Mediation (statistics)

Baron and Kenny (1986) laid out several requirements that must be met to form a true mediation relationship.

Relationship Duration The following example, drawn from Howell (2009),[6] explains each step of Baron and Kenny's requirements to understand further how a mediation effect is characterized.

Sometimes there is actually a significant relationship between independent and dependent variables but because of small sample sizes, or other extraneous factors, there could not be enough power to predict the effect that actually exists.

[8][9] In linear systems, the total effect is equal to the sum of the direct and indirect (C' + AB in the model above).

Thus, it is imperative to show a significant reduction in variance explained by the independent variable before asserting either full or partial mediation.

This implies that the terms 'partial' and 'full' mediation should always be interpreted relative to the set of variables that are present in the model.

The Sobel test is more accurate than the Baron and Kenny steps explained above; however, it does have low statistical power.

As such, large sample sizes are required in order to have sufficient power to detect significant effects.

The Preacher and Hayes bootstrapping method is a non-parametric test and does not impose the assumption of normality.

[14] Bootstrapping involves repeatedly randomly sampling observations with replacement from the data set to compute the desired statistic in each resample.

Computing over hundreds, or thousands, of bootstrap resamples provide an approximation of the sampling distribution of the statistic of interest.

The Preacher–Hayes method provides point estimates and confidence intervals by which one can assess the significance or nonsignificance of a mediation effect.

Bootstrapping[15][16] is becoming the most popular method of testing mediation because it does not require the normality assumption to be met, and because it can be effectively utilized with smaller sample sizes (N < 25).

However, mediation continues to be most frequently determined using the logic of Baron and Kenny[17] or the Sobel test.

First, it is important to have strong theoretical support for the exploratory investigation of a potential mediating variable.

Specifically, the following counter-arguments have been put forward:[4] Mediation can be an extremely useful and powerful statistical test; however, it must be used properly.

They include common sources of measurement error (as discussed above) as well as other influences shared by both the independent and dependent variables.

Any of these problems may produce spurious relationships between the independent and dependent variables as measured.

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.

Such variables further characterize interactions in regression by affecting the direction and/or strength of the relationship between X and Y.

Regression analyses revealed that the type of prime (morality vs. might) mediated the moderating relationship of participants’ social value orientation on PDG behaviour.

Mediation analysis quantifies the extent to which a variable participates in the transmittance of change from a cause to its effect.

Traditionally, however, the bulk of mediation analysis has been conducted within the confines of linear regression, with statistical terminology masking the causal character of the relationships involved.

The source of these difficulties lies in defining mediation in terms of changes induced by adding a third variables into a regression equation.

The basic premise of the causal approach is that it is not always appropriate to "control" for the mediator M when we seek to estimate the direct effect of X on Y (see the Figure above).

Unfortunately, "controlling for M" does not physically prevent M from changing; it merely narrows the analyst's attention to cases of equal M values.

Moreover, the language of probability theory does not possess the notation to express the idea of "preventing M from changing" or "physically holding M constant".

The result is that, instead of physically holding M constant (say at M = m) and comparing Y for units under X = 1' to those under X = 0, we allow M to vary but ignore all units except those in which M achieves the value M = m. These two operations are fundamentally different, and yield different results,[23][24] except in the case of no omitted variables.

In non-linear systems, more stringent conditions are needed for estimating the direct and indirect effects.

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