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Moved page from wikipedia:en:Mediation (statistics) (history)
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[[File:Simple Mediation Model.png|thumb|Simple Mediation Model]]
Simple Mediation Model
简单调解模式
In [[statistics]], a '''mediation''' model seeks to identify and explain the mechanism or process that underlies an observed relationship between an [[independent variable]] and a [[dependent variable]] via the inclusion of a third hypothetical variable, known as a '''mediator variable''' (also a '''mediating variable''', '''intermediary variable''', or '''intervening variable''').<ref>{{Cite web|title=Types of Variables|website=[[University of Indiana]]|url=http://www.indiana.edu/~educy520/sec5982/week_2/variable_types.pdf}}</ref> Rather than a direct causal relationship between the independent variable and the dependent variable, a mediation model proposes that the independent variable influences the (non-observable) 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.<ref>MacKinnon, D. P. (2008). ''Introduction to Statistical Mediation Analysis''. New York: Erlbaum.</ref>
In statistics, a mediation model seeks to identify and explain the mechanism or process that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third hypothetical variable, known as a mediator variable (also a mediating variable, intermediary variable, or intervening variable). Rather than a direct causal relationship between the independent variable and the dependent variable, a mediation model proposes that the independent variable influences the (non-observable) 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.
在统计学中，调解模型试图通过加入第三个假设变量，即中介变量(也是中介变量、中介变量或中间变量) ，来确定和解释自变量和因变量之间的观察关系所依据的机制或过程。一个调解模型没有在自变量和因变量之间建立直接的因果关系，而是提出自变量影响(不可观察的)调解变量，这反过来又影响因变量。因此，中介变量的作用是阐明自变量和因变量之间关系的性质。
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.<ref name=CCWA>Cohen, J.; Cohen, P.; West, S. G.; [[Leona S. Aiken|Aiken, L. S.]] (2003) ''Applied multiple regression/correlation analysis for the behavioral sciences'' (3rd ed.). Mahwah, NJ: Erlbaum.</ref> In particular, mediation analysis can contribute to better understanding the relationship between an independent variable and a dependent variable when these variables do not have an obvious direct connection.
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 independent variable and a dependent variable when these variables do not have an obvious direct connection.
中介分析通过探索一个变量通过一个中介变量影响另一个变量的潜在机制或过程来理解一个已知的关系。特别是，中介分析有助于更好地理解自变量和因变量之间的关系，当这些变量没有明显的直接联系。
==Baron and Kenny's (1986) steps for mediation==
Baron and Kenny (1986) <ref>Baron, R. M. and Kenny, D. A. (1986) "The Moderator-Mediator Variable Distinction in Social Psychological Research – Conceptual, Strategic, and Statistical Considerations", [[Journal of Personality and Social Psychology]], Vol. 51(6), pp. 1173–1182.</ref> 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. Note: Hayes (2009)<ref name=Hayes/> critiqued Baron and Kenny's mediation steps approach, and as of 2019, [[David A. Kenny]] on his website stated that mediation can exist in the absence of a 'significant' total effect, and therefore step 1 below may not be needed. This situation is sometimes referred to as "inconsistent mediation". Later publications by Hayes also questioned the concepts of full or partial mediation and advocated for these terms, along with the classical mediation steps approach outlined below, to be abandoned.
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. Note: Hayes (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 multiple regression analysis.
巴伦和肯尼(1986)提出了若干必须满足的要求，以形成一个真正的调解关系。下面用一个现实世界的例子对它们进行了概述。请参阅上面的图表以了解整个中介关系的可视化表示形式。注: Hayes (2009)解释了 Baron 和 Kenny 的每一步要求，以进一步了解调解效应是如何表现的。第一步和第二步使用简单的回归分析/回归分析，而第三步使用多个/频率/频率。
'''Step 1:'''
Step 1:
第一步:
:Regress the dependent variable on the independent variable to confirm that the independent variable is a significant predictor of the dependent variable.
How you were parented (i.e., independent variable) predicts how confident you feel about parenting your own children (i.e., dependent variable).
你是如何被抚养的(即，独立变量)预示着你对抚养自己的孩子有多自信(即，因变量)。
: Independent variable <math> \to </math> dependent variable
How you were parented <math> \to </math> confidence in own parenting abilities.
你是如何培养孩子对自己养育能力的信心的。
:: <math>Y=\beta_{10} +\beta_{11}X + \varepsilon_1</math>
* ''β''<sub>11</sub> is significant
Step 2:
第二步:
'''Step 2:'''
How you were parented (i.e., independent variable) predicts your feelings of competence and self-esteem (i.e., mediator).
你是如何被抚养的(即，独立变量)可以预测你的能力和自尊的感受(即，调解人)。
: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 anything.
How you were parented <math> \to </math> Feelings of competence and self-esteem.
你是如何培养自己的能力和自尊心的。
: Independent variable <math> \to </math> mediator
Step 3:
第三步:
:: <math>Me=\beta_{20} +\beta_{21}X + \varepsilon_2</math>
* ''β''<sub>21</sub> is significant
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 variable).
你的能力和自尊感(即中介者)能够预测你对抚养自己的孩子的自信程度(即因变量) ，同时控制你是如何被抚养的(即自变量)。
'''Step 3:'''
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.
这些发现会导致这样的结论，即你的能力和自尊感会调节你是如何被抚养的和你对抚养自己的孩子有多自信之间的关系。
: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 rendered nonsignificant.
Note: 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 the effect that actually exists (See Shrout & Bolger, 2002 for more info).
注意: 如果步骤1没有产生显著的结果，一个人可能仍然有理由移动到步骤2。有时，独立变量和因变量之间确实存在显著的关系，但是由于样本量小，或者其他额外的因素，没有足够的能量来预测实际存在的影响(参见 Shrout & Bolger，2002)。
:: <math>Y=\beta_{30} +\beta_{31}X +\beta_{32}Me + \varepsilon_3</math>
* ''β''<sub>32</sub> is significant
Direct Effect in a Mediation Model
调解模式中的直接效果
* ''β''<sub>31</sub> should be smaller in absolute value than the original effect for the independent variable (β<sub>11</sub> above)
In the diagram shown above, the indirect effect is the product of path coefficients "A" and "B". The direct effect is the coefficient " C' ".
在上图中，间接效应是路径系数“ a”和“ b”的乘积。直接的影响是系数“ c”。
The direct effect measures the extent to which the dependent variable changes when the independent variable increases by one unit and the mediator variable remains unaltered. In contrast, the indirect effect measures the extent to which the dependent variable changes when the independent variable is held fixed and the mediator variable changes by the amount it would have changed had the independent variable increased by one unit. 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.
直接效应衡量的是当自变量增加一个单位而中介变量保持不变时，因变量变化的程度。相比之下，间接效应衡量的是因变量在自变量固定和中介变量增加一个单位时变化的程度。在引入调解人时，因为只解释了微小的方差(即，不是真正的调解) ，所以自变量对因变量的影响可能变得不重要。因此，在进行全部或部分调解之前，必须显示由独立变量解释的差异显著减少。
'''Example'''
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.
在没有全面影响的情况下，有可能产生统计上显著的间接影响。这可以通过存在几个相互抵消的调解路径来解释，并且在控制其中一个取消调解器时变得显而易见。这意味着“部分”和“完全”中介术语应该始终相对于模型中存在的一组变量进行解释。
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. 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.
在所有情况下，“固定一个变量”的操作必须与“控制一个变量”的操作区分开来，后者在文献中被不恰当地使用。检测小效应需要1000个样本量，检测中等效应需要100个样本量，检测大效应需要50个样本量。
The following example, drawn from Howell (2009),<ref>Howell, D. C. (2009). Statistical methods for psychology (7th ed.). Belmot, CA: Cengage Learning.</ref> 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 [[multiple regression analysis]].
