Mediation (statistics)

565:. The effect of an independent variable on the dependent variable can become nonsignificant when the mediator is introduced simply because a trivial amount of variance is explained (i.e., not true mediation). Thus, it is imperative to show a significant reduction in variance explained by the independent variable before asserting either full or partial mediation. It is possible to have statistically significant indirect effects in the absence of a total effect. This can be explained by the presence of several mediating paths that cancel each other out, and become noticeable when one of the cancelling mediators is controlled for. 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. In all cases, the operation of "fixing a variable" must be distinguished from that of "controlling for a variable," which has been inappropriately used in the literature. The former stands for physically fixing, while the latter stands for conditioning on, adjusting for, or adding to the regression model. The two notions coincide only when all error terms (not shown in the diagram) are statistically uncorrelated. When errors are correlated, adjustments must be made to neutralize those correlations before embarking on mediation analysis (see 788:

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:

902:). 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. 848: 714:

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. Point estimates reveal the mean over the number of bootstrapped samples and if zero does not fall between the resulting confidence intervals of the bootstrapping method, one can confidently conclude that there is a significant mediation effect to report.

2939: 481: 3621: 1085: 1067: 1053: 1039: 1025: 1105: 31: 3608: 529: 865: 493: 603: 1162:(PDG), in which participants pretend that they and their partner in crime have been arrested, and they must decide whether to remain loyal to their partner or to compete with their partner and cooperate with the authorities. The researchers found that prosocial individuals were affected by the morality and might primes, whereas proself individuals were not. Thus, 550: 1141:) differs depending on the level of a third variable (the moderator variable). Researchers next look for the presence of mediated moderation when they have a theoretical reason to believe that there is a fourth variable that acts as the mechanism or process that causes the relationship between the independent variable and the moderator (path 3574: 4286: 3815: 807:

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

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on PDG behaviour. Prosocial participants who experienced the morality prime expected their partner to cooperate with them, so they chose to cooperate themselves. Prosocial participants who experienced the might prime expected their partner to compete with them, which made them more likely to compete

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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

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A moderator variable that increases the predictive validity of another variable is known as a suppression variable. When a third variable (a moderator variable here) is added, the magnitude of a relationship becomes larger between an independent variable and a dependent variable. This would indicate

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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

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Baron and Kenny (1986) laid out several requirements that must be met to form a true mediation relationship. They are outlined below using a real-world example. See the diagram above for a visual representation of the overall mediating relationship to be explained. The original steps are as follows.

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vanishes and, moreover, a total effect can be sustained even when both the direct and indirect effects vanish. This illustrates that estimating parameters in isolation tells us little about the effect of mediation and, more generally, mediation and moderation are intertwined and cannot be assessed

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A measurement-of-mediation design can be conceptualized as a statistical approach. 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,

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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. This is because the key assumption of Sobel's test is the assumption

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In the diagram shown above, the indirect effect is the product of path coefficients "A" and "B". The direct effect is the coefficient " C' ". The direct effect measures the extent to which the dependent variable changes when the independent variable increases by one unit and the mediator

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Mediation analysis quantifies the extent to which a variable participates in the transmittance of change from a cause to its effect. It is inherently a causal notion, hence it cannot be defined in statistical terms. Traditionally, however, the bulk of mediation analysis has been conducted within

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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

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In addition to the models mentioned above, a new variable can also exist which moderates the relationship between the independent variable and mediator (the A path) while at the same time have the new variable moderate the relationship between the independent variable and dependent variable (the C

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on his website stated that mediation can exist in the absence of a 'significant' total effect (sometimes referred to as "inconsistent mediation"), and therefore step 1 of the original 1986 approach may not be needed. Later publications by Hayes questioned the concepts of full mediation and partial

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Partial mediation maintains that the mediating variable accounts for some, but not all, of the relationship between the independent variable and dependent variable. Partial mediation implies that there is not only a significant relationship between the mediator and the dependent variable, but also

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If step 1 does not yield a significant result, one may still have grounds to move to step 2. 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

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The source of these difficulties lies in defining mediation in terms of changes induced by adding a third variables into a regression equation. Such statistical changes are epiphenomena which sometimes accompany mediation but, in general, fail to capture the causal relationships that mediation

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Mediation analyses are employed to understand a known relationship by exploring the underlying mechanism or process by which one variable influences another variable through a mediator variable. In particular, mediation analysis can contribute to better understanding the relationship between an

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Regress the dependent variable on both the mediator and independent variable to confirm that a) the mediator is a significant predictor of the dependent variable, and b) the strength of the coefficient of the previously significant independent variable in Step #1 is now greatly reduced, if not

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on the dependent variable depend in turn on levels of another variable (moderator). 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

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Experimental approaches to mediation must be carried out with caution. 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

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and does not impose the assumption of normality. Therefore, if the raw data is available, the bootstrap method is recommended. Bootstrapping involves repeatedly randomly sampling observations with replacement from the data set to compute the desired statistic in each resample. Computing over

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is performed to determine if the relationship between the independent variable and dependent variable has been significantly reduced after inclusion of the mediator variable. In other words, this test assesses whether a mediation effect is significant. It examines the relationship between the

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Sobel test where the IV is remote work, mediating variable is work-family conflict and DV is burnout. a is the raw regression coefficient between the IV and mediator and as is the standard deviation of error a. B is the raw coefficient between mediator and DV and sb is the standard error of

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the confines of linear regression, with statistical terminology masking the causal character of the relationships involved. This led to difficulties, biases, and limitations that have been alleviated by modern methods of causal analysis, based on causal diagrams and counterfactual logic.

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variable remains unaltered. In contrast, the indirect effect measures the extent to which the dependent variable changes when the independent variable is held constant and the mediator variable changes by the amount it would have changed had the independent variable increased by one unit.

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for more details). Thus, the rule of thumb as suggested by MacKinnon et al., (2002) is that a sample size of 1000 is required to detect a small effect, a sample size of 100 is sufficient in detecting a medium effect, and a sample size of 50 is required to detect a large effect.

2331:), respectively, we obtain what came to be known as "potential outcomes" or "structural counterfactuals". These new variables provide convenient notation for defining direct and indirect effects. In particular, four types of effects have been defined for the transition from 1184: 736:. It is becoming increasingly more difficult to publish tests of mediation based purely on the Baron and Kenny method or tests that make distributional assumptions such as the Sobel test. Thus, it is important to consider your options when choosing which test to conduct. 74:, a mediation model proposes that the independent variable influences the mediator variable, which in turn influences the dependent variable. Thus, the mediator variable serves to clarify the nature of the relationship between the independent and dependent variables. 3105: 3081: 1643: 843:

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.

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For example, should one identify other third variables and prove that they do not alter the relationship between the independent variable and the dependent variable he/she would have a stronger argument for their mediation effect. See other 3rd variables

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An experimental-causal-chain design is used when the proposed mediator is experimentally manipulated. 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

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These fractions involve non-obvious combinations of the model's parameters, and can be constructed mechanically with the help of the Mediation Formula. Significantly, due to interaction, a direct effect can be sustained even when the parameter

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The following is a published example of mediated moderation in psychological research. Participants were presented with an initial stimulus (a prime) that made them think of morality or made them think of might. They then participated in the

925:. Moderators are variables that can make the relationship between two variables either stronger or weaker. Such variables further characterize interactions in regression by affecting the direction and/or strength of the relationship between 3583:

and have become the target of estimation in many studies of mediation. They give distribution-free expressions for direct and indirect effects and demonstrate that, despite the arbitrary nature of the error distributions and the functions

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The following example, drawn from Howell (2009), explains each step of Baron and Kenny's requirements to understand further how a mediation effect is characterized. Step 1 and step 2 use simple regression analysis, whereas step 3 uses

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Regress the mediator on the independent variable to confirm that the independent variable is a significant predictor of the mediator. If the mediator is not associated with the independent variable, then it couldn’t possibly mediate

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Therefore, all effects are estimable whenever the model is identified. In non-linear systems, more stringent conditions are needed for estimating the direct and indirect effects. For example, if no confounding exists, (i.e.,

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The power of these definitions lies in their generality; they are applicable to models with arbitrary nonlinear interactions, arbitrary dependencies among the disturbances, and both continuous and categorical variables.

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While the concept of mediation as defined within psychology is theoretically appealing, the methods used to study mediation empirically have been challenged by statisticians and epidemiologists and interpreted formally.

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Smeesters, D.; Warlop, L.; Avermaet, E. V.; Corneille, O.; Yzerbyt, V. (2003). "Do not prime hawks with doves: The interplay of construct activation and consistency of social value orientation on cooperative behavior".

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Such findings would lead to the conclusion implying that your feelings of competence and self-esteem mediate the relationship between how you were parented and how confident you feel about parenting your own children.

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Your feelings of competence and self-esteem (i.e., mediator) predict how confident you feel about parenting your own children (i.e., dependent variable), while controlling for how you were parented (i.e., independent

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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

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The researchers next looked for the presence of a mediated moderation effect. Regression analyses revealed that the type of prime (morality vs. might) mediated the moderating relationship of participants’

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Maximum evidence for mediation, also called full mediation, would occur if inclusion of the mediation variable drops the relationship between the independent variable and dependent variable (see pathway

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In order for either full or partial mediation to be established, the reduction in variance explained by the independent variable must be significant as determined by one of several tests, such as the

1166:(proself vs. prosocial) moderated the relationship between the prime (independent variable: morality vs. might) and the behaviour chosen in the PDG (dependent variable: competitive vs. cooperative). 3604:

fall as special cases of the causal mediation analysis, and the mediation formulas identify how various interactions coefficients contribute to the necessary and sufficient components of mediation.

