# Mediated relationship definition of single

### Mediation (David A. Kenny)

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Such a design implies that one manipulates some controlled third variable that they have reason to believe could be the underlying mechanism of a given relationship. Such a design implies that one measures the proposed intervening variable and then uses statistical analyses to establish mediation. This approach does not involve manipulation of the hypothesized mediating variable, but only involves measurement. First, it is important to have strong theoretical support for the exploratory investigation of a potential mediating variable.

A criticism of a mediation approach rests on the ability to manipulate and measure a mediating variable. Thus, one must be able to manipulate the proposed mediator in an acceptable and ethical fashion.

As such, one must be able to measure the intervening process without interfering with the outcome. The mediator must also be able to establish construct validity of manipulation. One of the most common criticisms of the measurement-of-mediation approach is that it is ultimately a correlational design. Consequently, it is possible that some other third variable, independent from the proposed mediator, could be responsible for the proposed effect. However, researchers have worked hard to provide counter evidence to this disparagement.

Specifically, the following counter arguments have been put forward: For example, if the independent variable precedes the dependent variable in time, this would provide evidence suggesting a directional, and potentially causal, link from the independent variable to the dependent variable.

See other 3rd variables below. Mediation can be an extremely useful and powerful statistical test, however it must be used properly.

It is important that the measures used to assess the mediator and the dependent variable are theoretically distinct and that the independent variable and mediator cannot interact. Should there be an interaction between the independent variable and the mediator one would have grounds to investigate moderation.

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.

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.

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.

## Mediated communication

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.

## Mediation (statistics)

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. 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.

Mediation is not defined statistically; rather statistics can be used to evaluate a presumed mediational model.

- A General Model for Testing Mediation and Moderation Effects

Mediation is a very popular topic. This page averages over visitors a day and Baron and Kenny has over 70, citations, according to Google Scholar, and there are four books on the topic Hayes, ; Jose, ; MacKinnon, ;VanderWeele, There are several reasons for the intense interest in this topic: One reason for testing mediation is trying to understand the mechanism through which the causal variable affects the outcome. Mediation and moderation analyses are a key part of what has been called process analysis, but mediation analyses tend to be more powerful than moderation analyses.

Moreover, when most causal or structural models are examined, the mediational part of the model is often the most interesting part of that model. The Four Steps If the mediational model see above is correctly specified, the paths of c, a, b, and c' can be estimated by multiple regressionsometimes called ordinary least squares or OLS.

In some cases, other methods of estimation e. Regardless of which data analytic method is used, the steps necessary for testing mediation are the same. This section describes the analyses required for testing mediational hypotheses [previously presented by Baron and KennyJudd and Kennyand James and Brett ]. See also Frazier, Tix, and Barron for a more contemporary introduction. We note that these steps are at best a starting point in a mediational analysis.

More contemporary analyses focus on the indirect effect. Show that the causal variable is correlated with the outcome. Use Y as the criterion variable in a regression equation and X as a predictor estimate and test path c in the above figure. This step establishes that there is an effect that may be mediated.

Show that the causal variable is correlated with the mediator. Use M as the criterion variable in the regression equation and X as a predictor estimate and test path a. This step essentially involves treating the mediator as if it were an outcome variable. Show that the mediator affects the outcome variable. 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. 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.

### A General Model for Testing Mediation and Moderation Effects

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.

### Mediation (statistics) - Wikipedia

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.