Step 1:
The bootstrapping method provides some advantages to the Sobel's test, primarily an increase in power. The Preacher and Hayes Bootstrapping method is a non-parametric test (See Non-parametric statistics for a discussion on non-parametric tests and their power). As such, the bootstrap method does not violate assumptions of normality and is therefore recommended for small sample sizes.
自举方法为 Sobel 的测试提供了一些优点，主要是增加了功耗。传道者和 Hayes Bootstrapping 方法是一种非参数检验(参见无母数统计非参数检验及其效力的讨论)。因此，自助法并不违反常态假设，因此建议小样本情况下使用。
:How you were parented (i.e., independent variable) predicts how confident you feel about parenting your own children (i.e., dependent variable).
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. Hayes offers a macro <http://www.afhayes.com/> that calculates bootstrapping directly within SPSS, a computer program used for statistical analyses. This 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.
自举涉及重复随机抽样观察和替换从数据集计算期望的统计量在每个重采样。通过计算数百个或数千个引导重采样提供了感兴趣统计量的抽样分布的近似值。提供了一个宏 < http://www.afhayes.com/ > ，它可以直接计算 SPSS 中的自举，这是一个用于统计分析的计算机程序。这种方法提供了点估计和置信区间，通过这些点估计和置信区间可以评估中介效应的重要性或非重要性。点估计揭示了引导样本数目的平均值，如果零没有落在引导方法产生的置信区间之间，人们可以自信地得出结论，有一个重要的中介效应要报告。
: How you were parented <math> \to </math> confidence in own parenting abilities.
Step 2:
As outlined above, there are a few different options one can choose from to evaluate a mediation model.
如上所述，在评估一个中介模型时，可以从几个不同的选项中进行选择。
:How you were parented (i.e., independent variable) predicts your feelings of competence and self-esteem (i.e., mediator).
Bootstrapping 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 or the Sobel test. 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. and interpreted formally.
引导法因为不需要满足正态性假设，并且在样本量较小时(n < 25)可以有效地利用，因此成为最流行的检验中介的方法。然而，调解仍然是最常用的决定使用的逻辑的巴伦和肯尼或索贝尔测试。发布纯粹基于 Baron 和 Kenny 方法的调解测试或者进行分布性假设(如 Sobel 测试)的测试变得越来越困难。因此，在选择进行哪项测试时，考虑你的选择是很重要的。并正式解释。
: How you were parented <math> \to </math> Feelings of competence and self-esteem.
(1) Experimental-causal-chain design
(1)实验因果链设计
Step 3:
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 relationship.
实验因果链设计时，所提出的中介体是实验操纵。这样的设计意味着一个人操纵一些他们有理由相信可能是给定关系的潜在机制的受控的第三变量。
: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 variable).
(2) Measurement-of-mediation design
(2)测量调解设计
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.
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, but only involves measurement.
度量中介设计可以概念化为统计方法。这样的设计意味着一个人衡量所提议的中间变量，然后使用统计分析来建立调解。这种方法不涉及对虚拟中介变量的操作，而只涉及测量。
Note: 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 the effect that actually exists (See Shrout & Bolger, 2002 <ref>{{cite journal | last1 = Shrout | first1 = P. E. | last2 = Bolger | first2 = N. | year = 2002 | title = Mediation in experimental and nonexperimental studies: New procedures and recommendations | journal = Psychological Methods | volume = 7 | issue = 4| pages = 422–445 | doi=10.1037/1082-989x.7.4.422}}</ref> for more info).
==Direct versus indirect effects==
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.
调解的试验办法必须谨慎进行。首先，对潜在中介变量的探索性研究必须有强有力的理论支持。
[[File:Direct Effect in a Mediation Model.jpg|thumb|Direct Effect in a Mediation Model]]
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.
对调解方法的批评取决于操纵和测量调解变量的能力。因此，人们必须能够以可以接受和符合道德的方式操纵拟议的调解人。因此，人们必须能够在不干扰结果的情况下衡量干预过程。中介者还必须能够建立操纵的结构效度。
In the diagram shown above, the indirect effect is the product of path coefficients "A" and "B". The direct effect is the coefficient " C' ".
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: and Preacher, Rucker, and Hayes (2007).
对中介测量方法最常见的批评之一是，它最终是一种相关设计。因此，可能是其他第三个变数，独立于拟议的调解员，可负责拟议的效果。然而，研究人员一直在努力为这种蔑视提供反证据。具体来说，以下的反论点已经提出: 和牧师，拉克尔，和海斯(2007年)。
The direct effect measures the extent to which the dependent variable changes when the independent variable increases by one unit and the mediator variable remains unaltered. In contrast, the indirect effect measures the extent to which the dependent variable changes when the independent variable is held fixed and the mediator variable changes by the amount it would have changed had the independent variable increased by one unit.<ref name="Robins"/><ref name="Pearl-01"/>
[[File:Mediation Model.png|thumb|Indirect Effect in a Simple Mediation Model: The indirect effect constitutes the extent to which the X variable influences the Y variable through the mediator.]]
In linear systems, the total effect is equal to the sum of the direct and indirect (''C' + AB'' 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.<ref name="Pearl-01"/>
There are five possible models of moderated mediation, as illustrated in the diagrams below.
如下图所示，有节制的调解有五种可能的模式。
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 Prisoner's Dilemma Game (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, social value orientation (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).
研究人员向参与者提供了一个初始刺激物(初始刺激物) ，这个刺激物使他们想到道德或者让他们想到可能性。然后，他们参加了囚徒困境游戏(PDG) ，在这个游戏中，参与者假装他们和他们的犯罪同伙已经被逮捕，他们必须决定是继续忠于他们的同伙，还是与他们的同伙竞争并与当局合作。研究人员发现亲社会的个体受到道德和可能的优先权的影响，而亲社会的个体则不受影响。因此，社会价值取向(亲自与亲社会)调节了基本变量(自变量: 道德与可能)与 PDG 中选择的行为(因变量: 竞争与合作)之间的关系。
==Full versus partial mediation==
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’ social value orientation 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 with their partner and cooperate with the authorities. In contrast, participants with a pro-self social value orientation always acted competitively.
接下来，研究人员寻找中和效应的存在。回归分析显示，初始类型(道德与可能)中介了参与者的社会价值取向对 PDG 行为的调节关系。那些经历过道德优势的亲社会参与者希望他们的伴侣与他们合作，所以他们选择了自己合作。亲社会的参与者经历了可能的主要期望他们的伴侣与他们竞争，这使他们更有可能与他们的伴侣竞争并与当局合作。相比之下，具有亲自我社会价值取向的参与者总是在竞争中行动。
A mediator variable can either account for all or some of the observed relationship between two variables.
'''Full mediation'''
Muller, Judd, and Yzerbyt (2005) except in the case of no omitted variables.
Muller，Judd，and Yzerbyt (2005) ，除了没有省略变量的情况。
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 ''c'' in diagram above) to zero.
[[File:Full Mediation Model.png|thumb|Full Mediation Model]]
To illustrate, assume that the error terms of M and Y
为了说明，假设 m 和 y 的错误项
'''Partial mediation'''
are correlated. Under such conditions, the
是相关的。在这种情况下,
[[File:Mediation.jpg|thumb|The Partial Mediation Model Includes a Direct Effect]]
structural coefficient B and A (between M and Y and between Y and X)
结构系数 b 和 a (介于 m 和 y 之间，y 和 x 之间)
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 some direct relationship between the independent and dependent variable.
can no longer be estimated by regressing Y on X and M.