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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

3569:{\displaystyle {\begin{aligned}TE&=E(Y\mid X=1)-E(Y\mid X=0)\\CDE(m)&=E(Y\mid X=1,M=m)-E(Y\mid X=0,M=m)\\NDE&=\sum _{m}P(M=m\mid X=0)\\NIE&=\sum _{m}E(Y\mid X=0,M=m).\end{aligned}}} 5415:

Preacher, K. J., Rucker, D. D. & Hayes, A. F. (2007). Assessing moderated mediation hypotheses: Strategies, methods, and prescriptions. Multivariate Behavioral Research, 42, 185–227.

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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 (

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Spencer, S. J.; Zanna, M. P.; Fong, G. T. (2005). "Establishing a causal chain: why experiments are often more effective than mediational analyses in examining psychological processes".

1817:. These two operations are fundamentally different, and yield different results, except in the case of no omitted variables. Improperly conditioning mediated effects can be a type of 968:

moderated by different levels of another variable (i.e., a moderator). This definition has been outlined by Muller, Judd, and Yzerbyt (2005) and Preacher, Rucker, and Hayes (2007).

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Baron, R. M. and Kenny, D. A. (1986) "The Moderator-Mediator Variable Distinction in Social Psychological Research – Conceptual, Strategic, and Statistical Considerations",

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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,

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Baron, R. M.; Kenny, D. A. (1986). "The Moderator-Mediator Variable Distinction in Social Psychological Research : Conceptual, Strategic, and Statistical Considerations".

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of normality. Because Sobel's test evaluates a given sample on the normal distribution, small sample sizes and skewness of the sampling distribution can be problematic (see

4460: 4022:, and the two quantities coincide. In the presence of interaction, however, each fraction demands a separate analysis, as dictated by the Mediation Formula, which yields: 4020: 3967: 512:

in the model above). In nonlinear models, the total effect is not generally equal to the sum of the direct and indirect effects, but to a modified combination of the two.

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Pearl, Judea (2012). "The Mediation Formula: A guide to the assessment of causal pathways in nonlinear models". In Berzuini, C.; Dawid, P.; Bernardinelli, L. (eds.).

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independent variable and the dependent variable compared to the relationship between the independent variable and dependent variable including the mediation factor.

4660: 4281:{\displaystyle {\begin{aligned}NDE&=c_{1}+b_{0}c_{3}\\NIE&=b_{1}c_{2}\\TE&=c_{1}+b_{0}c_{3}+b_{1}(c_{2}+c_{3})\\&=NDE+NIE+b_{1}c_{3}.\end{aligned}}} 3845: 2699: 2598: 2405: 234: 122: 4301: 1918: 3915: 3888: 983:

The second possible model of moderated mediation involves a new variable which moderates the relationship between the independent variable and the mediator (the

3810:{\displaystyle {\begin{aligned}X&=\varepsilon _{1}\\M&=b_{0}+b_{1}X+\varepsilon _{2}\\Y&=c_{0}+c_{1}X+c_{2}M+c_{3}XM+\varepsilon _{3}\end{aligned}}} 1122:

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

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The third model of moderated mediation involves a new moderator variable which moderates the relationship between the mediator and the dependent variable (the

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Rucker, D.D., Preacher, K.J., Tormala, Z.L. & Petty, R.E. (2011). "Mediation analysis in social psychology: Current practices and new recommendations".

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Regress the dependent variable on the independent variable to confirm that the independent variable is a significant predictor of the dependent variable.

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The bootstrapping method provides some advantages to the Sobel's test, primarily an increase in power. The Preacher and Hayes bootstrapping method is a

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A controlled version of the indirect effect does not exist because there is no way of disabling the direct effect by fixing a variable to a constant.

6323: 3859:. Even when all parameters are estimated from data, it is still not obvious what combinations of parameters measure the direct and indirect effect of 1880:. Second, the basic definitions of direct and indirect effects must go beyond regression analysis, and should invoke an operation that mimics "fixing 1175:

with their partner and cooperate with the authorities. In contrast, participants with a pro-self social value orientation always acted competitively.

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Moderated mediation can also occur when one moderating variable affects both the relationship between the independent variable and the mediator (the

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Moderation of the relationship between the independent variable (X) and the dependent variable (Y), also called the overall treatment effect (path

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How you were parented (i.e., independent variable) predicts how confident you feel about parenting your own children (i.e., dependent variable).

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Preacher, K. J.; Kelley, K. (2011). "Effect sizes measures for mediation models: Quantitative strategies for communicating indirect effects".

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In general, the omission of suppressors or confounders will lead to either an underestimation or an overestimation of the effect of

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Simple mediation model. The independent variable causes the mediator variable; the mediator variable causes the dependent variable.

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Muller, Judd, and Yzerbyt (2005) outline three fundamental models that underlie both moderated mediation and mediated moderation.

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Shrout, P. E.; Bolger, N. (2002). "Mediation in experimental and nonexperimental studies: New procedures and recommendations".

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Imai, K.; Keele, L.; Yamamoto, T. (2010). "Identification, inference, and sensitivity analysis for causal mediation effects".

5220: 4871: 732: < 25). However, mediation continues to be most frequently determined using the logic of Baron and Kenny or the 980:

In the first model the independent variable also moderates the relationship between the mediator and the dependent variable.

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Preacher, K. J.; Zyphur, M. J.; Zhang, Z. (2010). "A general multilevel SEM framework for assessing multilevel mediation".

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regression weight is significant, the moderator affects the relationship between the independent variable and the mediator.

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in step 3 are significant, the moderator affects the relationship between the independent variable and the mediator (path

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values. Moreover, the language of probability theory does not possess the notation to express the idea of "preventing

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measured. Ignoring a confounding variable may bias empirical estimates of the causal effect of the independent variable.

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How you were parented (i.e., independent variable) predicts your feelings of competence and self-esteem (i.e., mediator).

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Balke, A.; Pearl, J. (1995). Besnard, P.; Hanks, S. (eds.). "Counterfactuals and Policy Analysis in Structural Models".

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in step 3 are significant, the moderator affects the relationship between the mediator and the dependent variable (path

3076:{\displaystyle {\begin{aligned}TE&=C+AB\\CDE(m)&=NDE=C,{\text{ independent of }}m\\NIE&=AB.\end{aligned}}} 1872:

is zero. This has two consequences. First, new strategies must be devised for estimating the structural coefficients

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The fifth and final possible model of moderated mediation involves two new moderator variables, one moderating the

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model seeks to identify and explain the mechanism or process that underlies an observed relationship between an

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constant". The only operator probability provides is "Conditioning" which is what we do when we "control" for

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independent variable and a dependent variable when these variables do not have an obvious direct connection.

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The basic premise of the causal approach is that it is not always appropriate to "control" for the mediator

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mediation, and advocated for the abandonment of these terms and of the steps in classical (1986) mediation.

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Tolman, E. C.; Honzik, C. H. (1930). "Degrees of hunger, reward and nonreward, and maze learning in rats".

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Sobel, M. E. (1982). "Asymptotic confidence intervals for indirect effects in structural equation models".

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Sobel, M. E. (1982). "Asymptotic confidence intervals for indirect effects in structural equation models".

913:, thereby either reducing or artificially inflating the magnitude of a relationship between two variables. 520:

A mediator variable can either account for all or some of the observed relationship between two variables.

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Book on moderation and mediation analysis, including an introduction to the PROCESS macro for SPSS and SAS

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Muller, D.; Judd, C. M.; Yzerbyt, V. Y. (2005). "When moderation is mediated and mediation is moderated".

5333: 6352: 70:). Rather than a direct causal relationship between the independent variable and the dependent variable, 5283: 5095:"A further critique of the analytic strategy of adjusting for covariates to identify biologic mediation" 722:

As outlined above, there are a few different options one can choose from to evaluate a mediation model.

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Rubin, D.B. (1974). "Estimating causal effects of treatments in randomized and nonrandomized studies".

725: 4624:{\displaystyle 1-{\frac {NDE}{TE}}={\frac {b_{1}(c_{2}+c_{3})}{c_{1}+b_{0}c_{3}+b_{1}(c_{2}+c_{3})}}.} 2946:

In linear analysis, all effects are determined by sums of products of structural coefficients, giving

886:) which in turn may cause a decrease in errors made at work on an assembly line (an outcome variable, 6061:

Hayes, A. F. (2009). "Beyond Baron and Kenny: Statistical mediation analysis in the new millennium".

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Pearl, Judea (1994). Lopez de Mantaras, R.; Poole, D. (eds.). "A probabilistic calculus of actions".

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Hayes, A. F. (2009). "Beyond Baron and Kenny: Statistical mediation analysis in the new millennium".

