation and moderation can co-occur in statistical models. It is possible to mediate moderation and moderate mediation.

Essentially, in moderated mediation, mediation is first established, and then one investigates if the mediation effect that describes the relationship between the independent variable and dependent variable is moderated by different levels of another variable i. The second possible model of moderated mediation involves a new variable which moderates the relationship between the independent variable and the mediator the A path. The third model of moderated mediation involves a new moderator variable which moderates the relationship between the mediator and the dependent variable the B path.

## Mediation (statistics)

Moderated mediation can also occur when one moderating variable affects both the relationship between the independent variable and the mediator the A path and the relationship between the mediator and the dependent variable the B path.

The fifth and final possible model of moderated mediation involves two new moderator variables, one moderating the A path and the other moderating the B path.

Mediated moderation[ edit ] Mediated moderation is a variant of both moderation and mediation. This is where there is initially overall moderation and the direct effect of the moderator variable on the outcome is mediated. The main difference between mediated moderation and moderated mediation is that for the former there is initial overall moderation and this effect is mediated and for the latter there is no moderation but the effect of either the treatment on the mediator path A is moderated or the effect of the mediator on the outcome path B is moderated.

Use Y as the criterion variable in a regression equation and X and M as predictors estimate and test path b.

It is not sufficient just to correlate the mediator with the outcome because the mediator and the outcome may be correlated because they are both caused by the causal variable X.

## Guidelines for the Investigation of Mediating Variables in Business Research

Thus, the causal variable must be controlled in establishing the effect of the mediator on the outcome. To establish that M completely mediates the X-Y relationship, the effect of X on Y controlling for M path c' should be zero see discussion below on significance testing. The effects in both Steps 3 and 4 are estimated in the same equation. If all four of these steps are met, then the data are consistent with the hypothesis that variable M completely mediates the X-Y relationship, and if the first three steps are met but the Step 4 is not, then partial mediation is indicated.

Meeting these steps does not, however, conclusively establish that mediation has occurred because there are other perhaps less plausible models that are consistent with the data. Some of these models are considered later in the Specification Error section.

James and Brett have argued that Step 3 should be modified by not controlling for the causal variable. Their rationale is that if there were complete mediation, there would be no need to control for the causal variable.

However, because complete mediation does not always occur, it would seem sensible to control for X in Step 3. Note that the steps are stated in terms of zero and nonzero coefficients, not in terms of statistical significance, as they were in Baron and Kenny Because trivially small coefficients can be statistically significant with large sample sizes and very large coefficients can be nonsignificant with small sample sizes, the steps should not be defined in terms of statistical significance.

Statistical significance is informative, but other information should be part of statistical decision making. For instance, consider the case in which path a is large and b is zero. It is very possible that the statistical test of c' is not significant due to the collinearity between X and Mwhereas c is statistically significant. Using just significance testing would make it appear that there is complete mediation when in fact there is no mediation at all. Following, Kenny, Kashy, and Bolgerone might ask whether all of the steps have to be met for there to be mediation.

Most contemporary analysts believe that the essential steps in establishing mediation are Steps 2 and 3. Certainly, Step 4 does not have to be met unless the expectation is for complete mediation.

### The Three Most Common Types of Hypotheses | Savvy Statistics

In the opinion of most though not all analysts, Step 1 is not required. See the Power section below why the test of c can be low power, even if paths a and b are non-trivial. Inconsistent Mediation If c' were opposite in sign to ab something that MacKinnon, Fairchild, and Fritz refer to as inconsistent mediation, then it could be the case that Step 1 would not be met, but there is still mediation. In this case the mediator acts like a suppressor variable.

One example of inconsistent mediation is the relationship between stress and mood as mediated by coping. Presumably, the direct effect is negative: However, likely the effect of stress on coping is positive more stress, more coping and the effect of coping on mood is positive more coping, better moodmaking the indirect effect positive.

The total effect of stress on mood then is likely to be very small because the direct and indirect effects will tend to cancel each other out. Note too that with inconsistent mediation that typically the direct effect is even larger than the total effect. The amount of mediation is called the indirect effect.

In contemporary mediational analyses, the indirect effect or ab is the measure of the amount of mediation.

However, the two are only approximately equal for multilevel models, logistic analysis and structural equation modeling with latent variables. Note also that the amount of reduction in the effect of X on Y due to M is not equivalent to either the change in variance explained or the change in an inferential statistic such as F or a p value. It is possible for the F from the causal variable to the outcome to decrease dramatically even when the mediator has no effect on the outcome!

It is also not equivalent to a change in partial correlations. The way to measure mediation is the indirect effect.