不能再通过 x 和 m 的 y 回归来估计。
In fact, the regression slopes may both be nonzero
事实上，回归斜率可能都是非零的
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 [[Sobel test]].<ref name="Sobel, M. E. 1982 pp. 290">{{cite journal | last1 = Sobel | first1 = M. E. | year = 1982 | title = Asymptotic confidence intervals for indirect effects in structural equation models | journal = Sociological Methodology | volume = 13 | pages = 290–312 | doi = 10.2307/270723 | jstor = 270723 }}</ref> 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.
even when C is zero. This has two
即使 c 是零。这里有两个
It is possible to have statistically significant indirect effects in the absence of a total effect.<ref name=Hayes>{{cite journal | last1 = Hayes | first1 = A. F. | year = 2009 | title = Beyond Baron and Kenny: Statistical mediation analysis in the new millennium | journal = Communication Monographs | volume = 76 | issue = 4| pages = 408–420 | doi = 10.1080/03637750903310360 }}</ref> 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.
consequences. First, new strategies must be devised for
后果。首先，必须制定新的战略
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.<ref name="Robins"/><ref name="Kaufman"/> 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 [[Bayesian Networks]]).
estimating the structural coefficients A,B and C. Second,
估计结构系数 a，b 和 c,
the basic definitions of direct and indirect effects
直接和间接影响的基本定义
==Sobel's test==
must go beyond regression analysis, and should
必须超越回归分析
{{main|Sobel test}}
invoke an operation that mimics "fixing M",
调用一个模仿“修理 m”的操作,
rather than "conditioning on M."
而不是“对 m 施加条件作用”
As mentioned above, [[Sobel test|Sobel's test]]<ref name="Sobel, M. E. 1982 pp. 290"/> 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 independent variable and the dependent variable compared to the relationship between the independent variable and dependent variable including the mediation factor.
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 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 [[Normal distribution]] for more details). Thus, the rule of thumb as suggested by MacKinnon et al., (2002) <ref>{{cite journal | last1 = MacKinnon | first1 = D. P. | last2 = Lockwood | first2 = C. M. | last3 = Lockwood | first3 = J. M. | last4 = West | first4 = S. G. | last5 = Sheets | first5 = V. | year = 2002 | title = A comparison of methods to test mediation and other intervening variable effects | journal = Psychological Methods| volume = 7 | issue = 1| pages = 83–104 | doi=10.1037/1082-989x.7.1.83| pmid = 11928892 | pmc=2819363}}</ref> 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.
Such an operator, denoted do(M = m), was defined in Pearl (1994) or "structural counterfactuals".
这样一个算子，表示 do (m = m) ，在 Pearl (1994)或“结构反事实”中定义。
These new variables provide convenient notation
这些新的变量提供了方便的符号
==Preacher and Hayes (2004) bootstrap method==
for defining direct and indirect effects. In particular,
定义直接和间接影响。特别是,
four types of effects have been defined for the
四种类型的影响已被定义为
The bootstrapping method provides some advantages to the Sobel's test, primarily an increase in power. The Preacher and Hayes Bootstrapping method is a non-parametric test (See [[Non-parametric statistics]] for a discussion on non-parametric tests and their power). As such, the bootstrap method does not violate assumptions of normality and is therefore recommended for small sample sizes.
transition from X = 0 to X = 1:
从 x = 0到 x = 1的跃迁:
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. Hayes offers a macro <http://www.afhayes.com/> that calculates bootstrapping directly within [[SPSS]], a computer program used for statistical analyses. This 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.
(a) Total effect –
(a)总效应 -
==Significance of mediation==
<math>TE = E [Y(1) - Y(0)] </math>
[ math > TE = e [ y (1)-y (0)]
(b) Controlled direct effect -
(b)受管制的直接影响 -
As outlined above, there are a few different options one can choose from to evaluate a mediation model.
<math> CDE(m) = E [Y(1,m) - Y(0,m) ] </math>
[ math > CDE (m) = e [ y (1，m)-y (0，m)] </math >
(c) Natural direct effect -
(c)天然直接效应 -
[[Bootstrapping (statistics)|Bootstrapping]]<ref>{{cite web |url=http://www.comm.ohio-state.edu/ahayes/sobel.htm |title=Testing of Mediation Models in SPSS and SAS |publisher=Comm.ohio-state.edu |access-date=2012-05-16 |archive-url=https://web.archive.org/web/20120518234943/http://www.comm.ohio-state.edu/ahayes/sobel.htm |archive-date=2012-05-18 |url-status=dead }}</ref><ref>{{cite web|url=http://www.comm.ohio-state.edu/ahayes/SPSS%20programs/indirect.htm |title=SPSS and SAS Macro for Bootstrapping Specific Indirect Effects in Multiple Mediation Models |publisher=Comm.ohio-state.edu |access-date=2012-05-16}}</ref> 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 <ref>[http://davidakenny.net/cm/mediate.htm "Mediation"]. ''davidakenny.net''. Retrieved April 25, 2012.</ref> or the [[Sobel test]]. 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.<ref name=Hayes/>
<math>NDE = E [Y(1,M(0)) - Y(0,M(0))] </math>
[ math > NDE = e [ y (1，m (0)-y (0，m (0)]
(d) Natural indirect effect
(d)自然间接影响
==Approaches to mediation==
<math> NIE = E [Y(0,M(1)) - Y(0,M(0))] </math>
[ math > NIE = e [ y (0，m (1))-y (0，m (0)]
Where E[ ] stands for expectation taken over the error terms.
其中 e []表示期望取代了错误项。
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<ref name="Robins">{{cite journal | last1 = Robins | first1 = J. M. | author-link = James Robins | author-link2 = Sander Greenland | last2 = Greenland | first2 = S. | year = 1992 | title = Identifiability and exchangeability for direct and indirect effects | journal = Epidemiology | volume = 3 | issue = 2| pages = 143–55 | doi = 10.1097/00001648-199203000-00013 | pmid = 1576220 }}</ref><ref name="Kaufman">{{cite journal|pmc=526390|doi=10.1186/1742-5573-1-4|year=2004|last1=Kaufman|first1=J. S.|title=A further critique of the analytic strategy of adjusting for covariates to identify biologic mediation|journal=Epidemiologic Perspectives & Innovations |volume=1|issue=1|pages=4|last2=MacLehose|first2=R. F.|last3=Kaufman|first3=S|pmid=15507130}}</ref><ref name="Bullock">{{cite journal|pmid=20307128|url=http://www2.psych.ubc.ca/~schaller/528Readings/BullockGreenHa2010.pdf|year=2010|last1=Bullock|first1=J. G.|title=Yes, but what's the mechanism? (don't expect an easy answer)|journal=Journal of Personality and Social Psychology|volume=98|issue=4|pages=550–8|last2=Green|first2=D. P.|last3=Ha|first3=S. E.|doi=10.1037/a0018933}}
</ref> and interpreted formally.<ref name="Pearl-01">[[Judea Pearl|Pearl, J.]] (2001) [http://ftp.cs.ucla.edu/pub/stat_ser/R273-U.pdf "Direct and indirect effects"]. Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, [[Morgan Kaufmann]], 411–420.</ref>
These effects have the following interpretations:
这些影响有以下解释:
(1) Experimental-causal-chain design
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 relationship.
(2) Measurement-of-mediation design
A controlled version of the indirect effect does not
间接效应的受控版本则不会
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, but only involves measurement.<ref>{{cite journal|pmid=16393019|url=http://www2.psych.ubc.ca/~schaller/528Readings/SpencerZannaFong2005.pdf|year=2005|last1=Spencer|first1=S. J.|title=Establishing a causal chain: Why experiments are often more effective than mediational analyses in examining psychological processes|journal=Journal of Personality and Social Psychology|volume=89|issue=6|pages=845–51|last2=Zanna|first2=M. P.|last3=Fong|first3=G. T.|doi=10.1037/0022-3514.89.6.845}}
exist because there is no way of disabling the
因为没有办法禁用
</ref>
direct effect by fixing a variable to a constant.