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Indirect effect in a simple mediation model: The indirect effect constitutes the extent to which the

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may obscure or confound the relationship between the independent and dependent variables. Potential

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interaction between the independent variable and the mediator one would have grounds to investigate

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can co-occur in statistical models. It is possible to mediate moderation and moderate mediation.

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from changing, then whatever changes we measure in Y are attributable solely to variations in

6017: 825: 2416: 5246:"SPSS and SAS Macro for Bootstrapping Specific Indirect Effects in Multiple Mediation Models" 4774: 4757: 4714: 3596:, mediated effects can nevertheless be estimated from data using regression. The analyses of 1159: 976:

There are five possible models of moderated mediation, as illustrated in the diagrams below.

821: 4440:{\displaystyle {\frac {NIE}{TE}}={\frac {b_{1}c_{2}}{c_{1}+b_{0}c_{3}+b_{1}(c_{2}+c_{3})}},} 2039:{\displaystyle X=f(\varepsilon _{1}),~~M=g(X,\varepsilon _{2}),~~Y=h(X,M,\varepsilon _{3}),} 434:

should be smaller in absolute value than the original effect for the independent variable (β

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Moderation of both the relationship between the independent and dependent variables (path

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A conceptual diagram that depicts a parallel mediation model with two mediator variables.

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regression weight must be significant (first step for establishing mediated moderation).

1317:{\displaystyle Y=\beta _{40}+\beta _{41}X+\beta _{42}Mo+\beta _{43}XMo+\varepsilon _{4}} 6193: 6123: 6098: 6078: 5902: 5877: 5855: 5772: 5718: 5692: 5652: 5621: 5586: 5526: 5492: 5314: 5170: 5145: 5072: 5032: 4998:. Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, 4965: 4844: 1354:

Moderation of the relationship between the independent variable and the mediator (path

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Establishing moderated mediation requires that there be no moderation effect, so the

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In linear systems, the total effect is equal to the sum of the direct and indirect (

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MacKinnon, D. P.; Lockwood, C. M.; Lockwood, J. M.; West, S. G.; Sheets, V. (2002).

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and we are justified then in proclaiming the effect observed as "direct effect of

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Hayes (2009) critiqued Baron and Kenny's mediation steps approach, and as of 2019,

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to mediation. In linear analysis, the former fraction is captured by the product

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path) and the relationship between the mediator and the dependent variable (the

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changes to whatever value it would have attained (for each individual) under

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Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences

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According to these definitions the total effect can be decomposed as a sum

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from changing; it merely narrows the analyst's attention to cases of equal

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ON A DISTINCTION BETWEEN HYPOTHETICAL CONSTRUCTS AND INTERVENING VARIABLES

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some direct relationship between the independent and dependent variable.

406:{\displaystyle Y=\beta _{30}+\beta _{31}X+\beta _{32}Me+\varepsilon _{3}} 30: 5265: 81: 6250:

Tolman, E. C. (1938). "The Determiners of Behavior at a Choice Point".

5946: 5929: 3867:, or, more practically, how to assess the fraction of the total effect 2159:{\displaystyle X=f(\varepsilon _{1}),~~M=m,~~Y=h(X,m,\varepsilon _{3})} 1912:. For example, if the basic mediation model consists of the equations: 733: 583: 578: 562: 528: 39: 6197: 5714: 5196: 5036: 1725:(see the Figure above). The classical rationale for "controlling" for 6299: 6263: 6153: 6031: 5956: 5814: 5617: 5574: 5463:"Identifiability and exchangeability for direct and indirect effects" 5302: 4936:"Identifiability and exchangeability for direct and indirect effects" 4672:

As of 19 June 2014, this article is derived in whole or in part from

2273:{\displaystyle X=x,M=g(x,\varepsilon _{2}),Y=h(x,M,\varepsilon _{3})} 694:{\displaystyle z={\frac {ab}{\sqrt {b^{2}s_{a}^{2}+a^{2}s_{b}^{2}}}}} 1179:

Regression equations for moderated mediation and mediated moderation

1133:

In order to establish mediated moderation, one must first establish

6189: 5028: 4291:

Thus, the fraction of output response for which mediation would be

5697: 5657: 5531: 1832:

are correlated. Under such conditions, the structural coefficient

1126:) is moderated or the effect of the mediator on the outcome (path 864: 492: 3099:

are mutually independent) the following formulas can be derived:

882:) may cause an increase in error detection (a mediator variable, 5424: 1108:

Model 8 of process Hayes: New variable moderates pathway A and C

1868:. In fact, the regression slopes may both be nonzero even when 54:

via the inclusion of a third hypothetical variable, known as a

6242:

Shaughnessy J.J., Zechmeister E. & Zechmeister J. (2006).

5284:"Yes, but what's the mechanism? (don't expect an easy answer)" 5191: 5189: 2791:= 1, while setting the mediator variable to whatever value it 1206:

represents the measurement error of each regression equation.

6324:

Online text of "The Determiner of Behavior at a Choice Point"

6238:. Chichester, UK: John Wiley and Sons, Ltd. pp. 151–179. 5143: 602: 5832:

Vansteelandt, Stijn; Bekaert, Maarten; Lange, Theis (2012).

5010: 5008: 1183: 1145:) or between the moderator and the dependent variable (path 549: 296:{\displaystyle Me=\beta _{20}+\beta _{21}X+\varepsilon _{2}} 5186: 181:{\displaystyle Y=\beta _{10}+\beta _{11}X+\varepsilon _{1}} 2765:= 1, while the mediator is fixed at a pre-specified level 515: 5005: 5831: 5556:"Interpretation and identification of causal mediation" 5092: 2734:, while the mediator is allowed to track the change in 6055:

Statistical power analysis for the behavioral sciences

764: 5934:

Behavior Research Methods, Instruments, and Computers

5093:

Kaufman, J. S.; MacLehose, R. F.; Kaufman, S (2004).

4641: 4463: 4304: 4031: 3975: 3927: 3900: 3873: 3826: 3637: 3611:

A serial mediation model with two mediator variables.

3108: 2955: 2860: 2612: 2511: 2419: 2351: 2299:

remain unaltered. If we further rename the variables

2186: 2066: 1921: 1777:. The result is that, instead of physically holding 1504: 1367: 1227: 617: 338: 244: 222: 132: 110: 82:

Baron and Kenny's (1986) steps for mediation analysis

6236:

Causality: Statistical Perspectives and Applications

5827: 5825: 1805:

to vary but ignore all units except those in which

933:. A moderating relationship can be thought of as an 553:

The partial mediation model includes a direct effect

6312:

Example of Causal Mediation Using Propensity Scores

6273:

University of California Publications in Psychology

6007: 5736: 5734: 5732: 2708:stands for expectation taken over the error terms. 2291:, as well as the distributions of the error terms ε 1691:

Either or both of the conditions above may be true.