把一个变量固定在一个常数上的直接效果。
==Criticisms of mediation measurement==
According to these definitions the total effect can be decomposed as a sum
根据这些定义，总效应可以分解为总和
<math>TE = NDE - NIE_r </math>
<math>TE = NDE - NIE_r </math>
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.
where NIE<sub>r</sub> stands for the reverse transition, from
其中 NIE < sub > r </sub > 代表反向过渡，从
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.
X = 1 to X = 0; it becomes additive in linear systems,
1 to x = 0; 它成为线性系统的可加性,
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:<ref name=CCWA/>
where reversal of transitions entails sign reversal.
转变的逆转导致了标志的逆转。
(1) Temporal precedence. 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.
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.
这些定义的力量在于它们的普遍性，它们适用于任意非线性相互作用的模型，干扰之间的任意依赖，以及连续变量和分类变量。
(2) Nonspuriousness and/or no confounds. 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 below.
Formulation of the indirect effect
间接效应的表述
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 (statistics)|moderation]].
In linear analysis, all effects are determined by sums
在线性分析中，所有的影响都是由和决定的
==Other third variables==
of products of structural coefficients, giving
结构系数的乘积，给出
<math>
《数学》
(1) Confounding:
\begin{align}
开始{ align }
TE & = C + AB \\
等于 c + AB
: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.
CDE(m) & = NDE = C, \text{ independent of } m\\
CDE (m) & = NDE = c，文本{独立于} m
NIE & = AB.
和 = AB。
[[File:Mediation model with two covariates.jpg|thumb|Mediation model with two covariates]]
\end{align}
结束{ align }
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.
</math>
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Therefore, all effects are estimable whenever the model
因此，无论何时模型都可以估计所有的影响
(2) Suppression:
is identified. In non-linear systems, more stringent
被识别出来。在非线性系统中，更为严格
conditions are needed for estimating the
我们需要一些条件来估计
: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 (''C''), which 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.
direct and indirect effects
直接和间接影响
.
.
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.
For example, if no confounding exists,
例如，如果不存在混淆,
(i.e., ε<sub >1</sub>, ε<sub>2</sub>, and ε<sub>3</sub> are mutually independent) the
(即 ε < sub > 1 </sub > ，ε < sub > 2 </sub > ，ε < sub > 3 </sub > 是相互独立的)
(3) Moderators:
following formulas can be derived:
可以推导出以下公式:
and have become the target of estimation in many studies of mediation. They give
并成为许多中介研究评价的对象。他们给予
:Other important third variables are moderators. 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 ''X'' and ''Y''. A moderating relationship can be thought of as an [[interaction effect|interaction]]. It occurs when the relationship between variables A and B depends on the level of C. See [[moderation (statistics)|moderation]] for further discussion.
distribution-free expressions for direct and indirect
直接和间接的分布-自由表达式
effects and demonstrate that, despite the arbitrary nature of
尽管我们的研究结果具有随意性
==Moderated mediation==
the error distributions and the functions f, g, and h,
误差分布和函数 f，g，h,
mediated effects can nevertheless be estimated from data using
然而，我们可以通过使用数据来估计中介效应
Mediation and [[moderation (statistics)|moderation]] can co-occur in statistical models. It is possible to mediate moderation and moderate mediation.
regression.
回归。
The analyses of moderated mediation
有调节的中介分析
[[Moderated mediation]] is when the effect of the treatment ''A'' on the mediator and/or the partial effect ''B'' 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 moderated by different levels of another variable (i.e., a moderator). This definition has been outlined by Muller, Judd, and Yzerbyt (2005)<ref name="Muller">{{cite journal | last1 = Muller | first1 = D. | last2 = Judd | first2 = C. M. | last3 = Yzerbyt | first3 = V. Y. | year = 2005 | title = When moderation is mediated and mediation is moderated | journal = Journal of Personality and Social Psychology | volume = 89 | issue = 6| pages = 852–863 | doi = 10.1037/0022-3514.89.6.852 | pmid = 16393020 }}</ref> and Preacher, Rucker, and Hayes (2007).<ref name="Preacher">Preacher, K. J., Rucker, D. D. & Hayes, A. F. (2007). Assessing moderated mediation hypotheses: Strategies, methods, and prescriptions. Multivariate Behavioral Research, 42, 185–227.</ref>
and mediating moderators fall as special cases of the causal mediation
和调解人作为因果调解的特殊案例下降
analysis, and the mediation formulas identify how various interactions coefficients contribute to the necessary and sufficient components of mediation.
分析，以及调解公式确定各种相互作用系数如何有助于调解的必要和充分的组成部分。
===Models of moderated mediation===
There are five possible models of moderated mediation, as illustrated in the diagrams below.<ref name="Muller" />
A serial mediation model with two mediator variables.
一个具有两个中介变量的串行中介模型。
# In the first model the independent variable also moderates the relationship between the mediator and the dependent variable.
# 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).
A conceptual diagram that depicts a parallel mediation model with two mediator variables.
描述具有两个中介变量的并行中介模型的概念图。
# 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).
Assume the model takes the form
假设模型采用这种形式
# 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).
<math>
《数学》
# 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.
\begin{align}
开始{ align }
X & = \varepsilon_1 \\
1
{|
M & = b_0 + b_1X + \varepsilon_2 \\
0 + b 1x + varepsilon 2
Y & = c_0 + c_1X + c_2M + c_3XM + \varepsilon_3
Y & = c _ 0 + c _ 1x + c _ 2m + c _ 3xm + varepsilon _ 3
| [[File:Mediated moderation model 1.png|centre|thumb|
\end{align}
结束{ align }
First option: independent variable moderates the ''B'' path.]]
</math>
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| [[File:Mediated moderation model 2.png|centre|thumb|
where the parameter <math>c_3</math> quantifies the degree to which M modifies the effect of X on Y. Even when all parameters are estimated from data, it is still not obvious what combinations of parameters measure the direct and indirect effect of X on Y, or, more practically, how to assess the fraction of the total effect <math>TE</math> that is explained by mediation and the fraction of <math>TE</math> that is owed to mediation. In linear analysis, the former fraction is captured by the product <math>b_1 c_2 / TE</math>, the latter by the difference <math>(TE - c_1)/TE</math>, 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:
其中参数 c _ 3 </math > 量化了 m 修改 x 对 y 影响的程度。即使所有的参数都是从数据中估计出来的，仍然不清楚哪些参数组合可以衡量 x 对 y 的直接和间接影响，或者更实际地说，如何评估调解和归因于调解的“数学”“数学”“数学”所占总影响的比例。在线性分析中，前者由乘积 < math > b1c2/TE </math > 获得，后者由差 < math > (TE-c1)/TE </math > 获得，两个量重合。然而，在存在相互作用的情况下，每个部分都需要按照调解公式进行单独分析，分析结果如下:
Second option: fourth variable moderates the ''A'' path.]]
<math>
《数学》
| [[File:Mediated moderation model 3.png|centre|thumb|
\begin{align}
开始{ align }
Third option: fourth variable moderates the ''B'' path.]]
NDE & = c_1 + b_0 c_3 \\
NDE & = c 1 + b 0 c 3
| [[File:Mediated moderation model 4.png|centre|thumb|
NIE & = b_1 c_2 \\
1 c 2
Fourth option: fourth variable moderates both the ''A'' path and the ''B'' path.]]
TE & = c_1 + b_0 c_3 + b_1(c_2 + c_3) \\
TE & = c1 + b0 c3 + b1(c2 + c3)
| [[File:Mediated moderation model 5.png|centre|thumb|
& = NDE + NIE + b_1 c_3.
& = NDE + NIE + b 1 c 3.
Fifth option: fourth variable moderates the ''A'' path and a fifth variable moderates the ''B'' path.]]
\end{align}
结束{ align }
|}
</math>
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==Mediated moderation==
Thus, the fraction of output response for which mediation would be sufficient is
因此，输出响应中中介足够的部分是
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.<ref name="Muller" />
<math> \frac{NIE}{TE} = \frac{b_1 c_2}{c_1 + b_0 c_3 + b_1 (c_2 + c_3)}, </math>
1 + b _ 0 c _ 3 + b _ 1(c _ 2 + c _ 3) ，</math >
In order to establish mediated moderation, one must first establish [[Moderation (statistics)|moderation]], meaning that the direction and/or the strength of the relationship between the independent and dependent variables (path ''C'') 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 ''A'') or between the moderator and the dependent variable (path ''C'').
while the fraction for which mediation would be necessary is
而调解的必要部分是
'''Example'''
<math> 1- \frac{NDE}{TE} = \frac{b_1 (c_2 +c_3)}{c_1 + b_0c_3 + b_1 (c_2 + c_3)}. </math>
1-frac { NDE }{ TE } = frac { b _ 1(c _ 2 + c _ 3)}{ c _ 1 + b _ 0c _ 3 + b _ 1(c _ 2 + c _ 3)}.数学
The following is a published example of mediated moderation in psychological research.<ref>{{cite journal | last1 = Smeesters | first1 = D. | last2 = Warlop | first2 = L. | last3 = Avermaet | first3 = E. V. | last4 = Corneille | first4 = O. | last5 = Yzerbyt | first5 = V. | year = 2003 | title = Do not prime hawks with doves: The interplay of construct activation and consistency of social value orientation on cooperative behavior | journal = Journal of Personality and Social Psychology | volume = 84 | issue = 5| pages = 972–987 | doi = 10.1037/0022-3514.84.5.972 | pmid = 12757142 }}</ref>
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 [[Prisoner's dilemma|Prisoner's Dilemma Game]] (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, [[Social value orientations|social value orientation]] (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).
These fractions involve non-obvious combinations
这些分数包含不明显的组合
of the model's parameters, and can be constructed
模型的参数，可以构造出
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’ [[Social value orientations|social value orientation]] 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 with their partner and cooperate with the authorities. In contrast, participants with a pro-self social value orientation always acted competitively.
mechanically with the help of the Mediation Formula. Significantly, due to interaction, a direct effect can be sustained even when the parameter <math>c_1</math> 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 separately.
借助调解公式机械地进行调解。值得注意的是，由于相互作用，即使参数 c _ 1 </math > 消失，直接影响也可以持续，而且，即使直接和间接影响消失，总体影响也可以持续。这表明，孤立地估计参数并不能告诉我们有关调解效果的信息，更普遍地说，调解和调节是相互交织的，不能单独进行评估。
==Regression equations for moderated mediation and mediated moderation==
Muller, Judd, and Yzerbyt (2005)<ref name="Muller"/> outline three fundamental models that underlie both moderated mediation and mediated moderation. ''Mo'' represents the moderator variable(s), ''Me'' represents the mediator variable(s), and ''ε<sub>i</sub>'' represents the measurement error of each regression equation.
Notes
注释
[[File:Mediation.jpg|434px|right|A simple statistical mediation model.]]
Bibliography
参考书目
'''Step 1''': Moderation of the relationship between the independent variable (X) and the dependent variable (Y), also called the overall treatment effect (path ''C'' in the diagram).
: <math>Y=\beta_{40} +\beta_{41}X +\beta_{42}Mo +\beta_{43}XMo + \varepsilon_4</math>
| last = Preacher
| last = Preacher
* To establish overall moderation, the ''β''<sub>43</sub> regression weight must be significant (first step for establishing mediated moderation).
| first = Kristopher J.
第一，克里斯托弗 j。
* Establishing moderated mediation requires that there be no moderation effect, so the ''β''<sub>43</sub> regression weight must not be significant.
| last2 = Hayes
2 = Hayes
| first2 = Andrew F.
2 = Andrew f.
'''Step 2''': Moderation of the relationship between the independent variable and the mediator (path ''A'').
| title = SPSS and SAS procedures for estimating indirect effects in simple mediation models
| title = 用于估计简单调解模型中的间接影响的 SPSS 和 SAS 程序
: <math>Me=\beta_{50} +\beta_{51}X +\beta_{52}Mo +\beta_{53}XMo + \varepsilon_5</math>
| journal = Behavior Research Methods, Instruments, and Computers
行为研究方法，仪器和计算机
* If the ''β''<sub>53</sub> regression weight is significant, the moderator affects the relationship between the independent variable and the mediator.
| volume = 36
36
| issue = 4
第四期
'''Step 3''': Moderation of both the relationship between the independent and dependent variables (path ''A'') and the relationship between the mediator and the dependent variable (path ''B'').
| pages = 717–731
| 页数 = 717-731
: <math>Y=\beta_{60} +\beta_{61}X +\beta_{62}Mo +\beta_{63}XMo +\beta_{64}Me +\beta_{65}MeMo + \varepsilon_6</math>
| url = http://www.afhayes.com/spss-sas-and-mplus-macros-and-code.html
Http://www.afhayes.com/spss-sas-and-mplus-macros-and-code.html
* If both ''β''<sub>53</sub> in step 2 and ''β''<sub>63</sub> in step 3 are significant, the moderator affects the relationship between the independent variable and the mediator (path ''A'').
| year = 2004
2004年
* If both ''β''<sub>53</sub> in step 2 and ''β<sub>65</sub>'' in step 3 are significant, the moderator affects the relationship between the mediator and the dependent variable (path ''B'').
| doi = 10.3758/BF03206553
| doi = 10.3758/BF03206553
* Either or both of the conditions above may be true.
| pmid = 15641418
15641418
| doi-access = free
免费访问
==Causal mediation analysis==
}}
}}
===Fixing versus conditioning===
| last = Preacher
| last = Preacher
| first = Kristopher J.
第一，克里斯托弗 j。
Mediation analysis quantifies the
| last2 = Hayes
2 = Hayes
extent to which a variable participates in the transmittance
| first2 = Andrew F.
2 = Andrew f.
of change from a cause to its effect. It is inherently a causal
| title = Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models
| title = 评估和比较多重介质模型中间接影响的渐近和重采样策略
notion, hence it cannot be defined in statistical terms. Traditionally,
| journal = Behavior Research Methods
行为研究方法
however, the bulk of mediation analysis has been conducted
| volume = 40
40
within the confines of linear regression, with statistical
| issue = 3
第三期
terminology masking the causal character of the
| pages = 879–891
879-891
relationships involved. This led to difficulties,
| url = http://www.afhayes.com/spss-sas-and-mplus-macros-and-code.html
Http://www.afhayes.com/spss-sas-and-mplus-macros-and-code.html
biases, and limitations that have been alleviated by
| year = 2008
2008年
modern methods of causal analysis, based on causal diagrams
| doi = 10.3758/BRM.40.3.879
| doi = 10.3758/BRM. 40.3.879
and counterfactual logic.
| pmid = 18697684
18697684
| doi-access = free
免费访问
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
| last = Preacher
| last = Preacher
epiphenomena which sometimes accompany mediation but,
| first = K. J.
| 第一 = k. j。
in general, fail to capture the causal relationships that
| last2 = Zyphur
2 = Zyphur
mediation analysis aims to quantify.
| first2 = M. J.
2 = m. j.
| last3 = Zhang
3 = Zhang
The basic premise of the causal approach is that it is
| first3 = Z.