5973:Preacher, Kristopher J.; Hayes, Andrew F. (2008). 5928:Preacher, Kristopher J.; Hayes, Andrew F. (2004). 5788: 5786: 5332:Spencer, S. J.; Zanna, M. P.; Fong, G. T. (2005). 4654: 4623: 4439: 4280: 4014: 3961: 3909: 3882: 3839: 3809: 3568: 3075: 2900: 2749:CDE measures the expected increase in the outcome 2711:These effects have the following interpretations: 2693: 2592: 2491: 2399: 2272: 2158: 2038: 1637: 1459: 1316: 1070:Fourth option: fourth variable moderates both the 704: 693: 405: 295: 228: 180: 116: 6246:(7th ed., pp. 51–52). New York: McGraw Hill. 6096: 5822: 5682: 5678: 5676: 5380: 1028:First option: independent variable moderates the 475: 6344: 6204: 5729: 5331: 5282:Bullock, J. G.; Green, D. P.; Ha, S. E. (2010). 4450:while the fraction for which mediation would be 971: 5783: 5460: 4926: 769: 6139: 5871: 5869: 5673: 5281: 4866:(7th ed.). Belmot, CA: Cengage Learning. 4744:Introduction to Statistical Mediation Analysis 2718:measures the expected increase in the outcome 1824:To illustrate, assume that the error terms of 1717:when we seek to estimate the direct effect of 6314:The Methodology Center, Penn State University 5972: 5927: 5795:"Causal inference in statistics: An overview" 5221:"Testing of Mediation Models in SPSS and SAS" 1700: 1042:Second option: fourth variable moderates the 6270: 6207:Journal of Personality and Social Psychology 6048:Journal of Personality and Social Psychology 5508: 5506: 5428:Journal of Personality and Social Psychology 5383:Journal of Personality and Social Psychology 5341:Journal of Personality and Social Psychology 5291:Journal of Personality and Social Psychology 5099:Epidemiologic Perspectives & Innovations 4886: 4820:Journal of Personality and Social Psychology 4758:"Mediation analysis: a practitioner's guide" 1695: 1088:Fifth option: fourth variable moderates the 1056:Third option: fourth variable moderates the 717: 6283: 5866: 5740: 4755: 1856:) can no longer be estimated by regressing 6097:MacKinnon, D. P.; Lockwood, C. M. (2003). 5638: 5088: 5086: 4987: 4985: 4983: 4981: 4979: 4816: 2840:measures the extent to which mediation is 2832:measures the extent to which mediation is 1345:regression weight must not be significant. 963:on the mediator and/or the partial effect 739: 6300:Summary of mediation methods at PsychWiki 6170:Social and Personality Psychology Compass 6122: 6021: 5990: 5955: 5945: 5901: 5849: 5813: 5758: 5696: 5656: 5641:Uncertainty in Artificial Intelligence 11 5530: 5515:Uncertainty in Artificial Intelligence 10 5503: 5478: 5376: 5374: 5372: 5370: 5169: 5120: 5110: 4951: 4773: 1199:represents the mediator variable(s), and 6093:(7th ed.). Belmot, CA: Cengage Learning. 6057:(2nd ed.). New York, NY: Academic Press. 5409: 5050: 5048: 5046: 4922: 4920: 4918: 4775:10.1146/annurev-publhealth-032315-021402 3619: 3606: 2937: 2933: 2918:stands for the reverse transition, from 1729:" is that, if we succeed in preventing 1182: 1103: 1092:path and a fifth variable moderates the 1083: 1065: 1051: 1037: 1023: 863: 846: 815: 782: 601: 548: 527: 491: 479: 29: 6050:, Vol. 51(6), pp. 1173–1182. 5275: 5083: 4976: 516:Full mediation versus partial mediation 14: 6345: 6320:Andrew F. Hayes, Ohio State University 6249: 5875: 5367: 4861: 4795: 4793: 4686:. All relevant terms must be followed. 4675:Causal Analysis in Theory and Practice 1761:from changing" or "physically holding 1195:represents the moderator variable(s), 1116: 944: 6337:Classics in the History of Psychology 6233: 6175: 6060: 5792: 5603: 5553: 5512: 5223:. Comm.ohio-state.edu. Archived from 5054: 5043: 5014: 4915: 2836:for explaining the effect, while the 1328:To establish overall moderation, the 1187:A simple statistical mediation model. 5461:Robins, J.M.; Greenland, S. (1992). 4701: 4699: 2769:uniformly over the entire population 2049:then after applying the operator do( 959:is when the effect of the treatment 921:Other important third variables are 544: 4799:Cohen, J.; Cohen, P.; West, S. G.; 4790: 2169:and after applying the operator do( 1773:as a regressor in the equation for 1745:." Unfortunately, "controlling for 851:Mediation model with two covariates 799:Nonspuriousness and/or no confounds 765:Criticisms of mediation measurement 24: 6091:Statistical methods for psychology 4864:Statistical Methods for Psychology 3579:The last two equations are called 2942:Formulation of the indirect effect 2805:measures the expected increase in 2775:measures the expected increase in 1012:path and the other moderating the 484:Direct effect in a mediation model 25: 6369: 6358:Independence (probability theory) 6293: 5606:Journal of Educational Psychology 4696: 3894:by mediation and the fraction of 523: 472:the effect that actually exists. 5480:10.1097/00001648-199203000-00013 4953:10.1097/00001648-199203000-00013 3628:Assume the model takes the form 1884:", rather than "conditioning on 1797: = 1' to those under 749:Experimental-causal-chain design 6286:Explanation in Causal Inference 5632: 5597: 5547: 5454: 5418: 5325: 5259: 5238: 5213: 5137: 4807:(3rd ed.). Mahwah, NJ: Erlbaum. 3969:, the latter by the difference 3847:quantifies the degree to which 2410:(b) Controlled direct effect - 1908:and replacing it by a constant 756:Measurement-of-mediation design 705:Preacher–Hayes bootstrap method 572: 6284:Vanderweele, Tyler J. (2015). 6244:Research Methods in Psychology 4880: 4855: 4810: 4762:Annual Review of Public Health 4749: 4736: 4612: 4586: 4535: 4509: 4428: 4402: 4214: 4188: 3998: 3976: 3556: 3526: 3520: 3517: 3493: 3484: 3460: 3454: 3421: 3397: 3391: 3388: 3358: 3349: 3324: 3317: 3311: 3278: 3248: 3239: 3209: 3196: 3190: 3174: 3156: 3147: 3129: 3004: 2998: 2901:{\displaystyle TE=NDE-NIE_{r}} 2688: 2685: 2682: 2676: 2664: 2655: 2652: 2646: 2634: 2628: 2587: 2584: 2581: 2575: 2563: 2554: 2551: 2545: 2533: 2527: 2486: 2483: 2471: 2462: 2450: 2444: 2435: 2429: 2394: 2391: 2385: 2376: 2370: 2364: 2267: 2242: 2227: 2208: 2153: 2128: 2089: 2076: 2030: 2005: 1984: 1965: 1944: 1931: 1891: 1749:" does not physically prevent 894:), which in turn may cause an 859: 830: 760:but only involves measurement. 504:variable through the mediator. 476:Direct versus indirect effects 223: 111: 13: 1: 5197:"Interactive Mediation Tests" 4996:"Direct and indirect effects" 4666: 4015:{\displaystyle (TE-c_{1})/TE} 3962:{\displaystyle b_{1}c_{2}/TE} 2799:= 0, i.e., before the change. 