3 = z.
not always appropriate to "control" for the mediator ''M''
| title = A general multilevel SEM framework for assessing multilevel mediation
| title = 用于评估多层次调解的通用多层次结构方程模型框架
when we seek to estimate the direct effect of ''X'' on ''Y''
| journal = Psychological Methods
心理学方法
(see the Figure above).
| volume = 15
15
The classical rationale for "controlling" for ''M''"
| issue = 3
第三期
is that, if we succeed in preventing ''M'' from changing, then
| pages = 209–233
| pages = 209-233
whatever changes we measure in Y are attributable solely
| year = 2010
2010年
to variations in ''X'' and we are justified then in proclaiming the
| doi = 10.1037/a0020141
| doi = 10.1037/a0020141
effect observed as "direct effect of ''X'' on ''Y''." Unfortunately,
| pmid = 20822249
20822249
"controlling for ''M''" does not physically prevent ''M'' from changing;
| citeseerx = 10.1.1.570.7747
10.1.1.570.7747
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 only operator probability provides is "Conditioning"
which is what we do when we "control" for ''M'',
or add ''M'' as a regressor in the equation for ''Y''.
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,<ref>{{cite journal|last1=Robins|first1=J.M.|last2=Greenland|first2=S.|title=Identifiability and exchangeability for direct and indirect effects|journal=Epidemiology|date=1992|volume=3|issue=2|pages=143–155|doi=10.1097/00001648-199203000-00013|pmid=1576220}}</ref><ref name="pearl1994" >{{cite journal|last1=Pearl|first1=Judea|editor1-last=Lopez de Mantaras|editor1-first=R.|editor2-last=Poole|editor2-first=D.|title=A probabilistic calculus of actions|journal=Uncertainty in Artificial Intelligence 10|volume=1302|date=1994|pages=454–462|publisher=[[Morgan Kaufmann]]|location=San Mateo, CA|bibcode=2013arXiv1302.6835P|arxiv=1302.6835}}</ref> except in the case of no omitted variables.
To illustrate, assume that the error terms of ''M'' and ''Y''
are correlated. Under such conditions, the
structural coefficient ''B'' and ''A'' (between ''M'' and ''Y'' and between ''Y'' and ''X'')
can no longer be estimated by regressing ''Y'' on ''X'' and ''M''.
In fact, the regression slopes may both be nonzero
even when ''C'' is zero.<ref>{{cite journal|pmid=24885338|year=2014|last1=Pearl|first1=J|title=Interpretation and identification of causal mediation|journal=Psychological Methods|volume=19|issue=4|pages=459–81|doi=10.1037/a0036434|url=ftp://ftp.cs.ucla.edu/pub/stat_ser/r389-imai-etal-commentary-r421-reprint.pdf}}</ref> This has two
consequences. First, new strategies must be devised for
estimating the structural coefficients ''A,B'' and ''C''. Second,
the basic definitions of direct and indirect effects
must go beyond regression analysis, and should
invoke an operation that mimics "fixing ''M''",
rather than "conditioning on ''M''."
Category:Statistical models
类别: 统计模型
Category:Independence (probability theory)
类别: 独立概率论
===Definitions===
Category:Psychometrics
类别: 心理测量学
<noinclude>
<small>This page was moved from [[wikipedia:en:Mediation (statistics)]]. Its edit history can be viewed at [[中介变量/edithistory]]</small></noinclude>
[[Category:待整理页面]]
[[File:Simple Mediation Model.png|thumb|Simple Mediation Model]]
Simple Mediation Model
简单调解模式
In [[statistics]], a '''mediation''' model seeks to identify and explain the mechanism or process that underlies an observed relationship between an [[independent variable]] and a [[dependent variable]] via the inclusion of a third hypothetical variable, known as a '''mediator variable''' (also a '''mediating variable''', '''intermediary variable''', or '''intervening variable''').<ref>{{Cite web|title=Types of Variables|website=[[University of Indiana]]|url=http://www.indiana.edu/~educy520/sec5982/week_2/variable_types.pdf}}</ref> Rather than a direct causal relationship between the independent variable and the dependent variable, a mediation model proposes that the independent variable influences the (non-observable) 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.<ref>MacKinnon, D. P. (2008). ''Introduction to Statistical Mediation Analysis''. New York: Erlbaum.</ref>
In statistics, a mediation model seeks to identify and explain the mechanism or process that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third hypothetical variable, known as a mediator variable (also a mediating variable, intermediary variable, or intervening variable). Rather than a direct causal relationship between the independent variable and the dependent variable, a mediation model proposes that the independent variable influences the (non-observable) 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.
在统计学中，调解模型试图通过加入第三个假设变量，即中介变量(也是中介变量、中介变量或中间变量) ，来确定和解释自变量和因变量之间的观察关系所依据的机制或过程。一个调解模型没有在自变量和因变量之间建立直接的因果关系，而是提出自变量影响(不可观察的)调解变量，这反过来又影响因变量。因此，中介变量的作用是阐明自变量和因变量之间关系的性质。
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.<ref name=CCWA>Cohen, J.; Cohen, P.; West, S. G.; [[Leona S. Aiken|Aiken, L. S.]] (2003) ''Applied multiple regression/correlation analysis for the behavioral sciences'' (3rd ed.). Mahwah, NJ: Erlbaum.</ref> In particular, mediation analysis can contribute to better understanding the relationship between an independent variable and a dependent variable when these variables do not have an obvious direct connection.
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 independent variable and a dependent variable when these variables do not have an obvious direct connection.
中介分析通过探索一个变量通过一个中介变量影响另一个变量的潜在机制或过程来理解一个已知的关系。特别是，中介分析有助于更好地理解自变量和因变量之间的关系，当这些变量没有明显的直接联系。
==Baron and Kenny's (1986) steps for mediation==
Baron and Kenny (1986) <ref>Baron, R. M. and Kenny, D. A. (1986) "The Moderator-Mediator Variable Distinction in Social Psychological Research – Conceptual, Strategic, and Statistical Considerations", [[Journal of Personality and Social Psychology]], Vol. 51(6), pp. 1173–1182.</ref> 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. Note: Hayes (2009)<ref name=Hayes/> critiqued Baron and Kenny's mediation steps approach, and as of 2019, [[David A. Kenny]] on his website stated that mediation can exist in the absence of a 'significant' total effect, and therefore step 1 below may not be needed. This situation is sometimes referred to as "inconsistent mediation". Later publications by Hayes also questioned the concepts of full or partial mediation and advocated for these terms, along with the classical mediation steps approach outlined below, to be abandoned.
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. Note: Hayes (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 multiple regression analysis.
巴伦和肯尼(1986)提出了若干必须满足的要求，以形成一个真正的调解关系。下面用一个现实世界的例子对它们进行了概述。请参阅上面的图表以了解整个中介关系的可视化表示形式。注: Hayes (2009)解释了 Baron 和 Kenny 的每一步要求，以进一步了解调解效应是如何表现的。第一步和第二步使用简单的回归分析/回归分析，而第三步使用多个/频率/频率。
'''Step 1:'''
Step 1:
第一步:
:Regress the dependent variable on the independent variable to confirm that the independent variable is a significant predictor of the dependent variable.
How you were parented (i.e., independent variable) predicts how confident you feel about parenting your own children (i.e., dependent variable).
你是如何被抚养的(即，独立变量)预示着你对抚养自己的孩子有多自信(即，因变量)。
: Independent variable <math> \to </math> dependent variable
How you were parented <math> \to </math> confidence in own parenting abilities.
你是如何培养孩子对自己养育能力的信心的。
:: <math>Y=\beta_{10} +\beta_{11}X + \varepsilon_1</math>
* ''β''<sub>11</sub> is significant
Step 2:
第二步:
'''Step 2:'''
How you were parented (i.e., independent variable) predicts your feelings of competence and self-esteem (i.e., mediator).
你是如何被抚养的(即，独立变量)可以预测你的能力和自尊的感受(即，调解人)。
: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 anything.
How you were parented <math> \to </math> Feelings of competence and self-esteem.
你是如何培养自己的能力和自尊心的。
: Independent variable <math> \to </math> mediator
Step 3:
第三步:
:: <math>Me=\beta_{20} +\beta_{21}X + \varepsilon_2</math>
* ''β''<sub>21</sub> is significant
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 variable).
你的能力和自尊感(即中介者)能够预测你对抚养自己的孩子的自信程度(即因变量) ，同时控制你是如何被抚养的(即自变量)。
'''Step 3:'''
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.
这些发现会导致这样的结论，即你的能力和自尊感会调节你是如何被抚养的和你对抚养自己的孩子有多自信之间的关系。
: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 rendered nonsignificant.
Note: 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 the effect that actually exists (See Shrout & Bolger, 2002 for more info).
注意: 如果步骤1没有产生显著的结果，一个人可能仍然有理由移动到步骤2。有时，独立变量和因变量之间确实存在显著的关系，但是由于样本量小，或者其他额外的因素，没有足够的能量来预测实际存在的影响(参见 Shrout & Bolger，2002)。
:: <math>Y=\beta_{30} +\beta_{31}X +\beta_{32}Me + \varepsilon_3</math>
* ''β''<sub>32</sub> is significant
Direct Effect in a Mediation Model
调解模式中的直接效果
* ''β''<sub>31</sub> should be smaller in absolute value than the original effect for the independent variable (β<sub>11</sub> above)
In the diagram shown above, the indirect effect is the product of path coefficients "A" and "B". The direct effect is the coefficient " C' ".
在上图中，间接效应是路径系数“ a”和“ b”的乘积。直接的影响是系数“ c”。
The direct effect measures the extent to which the dependent variable changes when the independent variable increases by one unit and the mediator variable remains unaltered. In contrast, the indirect effect measures the extent to which the dependent variable changes when the independent variable is held fixed and the mediator variable changes by the amount it would have changed had the independent variable increased by one unit. 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.
直接效应衡量的是当自变量增加一个单位而中介变量保持不变时，因变量变化的程度。相比之下，间接效应衡量的是因变量在自变量固定和中介变量增加一个单位时变化的程度。在引入调解人时，因为只解释了微小的方差(即，不是真正的调解) ，所以自变量对因变量的影响可能变得不重要。因此，在进行全部或部分调解之前，必须显示由独立变量解释的差异显著减少。
'''Example'''
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.
在没有全面影响的情况下，有可能产生统计上显著的间接影响。这可以通过存在几个相互抵消的调解路径来解释，并且在控制其中一个取消调解器时变得显而易见。这意味着“部分”和“完全”中介术语应该始终相对于模型中存在的一组变量进行解释。
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. 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.
在所有情况下，“固定一个变量”的操作必须与“控制一个变量”的操作区分开来，后者在文献中被不恰当地使用。检测小效应需要1000个样本量，检测中等效应需要100个样本量，检测大效应需要50个样本量。
The following example, drawn from Howell (2009),<ref>Howell, D. C. (2009). Statistical methods for psychology (7th ed.). Belmot, CA: Cengage Learning.</ref> 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 [[multiple regression analysis]].
Step 1:
The bootstrapping method provides some advantages to the Sobel's test, primarily an increase in power. The Preacher and Hayes Bootstrapping method is a non-parametric test (See Non-parametric statistics for a discussion on non-parametric tests and their power). As such, the bootstrap method does not violate assumptions of normality and is therefore recommended for small sample sizes.
自举方法为 Sobel 的测试提供了一些优点，主要是增加了功耗。传道者和 Hayes Bootstrapping 方法是一种非参数检验(参见无母数统计非参数检验及其效力的讨论)。因此，自助法并不违反常态假设，因此建议小样本情况下使用。
:How you were parented (i.e., independent variable) predicts how confident you feel about parenting your own children (i.e., dependent variable).
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. Hayes offers a macro <http://www.afhayes.com/> that calculates bootstrapping directly within SPSS, a computer program used for statistical analyses. This 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.
自举涉及重复随机抽样观察和替换从数据集计算期望的统计量在每个重采样。通过计算数百个或数千个引导重采样提供了感兴趣统计量的抽样分布的近似值。提供了一个宏 < http://www.afhayes.com/ > ，它可以直接计算 SPSS 中的自举，这是一个用于统计分析的计算机程序。这种方法提供了点估计和置信区间，通过这些点估计和置信区间可以评估中介效应的重要性或非重要性。点估计揭示了引导样本数目的平均值，如果零没有落在引导方法产生的置信区间之间，人们可以自信地得出结论，有一个重要的中介效应要报告。
: How you were parented <math> \to </math> confidence in own parenting abilities.
Step 2:
As outlined above, there are a few different options one can choose from to evaluate a mediation model.
如上所述，在评估一个中介模型时，可以从几个不同的选项中进行选择。
:How you were parented (i.e., independent variable) predicts your feelings of competence and self-esteem (i.e., mediator).
Bootstrapping 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 or the Sobel test. 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. and interpreted formally.
引导法因为不需要满足正态性假设，并且在样本量较小时(n < 25)可以有效地利用，因此成为最流行的检验中介的方法。然而，调解仍然是最常用的决定使用的逻辑的巴伦和肯尼或索贝尔测试。发布纯粹基于 Baron 和 Kenny 方法的调解测试或者进行分布性假设(如 Sobel 测试)的测试变得越来越困难。因此，在选择进行哪项测试时，考虑你的选择是很重要的。并正式解释。
: How you were parented <math> \to </math> Feelings of competence and self-esteem.
(1) Experimental-causal-chain design
(1)实验因果链设计
Step 3:
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 relationship.
实验因果链设计时，所提出的中介体是实验操纵。这样的设计意味着一个人操纵一些他们有理由相信可能是给定关系的潜在机制的受控的第三变量。
: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 variable).
(2) Measurement-of-mediation design
(2)测量调解设计
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.
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, but only involves measurement.
度量中介设计可以概念化为统计方法。这样的设计意味着一个人衡量所提议的中间变量，然后使用统计分析来建立调解。这种方法不涉及对虚拟中介变量的操作，而只涉及测量。
Note: 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 the effect that actually exists (See Shrout & Bolger, 2002 <ref>{{cite journal | last1 = Shrout | first1 = P. E. | last2 = Bolger | first2 = N. | year = 2002 | title = Mediation in experimental and nonexperimental studies: New procedures and recommendations | journal = Psychological Methods | volume = 7 | issue = 4| pages = 422–445 | doi=10.1037/1082-989x.7.4.422}}</ref> for more info).
==Direct versus indirect effects==
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.
调解的试验办法必须谨慎进行。首先，对潜在中介变量的探索性研究必须有强有力的理论支持。
[[File:Direct Effect in a Mediation Model.jpg|thumb|Direct Effect in a Mediation Model]]
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.
对调解方法的批评取决于操纵和测量调解变量的能力。因此，人们必须能够以可以接受和符合道德的方式操纵拟议的调解人。因此，人们必须能够在不干扰结果的情况下衡量干预过程。中介者还必须能够建立操纵的结构效度。
In the diagram shown above, the indirect effect is the product of path coefficients "A" and "B". The direct effect is the coefficient " C' ".
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: and Preacher, Rucker, and Hayes (2007).