1896:Such an operator, denoted do( 972:Models of moderated mediation 916: 5894:10.1097/ede.0b013e31826c2bb9 5760:10.1097/ede.0b013e31818f69ce 3615: 2738:as dictated by the function 2603:(d) Natural indirect effect 2502:(c) Natural direct effect - 1152: 770:Potentially unnecessary step 450:multiple regression analysis 7: 5272:. Retrieved April 25, 2012. 4833:10.1037/0022-3514.51.6.1173 1710:analysis aims to quantify. 1482: 1349: 1209: 599:The equation for Sobel is: 541:in diagram above) to zero. 10: 6374: 6328:Kenneth MacCorquodale and 6219:10.1037/0022-3514.89.6.845 5741:VanderWeele, T.J. (2009). 5440:10.1037/0022-3514.84.5.972 5395:10.1037/0022-3514.89.6.852 5353:10.1037/0022-3514.89.6.845 4756:VanderWeele, T.J. (2016). 3034: independent of 1701:Fixing versus conditioning 819: 576: 442: 6075:10.1080/03637750903310360 5979:Behavior Research Methods 5069:10.1080/03637750903310360 4901:10.1037/1082-989x.7.4.422 4742:MacKinnon, D. P. (2008). 1696:Causal mediation analysis 718:Significance of mediation 319: 204: 90: 6178:Sociological Methodology 6063:Communication Monographs 5876:Albert, Jeffrey (2012). 5162:10.1037/1082-989x.7.1.83 5057:Communication Monographs 5017:Sociological Methodology 2492:{\displaystyle CDE(m)=E} 1172:social value orientation 1164:social value orientation 941:for further discussion. 500:variable influences the 326:rendered nonsignificant. 6115:10.1023/A:1024649822872 3851:modifies the effect of 1160:Prisoner's Dilemma Game 740:Approaches to mediation 95:Relationship Duration 6089:Howell, D. C. (2009). 5851:10.1515/2161-962X.1014 4862:Howell, D. C. (2009). 4656: 4625: 4441: 4282: 4016: 3963: 3911: 3884: 3841: 3811: 3625: 3612: 3570: 3077: 2943: 2902: 2695: 2594: 2493: 2401: 2274: 2160: 2040: 1639: 1461: 1318: 1188: 1109: 1097: 1079: 1061: 1047: 1033: 870: 852: 826:Third-variable fallacy 695: 608: 554: 533: 505: 485: 407: 297: 230: 182: 118: 35: 6142:Psychological Methods 6010:Psychological Methods 5838:Epidemiologic Methods 5793:Pearl, Judea (2009). 5647:. San Francisco, CA: 5563:Psychological Methods 5248:. Comm.ohio-state.edu 5150:Psychological Methods 5112:10.1186/1742-5573-1-4 4889:Psychological Methods 4715:University of Indiana 4657: 4655:{\displaystyle c_{1}} 4626: 4442: 4283: 4017: 3964: 3912: 3885: 3842: 3840:{\displaystyle c_{3}} 3812: 3623: 3610: 3571: 3078: 2941: 2934:The mediation formula 2903: 2813:is held constant, at 2696: 2694:{\displaystyle NIE=E} 2595: 2593:{\displaystyle NDE=E} 2494: 2402: 2342:(a) Total effect – 2275: 2177:) the model becomes: 2161: 2057:) the model becomes: 2041: 1640: 1462: 1319: 1186: 1107: 1087: 1069: 1055: 1041: 1027: 867: 850: 822:Spurious relationship 816:Other third variables 783:Importance of caution 696: 605: 552: 531: 495: 483: 408: 298: 231: 216:Independent variable 183: 119: 104:Independent variable 64:intermediary variable 33: 6339:, retr. 22 Aug 2011. 6252:Psychological Review 5992:10.3758/BRM.40.3.879 4746:. New York: Erlbaum. 4707:"Types of Variables" 4639: 4461: 4302: 4029: 3973: 3925: 3898: 3871: 3824: 3820:where the parameter 3635: 3602:mediating moderators 3106: 2953: 2858: 2610: 2509: 2417: 2400:{\displaystyle TE=E} 2349: 2283:where the functions 2184: 2064: 1919: 1502: 1365: 1225: 615: 532:Full mediation model 336: 242: 229:{\displaystyle \to } 220: 130: 117:{\displaystyle \to } 108: 72:which is often false 68:intervening variable 48:independent variable 18:Intervening variable 5707:2010arXiv1011.1079I 5685:Statistical Science 5667:2013arXiv1302.4929B 5541:2013arXiv1302.6835P 3598:moderated mediation 2793:would have obtained 1809:achieves the value 1117:Mediated moderation 957:Moderated mediation 945:Moderated mediation 875:suppressor variable 792:Temporal precedence 711:non-parametric test 687: 659: 593:Normal distribution 124:dependent variable 6353:Statistical models 6305:2011-07-15 at the 6103:Prevention Science 6053:Cohen, J. (1988). 5947:10.3758/BF03206553 5802:Statistics Surveys 4652: 4621: 4437: 4278: 4276: 4012: 3959: 3910:{\displaystyle TE} 3907: 3883:{\displaystyle TE} 3880: 3837: 3807: 3805: 3626: 3613: 3581:Mediation Formulas 3566: 3564: 3453: 3310: 3073: 3071: 2944: 2922: = 1 to 2898: 2844:for sustaining it. 2691: 2590: 2489: 2397: 2335: = 0 to 2307:resulting from do( 2270: 2156: 2036: 1781:constant (say at 1635: 1457: 1314: 1189: 1110: 1098: 1080: 1062: 1048: 1034: 871: 853: 691: 673: 645: 609: 555: 534: 506: 486: 403: 293: 226: 178: 114: 60:mediating variable 52:dependent variable 36: 5715:10.1214/10-sts321 5554:Pearl, J (2014). 5521:. San Mateo, CA: 4873:978-0-495-59785-8 4616: 4491: 4432: 4326: 3444: 3301: 3035: 2118: 2115: 2100: 2097: 1995: 1992: 1955: 1952: 1218:in the diagram). 1102: 1101: 689: 688: 545:Partial mediation 56:mediator variable 27:Statistical model 16:(Redirected from 6365: 6289: 6280: 6267: 6264:10.1037/h0062733 6239: 6230: 6201: 6165: 6154:10.1037/a0022658 6136: 6126: 6086: 6043: 6032:10.1037/a0020141 6025: 6004: 5994: 5969: 5959: 5949: 5916: 5915: 5905: 5873: 5864: 5863: 5853: 5844:(1, Article 7). 5829: 5820: 5819: 5817: 5815:10.1214/09-ss057 5799: 5790: 5781: 5780: 5762: 5738: 5727: 5726: 5700: 5680: 5671: 5670: 5660: 5636: 5630: 5629: 5618:10.1037/h0037350 5601: 5595: 5594: 5575:10.1037/a0036434 5560: 5551: 5545: 5544: 5534: 5510: 5501: 5500: 5482: 5458: 5452: 5451: 5422: 5416: 5413: 5407: 5406: 5378: 5365: 5364: 5338: 5329: 5323: 5322: 5303:10.1037/a0018933 5288: 5279: 5273: 5263: 5257: 5256: 5254: 5253: 5242: 5236: 5235: 5233: 5232: 5217: 5211: 5210: 5208: 5207: 5193: 5184: 5183: 5173: 5141: 5135: 5134: 5124: 5114: 5090: 5081: 5080: 5052: 5041: 5040: 5012: 5003: 5002:, 411–420. 4989: 4974: 4973: 4955: 4924: 4913: 4912: 4884: 4878: 4877: 4859: 4853: 4852: 4827:(6): 1173–1182. 4814: 4808: 4797: 4788: 4787: 4777: 4753: 4747: 4740: 4734: 4733: 4731: 4730: 4724: 4718:. Archived from 4711: 4703: 4661: 4659: 4658: 4653: 4651: 4650: 4630: 4628: 4627: 4622: 4617: 4615: 4611: 4610: 4598: 4597: 4585: 4584: 4572: 4571: 4562: 4561: 4549: 4548: 4538: 4534: 4533: 4521: 4520: 4508: 4507: 4497: 4492: 4490: 4482: 4471: 4446: 4444: 4443: 4438: 4433: 4431: 4427: 4426: 4414: 4413: 4401: 4400: 4388: 4387: 4378: 4377: 4365: 4364: 4354: 4353: 4352: 4343: 4342: 4332: 4327: 4325: 4317: 4306: 4287: 4285: 4284: 4279: 4277: 4270: 4269: 4260: 4259: 4220: 4213: 4212: 4200: 4199: 4187: 4186: 4174: 4173: 4164: 4163: 4151: 4150: 4124: 4123: 4114: 4113: 4084: 4083: 4074: 4073: 4061: 4060: 4021: 4019: 4018: 4013: 4005: 3997: 3996: 3968: 3966: 3965: 3960: 3952: 3947: 3946: 3937: 3936: 3916: 3914: 3913: 3908: 3889: 3887: 3886: 3881: 3846: 3844: 3843: 3838: 3836: 3835: 3816: 3814: 3813: 3808: 3806: 3802: 3801: 3783: 3782: 3767: 3766: 3751: 3750: 3738: 3737: 3714: 3713: 3698: 3697: 3685: 3684: 3661: 3660: 3575: 3573: 3572: 3567: 3565: 3452: 3327: 3309: 3082: 3080: 3079: 3074: 3072: 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120: 115: 21: 6373: 6372: 6368: 6367: 6366: 6364: 6363: 6362: 6343: 6342: 6307:Wayback Machine 6296: 6172:, 5/6, 359–371. 6023:10.1.1.570.7747 5919: 5874: 5867: 5830: 5823: 5797: 5791: 5784: 5739: 5730: 5681: 5674: 5649:Morgan Kaufmann 5637: 5633: 5602: 5598: 5558: 5552: 5548: 5523:Morgan Kaufmann 5511: 5504: 5459: 5455: 5423: 5419: 5414: 5410: 5379: 5368: 5336: 5330: 5326: 5286: 5280: 5276: 5270:davidakenny.net 5264: 5260: 5251: 5249: 5244: 5243: 5239: 5230: 5228: 5219: 5218: 5214: 5205: 5203: 5195: 5194: 5187: 5142: 5138: 5091: 5084: 5053: 5044: 5013: 5006: 5000:Morgan Kaufmann 4990: 4977: 4925: 4916: 4885: 4881: 4874: 4860: 4856: 4815: 4811: 4798: 4791: 4754: 4750: 4741: 4737: 4728: 4726: 4722: 4709: 4705: 4704: 4697: 4669: 4646: 4642: 4640: 4637: 4636: 4606: 4602: 4593: 4589: 4580: 4576: 4567: 4563: 4557: 4553: 4544: 4540: 4539: 4529: 4525: 4516: 4512: 4503: 4499: 4498: 4496: 4483: 4472: 4470: 4462: 4459: 4458: 4422: 4418: 4409: 4405: 4396: 4392: 4383: 4379: 4373: 4369: 4360: 4356: 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6326: 6321: 6315: 6309: 6295: 6294:External links 6292: 6291: 6290: 6281: 6268: 6247: 6240: 6231: 6213:(6): 845–851. 6202: 6190:10.2307/270723 6173: 6166: 6137: 6109:(3): 155–171. 6094: 6087: 6069:(4): 408–420. 6058: 6051: 6044: 6016:(3): 209–233. 6005: 5985:(3): 879–891. 5970: 5940:(4): 717–731. 5924: 5923: 5918: 5917: 5888:(6): 879–888. 5865: 5821: 5782: 5728: 5672: 5631: 5612:(5): 688–701. 5596: 5546: 5502: 5473:(2): 143–155. 5453: 5434:(5): 972–987. 5417: 5408: 5389:(6): 852–863. 5366: 5324: 5274: 5258: 5237: 5212: 5185: 5136: 5082: 5063:(4): 408–420. 5042: 5029:10.2307/270723 5004: 4975: 4914: 4895:(4): 422–445. 4879: 4872: 4854: 4809: 4789: 4748: 4735: 4694: 4693: 4692: 4668: 4665: 4649: 4645: 4632: 4631: 4620: 4614: 4609: 4605: 4601: 4596: 4592: 4588: 4583: 4579: 4575: 4570: 4566: 4560: 4556: 4552: 4547: 4543: 4537: 4532: 4528: 4524: 4519: 4515: 4511: 4506: 4502: 4495: 4489: 4486: 4481: 4478: 4475: 4469: 4466: 4448: 4447: 4436: 4430: 4425: 4421: 4417: 4412: 4408: 4404: 4399: 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2235: 2232: 2229: 2224: 2220: 2216: 2213: 2210: 2207: 2204: 2201: 2198: 2195: 2192: 2189: 2167: 2166: 2155: 2150: 2146: 2142: 2139: 2136: 2133: 2130: 2127: 2124: 2121: 2112: 2109: 2106: 2103: 2094: 2091: 2086: 2082: 2078: 2075: 2072: 2069: 2047: 2046: 2035: 2032: 2027: 2023: 2019: 2016: 2013: 2010: 2007: 2004: 2001: 1998: 1989: 1986: 1981: 1977: 1973: 1970: 1967: 1964: 1961: 1958: 1949: 1946: 1941: 1937: 1933: 1930: 1927: 1924: 1893: 1890: 1801:= 0, we allow 1702: 1699: 1697: 1694: 1693: 1692: 1689: 1680: 1677:in step 2 and 1674: 1668: 1660: 1656:in step 2 and 1653: 1646: 1645: 1632: 1628: 1624: 1621: 1618: 1615: 1612: 1607: 1603: 1599: 1596: 1593: 1588: 1584: 1580: 1577: 1574: 1571: 1566: 1562: 1558: 1555: 1552: 1547: 1543: 1539: 1536: 1531: 1527: 1523: 1518: 1514: 1510: 1507: 1484: 1481: 1480: 1479: 1475: 1468: 1467: 1454: 1450: 1446: 1443: 1440: 1437: 1432: 1428: 1424: 1421: 1418: 1413: 1409: 1405: 1402: 1397: 1393: 1389: 1384: 1380: 1376: 1373: 1370: 1351: 1348: 1347: 1346: 1342: 1336: 1332: 1325: 1324: 1311: 1307: 1303: 1300: 1297: 1294: 1289: 1285: 1281: 1278: 1275: 1270: 1266: 1262: 1259: 1254: 1250: 1246: 1241: 1237: 1233: 1230: 1211: 1208: 1202: 1180: 1177: 1154: 1151: 1118: 1115: 1100: 1099: 1081: 1063: 1049: 1035: 1018: 1017: 1006: 995: 988: 981: 973: 970: 949:Mediation and 946: 943: 918: 915: 861: 858: 832: 829: 817: 814: 805: 804: 800: 797: 793: 784: 781: 776:David A. Kenny 771: 768: 766: 763: 762: 761: 757: 754: 750: 741: 738: 719: 716: 706: 703: 702: 701: 685: 680: 676: 670: 666: 662: 657: 652: 648: 642: 638: 632: 629: 623: 620: 577:Main article: 574: 571: 546: 543: 525: 524:Full mediation 522: 517: 514: 477: 474: 465: 464: 460: 457: 444: 441: 440: 439: 435: 431: 426: 425:is significant 422: 416: 415: 414: 413: 400: 396: 392: 389: 386: 381: 377: 373: 370: 365: 361: 357: 352: 348: 344: 341: 328: 327: 321: 318: 317: 316: 315:is significant 312: 306: 305: 304: 303: 290: 286: 282: 279: 274: 270: 266: 261: 257: 253: 250: 247: 225: 213: 212: 206: 203: 202: 201: 200:is significant 197: 191: 190: 189: 188: 175: 171: 167: 164: 159: 155: 151: 146: 142: 138: 135: 113: 101: 100: 92: 89: 83: 80: 26: 9: 6: 4: 3: 2: 6370: 6359: 6356: 6354: 6351: 6350: 6348: 6338: 6335: 6331: 6330:Paul E. Meehl 6327: 6325: 6322: 6319: 6316: 6313: 6310: 6308: 6304: 6301: 6298: 6297: 6287: 6282: 6278: 6274: 6269: 6265: 6261: 6257: 6253: 6248: 6245: 6241: 6237: 6232: 6228: 6224: 6220: 6216: 6212: 6208: 6203: 6199: 6195: 6191: 6187: 6183: 6179: 6174: 6171: 6167: 6163: 6159: 6155: 6151: 6148:(2): 93–115. 6147: 6143: 6138: 6134: 6130: 6125: 6120: 6116: 6112: 6108: 6104: 6100: 6095: 6092: 6088: 6084: 6080: 6076: 6072: 6068: 6064: 6059: 6056: 6052: 6049: 6045: 6041: 6037: 6033: 6029: 6024: 6019: 6015: 6011: 6006: 6002: 5998: 5993: 5988: 5984: 5980: 5976: 5971: 5967: 5963: 5958: 5953: 5948: 5943: 5939: 5935: 5931: 5926: 5925: 5921: 5920: 5913: 5909: 5904: 5899: 5895: 5891: 5887: 5883: 5879: 5872: 5870: 5861: 5857: 5852: 5847: 5843: 5839: 5835: 5828: 5826: 5816: 5811: 5807: 5803: 5796: 5789: 5787: 5778: 5774: 5770: 5766: 5761: 5756: 5752: 5748: 5744: 5737: 5735: 5733: 5724: 5720: 5716: 5712: 5708: 5704: 5699: 5694: 5690: 5686: 5679: 5677: 5668: 5664: 5659: 5654: 5650: 5646: 5642: 5635: 5627: 5623: 5619: 5615: 5611: 5607: 5600: 5592: 5588: 5584: 5580: 5576: 5572: 5569:(4): 459–81. 5568: 5564: 5557: 5550: 5542: 5538: 5533: 5528: 5524: 5520: 5516: 5509: 5507: 5498: 5494: 5490: 5486: 5481: 5476: 5472: 5468: 5464: 5457: 5449: 5445: 5441: 5437: 5433: 5429: 5421: 5412: 5404: 5400: 5396: 5392: 5388: 5384: 5377: 5375: 5373: 5371: 5362: 5358: 5354: 5350: 5347:(6): 845–51. 5346: 5342: 5335: 5328: 5320: 5316: 5312: 5308: 5304: 5300: 5296: 5292: 5285: 5278: 5271: 5267: 5262: 5247: 5241: 5227:on 2012-05-18 5226: 5222: 5216: 5202: 5198: 5192: 5190: 5181: 5177: 5172: 5167: 5163: 5159: 5156:(1): 83–104. 5155: 5151: 5147: 5140: 5132: 5128: 5123: 5118: 5113: 5108: 5104: 5100: 5096: 5089: 5087: 5078: 5074: 5070: 5066: 5062: 5058: 5051: 5049: 5047: 5038: 5034: 5030: 5026: 5022: 5018: 5011: 5009: 5001: 4997: 4993: 4988: 4986: 4984: 4982: 4980: 4971: 4967: 4963: 4959: 4954: 4949: 4946:(2): 143–55. 4945: 4941: 4937: 4933: 4932:Greenland, S. 4929: 4928:Robins, J. M. 4923: 4921: 4919: 4910: 4906: 4902: 4898: 4894: 4890: 4883: 4875: 4869: 4865: 4858: 4850: 4846: 4842: 4838: 4834: 4830: 4826: 4822: 4821: 4813: 4806: 4802: 4796: 4794: 4785: 4781: 4776: 4771: 4767: 4763: 4759: 4752: 4745: 4739: 4725:on 2020-03-31 4721: 4717: 4716: 4708: 4702: 4700: 4695: 4690: 4689: 4688: 4687: 4685: 4681: 4676: 4673: 4664: 4647: 4643: 4618: 4607: 4603: 4599: 4594: 4590: 4581: 4577: 4573: 4568: 4564: 4558: 4554: 4550: 4545: 4541: 4530: 4526: 4522: 4517: 4513: 4504: 4500: 4493: 4487: 4484: 4479: 4476: 4473: 4467: 4464: 4457: 4456: 4455: 4453: 4434: 4423: 4419: 4415: 4410: 4406: 4397: 4393: 4389: 4384: 4380: 4374: 4370: 4366: 4361: 4357: 4349: 4345: 4339: 4335: 4328: 4322: 4319: 4314: 4311: 4308: 4298: 4297: 4296: 4294: 4271: 4266: 4262: 4256: 4252: 4248: 4245: 4242: 4239: 4236: 4233: 4230: 4227: 4224: 4222: 4209: 4205: 4201: 4196: 4192: 4183: 4179: 4175: 4170: 4166: 4160: 4156: 4152: 4147: 4143: 4139: 4137: 4132: 4129: 4120: 4116: 4110: 4106: 4102: 4100: 4095: 4092: 4089: 4080: 4076: 4070: 4066: 4062: 4057: 4053: 4049: 4047: 4042: 4039: 4036: 4025: 4024: 4023: 4009: 4006: 4002: 3993: 3989: 3985: 3982: 3979: 3956: 3953: 3949: 3943: 3939: 3933: 3929: 3920: 3904: 3901: 3893: 3877: 3874: 3866: 3862: 3858: 3854: 3850: 3832: 3828: 3798: 3794: 3790: 3787: 3784: 3779: 3775: 3771: 3768: 3763: 3759: 3755: 3752: 3747: 3743: 3739: 3734: 3730: 3726: 3724: 3719: 3710: 3706: 3702: 3699: 3694: 3690: 3686: 3681: 3677: 3673: 3671: 3666: 3657: 3653: 3649: 3647: 3642: 3631: 3630: 3629: 3622: 3609: 3605: 3603: 3599: 3595: 3591: 3587: 3582: 3559: 3553: 3550: 3547: 3544: 3541: 3538: 3535: 3532: 3529: 3523: 3514: 3511: 3508: 3505: 3502: 3499: 3496: 3490: 3487: 3481: 3478: 3475: 3472: 3469: 3466: 3463: 3457: 3449: 3445: 3441: 3439: 3434: 3431: 3428: 3418: 3415: 3412: 3409: 3406: 3403: 3400: 3394: 3385: 3382: 3379: 3376: 3373: 3370: 3367: 3364: 3361: 3355: 3352: 3346: 3343: 3340: 3337: 3334: 3331: 3328: 3320: 3314: 3306: 3302: 3298: 3296: 3291: 3288: 3285: 3275: 3272: 3269: 3266: 3263: 3260: 3257: 3254: 3251: 3245: 3242: 3236: 3233: 3230: 3227: 3224: 3221: 3218: 3215: 3212: 3206: 3203: 3201: 3193: 3187: 3184: 3181: 3171: 3168: 3165: 3162: 3159: 3153: 3150: 3144: 3141: 3138: 3135: 3132: 3126: 3123: 3121: 3116: 3113: 3102: 3101: 3100: 3066: 3063: 3060: 3057: 3055: 3050: 3047: 3044: 3037: 3029: 3026: 3023: 3020: 3017: 3014: 3011: 3009: 3001: 2995: 2992: 2989: 2982: 2979: 2976: 2973: 2970: 2968: 2963: 2960: 2949: 2948: 2947: 2940: 2931: 2927: 2925: 2921: 2917: 2893: 2889: 2885: 2882: 2879: 2876: 2873: 2870: 2867: 2864: 2861: 2854: 2853: 2852: 2849: 2843: 2839: 2835: 2831: 2827: 2824: 2820: 2816: 2812: 2808: 2804: 2801: 2798: 2794: 2790: 2786: 2783:changes from 2782: 2778: 2774: 2771: 2768: 2764: 2760: 2757:changes from 2756: 2752: 2748: 2745: 2737: 2733: 2729: 2726:changes from 2725: 2721: 2717: 2714: 2713: 2712: 2709: 2707: 2679: 2673: 2670: 2667: 2661: 2658: 2649: 2643: 2640: 2637: 2631: 2625: 2622: 2619: 2616: 2613: 2606: 2605: 2604: 2578: 2572: 2569: 2566: 2560: 2557: 2548: 2542: 2539: 2536: 2530: 2524: 2521: 2518: 2515: 2512: 2505: 2504: 2503: 2480: 2477: 2474: 2468: 2465: 2459: 2456: 2453: 2447: 2441: 2438: 2432: 2426: 2423: 2420: 2413: 2412: 2411: 2388: 2382: 2379: 2373: 2367: 2361: 2358: 2355: 2352: 2345: 2344: 2343: 2340: 2338: 2334: 2330: 2326: 2322: 2318: 2314: 2311: = 2310: 2306: 2302: 2290: 2286: 2262: 2258: 2254: 2251: 2248: 2245: 2239: 2236: 2233: 2230: 2222: 2218: 2214: 2211: 2205: 2202: 2199: 2196: 2193: 2190: 2187: 2180: 2179: 2178: 2176: 2173: = 2172: 2148: 2144: 2140: 2137: 2134: 2131: 2125: 2122: 2119: 2110: 2107: 2104: 2101: 2092: 2084: 2080: 2073: 2070: 2067: 2060: 2059: 2058: 2056: 2053: = 2052: 2033: 2025: 2021: 2017: 2014: 2011: 2008: 2002: 1999: 1996: 1987: 1979: 1975: 1971: 1968: 1962: 1959: 1956: 1947: 1939: 1935: 1928: 1925: 1922: 1915: 1914: 1913: 1911: 1907: 1903: 1900: = 1899: 1889: 1887: 1883: 1879: 1875: 1871: 1867: 1863: 1859: 1855: 1851: 1847: 1843: 1839: 1835: 1831: 1827: 1822: 1820: 1816: 1813: = 1812: 1808: 1804: 1800: 1796: 1792: 1788: 1784: 1780: 1776: 1772: 1768: 1764: 1760: 1756: 1752: 1748: 1744: 1740: 1736: 1732: 1728: 1724: 1720: 1716: 1711: 1707: 1690: 1687: 1683: 1673: 1669: 1666: 1659: 1652: 1648: 1647: 1630: 1626: 1622: 1619: 1616: 1613: 1610: 1605: 1601: 1597: 1594: 1591: 1586: 1582: 1578: 1575: 1572: 1569: 1564: 1560: 1556: 1553: 1550: 1545: 1541: 1537: 1534: 1529: 1525: 1521: 1516: 1512: 1508: 1505: 1498: 1497: 1496: 1494: 1490: 1474: 1470: 1469: 1452: 1448: 1444: 1441: 1438: 1435: 1430: 1426: 1422: 1419: 1416: 1411: 1407: 1403: 1400: 1395: 1391: 1387: 1382: 1378: 1374: 1371: 1368: 1361: 1360: 1359: 1357: 1341: 1337: 1331: 1327: 1326: 1309: 1305: 1301: 1298: 1295: 1292: 1287: 1283: 1279: 1276: 1273: 1268: 1264: 1260: 1257: 1252: 1248: 1244: 1239: 1235: 1231: 1228: 1221: 1220: 1219: 1217: 1207: 1205: 1198: 1194: 1185: 1176: 1173: 1167: 1165: 1161: 1150: 1148: 1144: 1140: 1136: 1131: 1129: 1125: 1114: 1106: 1095: 1091: 1086: 1082: 1077: 1074:path and the 1073: 1068: 1064: 1059: 1054: 1050: 1045: 1040: 1036: 1031: 1026: 1022: 1021: 1015: 1011: 1007: 1004: 1000: 996: 993: 989: 986: 982: 979: 978: 977: 969: 966: 962: 958: 954: 952: 942: 940: 936: 932: 928: 924: 914: 912: 908: 903: 901: 897: 893: 889: 885: 881: 876: 866: 857: 849: 845: 842: 838: 827: 823: 813: 811: 801: 798: 794: 791: 790: 789: 780: 777: 758: 755: 753:relationship. 751: 748: 747: 746: 737: 735: 731: 727: 726:Bootstrapping 723: 715: 712: 683: 678: 674: 668: 664: 660: 655: 650: 646: 640: 636: 630: 627: 621: 618: 611: 610: 604: 600: 597: 594: 588: 585: 580: 570: 568: 564: 559: 551: 542: 540: 530: 521: 513: 511: 503: 499: 494: 490: 482: 473: 469: 461: 458: 455: 454: 453: 451: 430: 427: 421: 418: 417: 398: 394: 390: 387: 384: 379: 375: 371: 368: 363: 359: 355: 350: 346: 342: 339: 332: 331: 330: 329: 324: 323: 311: 308: 307: 288: 284: 280: 277: 272: 268: 264: 259: 255: 251: 248: 245: 238: 237: 215: 214: 209: 208: 196: 193: 192: 173: 169: 165: 162: 157: 153: 149: 144: 140: 136: 133: 126: 125: 103: 102: 98: 97: 96: 88: 79: 75: 73: 69: 65: 61: 57: 53: 49: 45: 41: 32: 19: 6336: 6285: 6276: 6272: 6255: 6251: 6243: 6235: 6210: 6206: 6181: 6177: 6169: 6145: 6141: 6106: 6102: 6090: 6066: 6062: 6054: 6013: 6009: 5982: 5978: 5937: 5933: 5922:Bibliography 5885: 5882:Epidemiology 5881: 5841: 5837: 5805: 5801: 5753:(1): 18–26. 5750: 5747:Epidemiology 5746: 5691:(1): 51–71. 5688: 5684: 5644: 5640: 5634: 5609: 5605: 5599: 5566: 5562: 5549: 5518: 5514: 5470: 5467:Epidemiology 5466: 5456: 5431: 5427: 5420: 5411: 5386: 5382: 5344: 5340: 5327: 5297:(4): 550–8. 5294: 5290: 5277: 5269: 5261: 5250:. Retrieved 5240: 5229:. Retrieved 5225:the original 5215: 5204:. Retrieved 5201:quantpsy.org 5200: 5153: 5149: 5139: 5102: 5098: 5060: 5056: 5020: 5016: 4943: 4940:Epidemiology 4939: 4892: 4888: 4882: 4863: 4857: 4824: 4818: 4812: 4804: 4801:Aiken, L. S. 4765: 4761: 4751: 4743: 4738: 4727:. Retrieved 4720:the original 4713: 4680:CC BY-SA 3.0 4677: 4671: 4670: 4663:separately. 4633: 4451: 4449: 4292: 4290: 3918: 3891: 3864: 3860: 3856: 3852: 3848: 3819: 3627: 3601: 3597: 3593: 3589: 3585: 3580: 3578: 3085: 2945: 2928: 2923: 2919: 2912: 2910: 2850: 2847: 2841: 2837: 2833: 2829: 2822: 2818: 2814: 2810: 2806: 2802: 2796: 2792: 2788: 2784: 2780: 2776: 2772: 2766: 2762: 2758: 2754: 2750: 2739: 2735: 2731: 2727: 2723: 2719: 2715: 2710: 2705: 2703: 2602: 2501: 2409: 2341: 2336: 2332: 2328: 2324: 2320: 2316: 2312: 2308: 2304: 2300: 2288: 2284: 2282: 2174: 2170: 2168: 2054: 2050: 2048: 1909: 1905: 1901: 1897: 1895: 1885: 1881: 1877: 1873: 1869: 1865: 1861: 1857: 1853: 1849: 1848:and between 1845: 1841: 1837: 1833: 1829: 1825: 1823: 1814: 1810: 1806: 1802: 1798: 1794: 1790: 1786: 1782: 1778: 1774: 1770: 1766: 1762: 1758: 1754: 1750: 1746: 1742: 1738: 1734: 1730: 1726: 1722: 1718: 1714: 1712: 1708: 1704: 1685: 1678: 1671: 1664: 1657: 1650: 1492: 1488: 1486: 1472: 1355: 1353: 1339: 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579:Sobel test 563:Sobel test 463:variable). 40:statistics 6018:CiteSeerX 5957:1808/1491 5777:205587487 5698:1011.1079 5658:1302.4929 5651:: 11–18. 5532:1302.6835 4992:Pearl, J. 4768:: 17–32. 4468:− 4452:necessary 3986:− 3892:explained 3795:ε 3707:ε 3654:ε 3533:∣ 3506:∣ 3488:− 3473:∣ 3446:∑ 3410:∣ 3365:∣ 3353:− 3303:∑ 3255:∣ 3243:− 3216:∣ 3163:∣ 3151:− 3136:∣ 2880:− 2834:necessary 2817:= 1, and 2809:when the 2732:X =1 2659:− 2558:− 2466:− 2380:− 2259:ε 2219:ε 2145:ε 2081:ε 2022:ε 1976:ε 1936:ε 1840:(between 1627:ε 1602:β 1583:β 1561:β 1542:β 1526:β 1513:β 1449:ε 1427:β 1408:β 1392:β 1379:β 1306:ε 1284:β 1265:β 1249:β 1236:β 796:variable. 395:ε 376:β 360:β 347:β 285:ε 269:β 256:β 236:mediator 224:→ 211:anything. 170:ε 154:β 141:β 112:→ 44:mediation 6303:Archived 6258:: 1–41. 6227:16393019 6162:21500915 6133:12940467 6083:53599087 6040:20822249 6001:18697684 5966:15641418 5912:23007042 5860:52207229 5769:19234398 5626:52832751 5583:24885338 5497:10757981 5448:12757142 5403:16393020 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3994:1 3990:c 3983:E 3980:T 3977:( 3957:E 3954:T 3950:/ 3944:2 3940:c 3934:1 3930:b 3905:E 3902:T 3878:E 3875:T 3865:Y 3861:X 3857:Y 3853:X 3849:M 3833:3 3829:c 3799:3 3791:+ 3788:M 3785:X 3780:3 3776:c 3772:+ 3769:M 3764:2 3760:c 3756:+ 3753:X 3748:1 3744:c 3740:+ 3735:0 3731:c 3727:= 3720:Y 3711:2 3703:+ 3700:X 3695:1 3691:b 3687:+ 3682:0 3678:b 3674:= 3667:M 3658:1 3650:= 3643:X 3594:h 3590:g 3586:f 3560:. 3557:) 3554:m 3551:= 3548:M 3545:, 3542:0 3539:= 3536:X 3530:Y 3527:( 3524:E 3521:] 3518:) 3515:0 3512:= 3509:X 3503:m 3500:= 3497:M 3494:( 3491:P 3485:) 3482:1 3479:= 3476:X 3470:m 3467:= 3464:M 3461:( 3458:P 3455:[ 3450:m 3442:= 3435:E 3432:I 3429:N 3422:) 3419:0 3416:= 3413:X 3407:m 3404:= 3401:M 3398:( 3395:P 3392:] 3389:) 3386:m 3383:= 3380:M 3377:, 3374:0 3371:= 3368:X 3362:Y 3359:( 3356:E 3350:) 3347:m 3344:= 3341:M 3338:, 3335:1 3332:= 3329:X 3325:| 3321:Y 3318:( 3315:E 3312:[ 3307:m 3299:= 3292:E 3289:D 3286:N 3279:) 3276:m 3273:= 3270:M 3267:, 3264:0 3261:= 3258:X 3252:Y 3249:( 3246:E 3240:) 3237:m 3234:= 3231:M 3228:, 3225:1 3222:= 3219:X 3213:Y 3210:( 3207:E 3204:= 3197:) 3194:m 3191:( 3188:E 3185:D 3182:C 3175:) 3172:0 3169:= 3166:X 3160:Y 3157:( 3154:E 3148:) 3145:1 3142:= 3139:X 3133:Y 3130:( 3127:E 3124:= 3117:E 3114:T 3097:3 3093:2 3089:1 3087:ε 3067:. 3064:B 3061:A 3058:= 3051:E 3048:I 3045:N 3038:m 3030:, 3027:C 3024:= 3021:E 3018:D 3015:N 3012:= 3005:) 3002:m 2999:( 2996:E 2993:D 2990:C 2983:B 2980:A 2977:+ 2974:C 2971:= 2964:E 2961:T 2924:X 2920:X 2915:r 2894:r 2890:E 2886:I 2883:N 2877:E 2874:D 2871:N 2868:= 2865:E 2862:T 2823:X 2819:M 2815:X 2811:X 2807:Y 2797:X 2789:X 2785:X 2781:X 2777:Y 2763:X 2759:X 2755:X 2751:Y 2746:. 2744:) 2742:2 2736:X 2724:X 2720:Y 2706:E 2689:] 2686:) 2683:) 2680:0 2677:( 2674:M 2671:, 2668:0 2665:( 2662:Y 2656:) 2653:) 2650:1 2647:( 2644:M 2641:, 2638:0 2635:( 2632:Y 2629:[ 2626:E 2623:= 2620:E 2617:I 2614:N 2588:] 2585:) 2582:) 2579:0 2576:( 2573:M 2570:, 2567:0 2564:( 2561:Y 2555:) 2552:) 2549:0 2546:( 2543:M 2540:, 2537:1 2534:( 2531:Y 2528:[ 2525:E 2522:= 2519:E 2516:D 2513:N 2487:] 2484:) 2481:m 2478:, 2475:0 2472:( 2469:Y 2463:) 2460:m 2457:, 2454:1 2451:( 2448:Y 2445:[ 2442:E 2439:= 2436:) 2433:m 2430:( 2427:E 2424:D 2421:C 2395:] 2392:) 2389:0 2386:( 2383:Y 2377:) 2374:1 2371:( 2368:Y 2365:[ 2362:E 2359:= 2356:E 2353:T 2337:X 2333:X 2329:x 2327:( 2325:Y 2321:x 2319:( 2317:M 2313:x 2309:X 2305:Y 2301:M 2297:3 2293:1 2289:g 2285:f 2268:) 2263:3 2255:, 2252:M 2249:, 2246:x 2243:( 2240:h 2237:= 2234:Y 2231:, 2228:) 2223:2 2215:, 2212:x 2209:( 2206:g 2203:= 2200:M 2197:, 2194:x 2191:= 2188:X 2175:x 2171:X 2154:) 2149:3 2141:, 2138:m 2135:, 2132:X 2129:( 2126:h 2123:= 2120:Y 2111:, 2108:m 2105:= 2102:M 2093:, 2090:) 2085:1 2077:( 2074:f 2071:= 2068:X 2055:m 2051:M 2034:, 2031:) 2026:3 2018:, 2015:M 2012:, 2009:X 2006:( 2003:h 2000:= 1997:Y 1988:, 1985:) 1980:2 1972:, 1969:X 1966:( 1963:g 1960:= 1957:M 1948:, 1945:) 1940:1 1932:( 1929:f 1926:= 1923:X 1910:m 1906:M 1902:m 1898:M 1886:M 1882:M 1878:C 1870:C 1866:M 1862:X 1858:Y 1854:X 1850:Y 1846:Y 1842:M 1838:A 1834:B 1830:Y 1826:M 1815:m 1811:M 1807:M 1803:M 1799:X 1795:X 1791:Y 1787:m 1783:M 1779:M 1775:Y 1771:M 1767:M 1763:M 1759:M 1755:M 1751:M 1747:M 1743:Y 1739:X 1735:X 1731:M 1727:M 1723:Y 1719:X 1715:M 1686:B 1679:β 1672:β 1665:A 1658:β 1651:β 1631:6 1623:+ 1620:o 1617:M 1614:e 1611:M 1598:+ 1595:e 1592:M 1579:+ 1576:o 1573:M 1570:X 1557:+ 1554:o 1551:M 1538:+ 1535:X 1522:+ 1509:= 1506:Y 1493:B 1489:A 1473:β 1453:5 1445:+ 1442:o 1439:M 1436:X 1423:+ 1420:o 1417:M 1404:+ 1401:X 1388:+ 1375:= 1372:e 1369:M 1356:A 1340:β 1330:β 1310:4 1302:+ 1299:o 1296:M 1293:X 1280:+ 1277:o 1274:M 1261:+ 1258:X 1245:+ 1232:= 1229:Y 1216:C 1203:i 1201:ε 1147:C 1143:A 1139:C 1128:B 1124:A 1094:B 1090:A 1076:B 1072:A 1058:B 1044:A 1030:B 1014:B 1010:A 1003:B 999:A 992:B 985:A 965:B 961:A 931:Y 927:X 911:X 907:A 900:X 892:C 888:X 884:B 880:A 730:N 684:2 679:b 675:s 669:2 665:a 661:+ 656:2 651:a 647:s 641:2 637:b 631:b 628:a 622:= 619:z 539:′ 537:c 502:Y 498:X 429:β 420:β 399:3 391:+ 388:e 385:M 372:+ 369:X 356:+ 343:= 340:Y 310:β 289:2 281:+ 278:X 265:+ 252:= 249:e 246:M 195:β 174:1 166:+ 163:X 150:+ 137:= 134:Y 20:)

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