对中介测量方法最常见的批评之一是，它最终是一种相关设计。因此，可能是其他第三个变数，独立于拟议的调解员，可负责拟议的效果。然而，研究人员一直在努力为这种蔑视提供反证据。具体来说，以下的反论点已经提出: 和牧师，拉克尔，和海斯(2007年)。
The direct effect measures the extent to which the dependent variable changes when the independent variable increases by one unit and the mediator variable remains unaltered. In contrast, the indirect effect measures the extent to which the dependent variable changes when the independent variable is held fixed and the mediator variable changes by the amount it would have changed had the independent variable increased by one unit.<ref name="Robins"/><ref name="Pearl-01"/>
[[File:Mediation Model.png|thumb|Indirect Effect in a Simple Mediation Model: The indirect effect constitutes the extent to which the X variable influences the Y variable through the mediator.]]
In linear systems, the total effect is equal to the sum of the direct and indirect (''C' + AB'' 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.<ref name="Pearl-01"/>
There are five possible models of moderated mediation, as illustrated in the diagrams below.
如下图所示，有节制的调解有五种可能的模式。
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 Prisoner's Dilemma Game (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, social value orientation (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).
研究人员向参与者提供了一个初始刺激物(初始刺激物) ，这个刺激物使他们想到道德或者让他们想到可能性。然后，他们参加了囚徒困境游戏(PDG) ，在这个游戏中，参与者假装他们和他们的犯罪同伙已经被逮捕，他们必须决定是继续忠于他们的同伙，还是与他们的同伙竞争并与当局合作。研究人员发现亲社会的个体受到道德和可能的优先权的影响，而亲社会的个体则不受影响。因此，社会价值取向(亲自与亲社会)调节了基本变量(自变量: 道德与可能)与 PDG 中选择的行为(因变量: 竞争与合作)之间的关系。
==Full versus partial mediation==
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’ social value orientation 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 with their partner and cooperate with the authorities. In contrast, participants with a pro-self social value orientation always acted competitively.
接下来，研究人员寻找中和效应的存在。回归分析显示，初始类型(道德与可能)中介了参与者的社会价值取向对 PDG 行为的调节关系。那些经历过道德优势的亲社会参与者希望他们的伴侣与他们合作，所以他们选择了自己合作。亲社会的参与者经历了可能的主要期望他们的伴侣与他们竞争，这使他们更有可能与他们的伴侣竞争并与当局合作。相比之下，具有亲自我社会价值取向的参与者总是在竞争中行动。
A mediator variable can either account for all or some of the observed relationship between two variables.
'''Full mediation'''
Muller, Judd, and Yzerbyt (2005) except in the case of no omitted variables.
Muller，Judd，and Yzerbyt (2005) ，除了没有省略变量的情况。
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 ''c'' in diagram above) to zero.
[[File:Full Mediation Model.png|thumb|Full Mediation Model]]
To illustrate, assume that the error terms of M and Y
为了说明，假设 m 和 y 的错误项
'''Partial mediation'''
are correlated. Under such conditions, the
是相关的。在这种情况下,
[[File:Mediation.jpg|thumb|The Partial Mediation Model Includes a Direct Effect]]
structural coefficient B and A (between M and Y and between Y and X)
结构系数 b 和 a (介于 m 和 y 之间，y 和 x 之间)
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 some direct relationship between the independent and dependent variable.
can no longer be estimated by regressing Y on X and M.
不能再通过 x 和 m 的 y 回归来估计。
In fact, the regression slopes may both be nonzero
事实上，回归斜率可能都是非零的
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 [[Sobel test]].<ref name="Sobel, M. E. 1982 pp. 290">{{cite journal | last1 = Sobel | first1 = M. E. | year = 1982 | title = Asymptotic confidence intervals for indirect effects in structural equation models | journal = Sociological Methodology | volume = 13 | pages = 290–312 | doi = 10.2307/270723 | jstor = 270723 }}</ref> 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.
even when C is zero. This has two
即使 c 是零。这里有两个
It is possible to have statistically significant indirect effects in the absence of a total effect.<ref name=Hayes>{{cite journal | last1 = Hayes | first1 = A. F. | year = 2009 | title = Beyond Baron and Kenny: Statistical mediation analysis in the new millennium | journal = Communication Monographs | volume = 76 | issue = 4| pages = 408–420 | doi = 10.1080/03637750903310360 }}</ref> 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.
consequences. First, new strategies must be devised for
后果。首先，必须制定新的战略
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.<ref name="Robins"/><ref name="Kaufman"/> 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 [[Bayesian Networks]]).
estimating the structural coefficients A,B and C. Second,
估计结构系数 a，b 和 c,
the basic definitions of direct and indirect effects
直接和间接影响的基本定义
==Sobel's test==
must go beyond regression analysis, and should
必须超越回归分析
{{main|Sobel test}}
invoke an operation that mimics "fixing M",
调用一个模仿“修理 m”的操作,
rather than "conditioning on M."
而不是“对 m 施加条件作用”
As mentioned above, [[Sobel test|Sobel's test]]<ref name="Sobel, M. E. 1982 pp. 290"/> 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 independent variable and the dependent variable compared to the relationship between the independent variable and dependent variable including the mediation factor.
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 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 [[Normal distribution]] for more details). Thus, the rule of thumb as suggested by MacKinnon et al., (2002) <ref>{{cite journal | last1 = MacKinnon | first1 = D. P. | last2 = Lockwood | first2 = C. M. | last3 = Lockwood | first3 = J. M. | last4 = West | first4 = S. G. | last5 = Sheets | first5 = V. | year = 2002 | title = A comparison of methods to test mediation and other intervening variable effects | journal = Psychological Methods| volume = 7 | issue = 1| pages = 83–104 | doi=10.1037/1082-989x.7.1.83| pmid = 11928892 | pmc=2819363}}</ref> 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.
Such an operator, denoted do(M = m), was defined in Pearl (1994) or "structural counterfactuals".
这样一个算子，表示 do (m = m) ，在 Pearl (1994)或“结构反事实”中定义。
These new variables provide convenient notation
这些新的变量提供了方便的符号
==Preacher and Hayes (2004) bootstrap method==
for defining direct and indirect effects. In particular,
定义直接和间接影响。特别是,
four types of effects have been defined for the
四种类型的影响已被定义为
The bootstrapping method provides some advantages to the Sobel's test, primarily an increase in power. The Preacher and Hayes Bootstrapping method is a non-parametric test (See [[Non-parametric statistics]] for a discussion on non-parametric tests and their power). As such, the bootstrap method does not violate assumptions of normality and is therefore recommended for small sample sizes.
transition from X = 0 to X = 1:
从 x = 0到 x = 1的跃迁:
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. Hayes offers a macro <http://www.afhayes.com/> that calculates bootstrapping directly within [[SPSS]], a computer program used for statistical analyses. This 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.
(a) Total effect –
(a)总效应 -
==Significance of mediation==
<math>TE = E [Y(1) - Y(0)] </math>
[ math > TE = e [ y (1)-y (0)]
(b) Controlled direct effect -
(b)受管制的直接影响 -
As outlined above, there are a few different options one can choose from to evaluate a mediation model.
<math> CDE(m) = E [Y(1,m) - Y(0,m) ] </math>
[ math > CDE (m) = e [ y (1，m)-y (0，m)] </math >
(c) Natural direct effect -
(c)天然直接效应 -
[[Bootstrapping (statistics)|Bootstrapping]]<ref>{{cite web |url=http://www.comm.ohio-state.edu/ahayes/sobel.htm |title=Testing of Mediation Models in SPSS and SAS |publisher=Comm.ohio-state.edu |access-date=2012-05-16 |archive-url=https://web.archive.org/web/20120518234943/http://www.comm.ohio-state.edu/ahayes/sobel.htm |archive-date=2012-05-18 |url-status=dead }}</ref><ref>{{cite web|url=http://www.comm.ohio-state.edu/ahayes/SPSS%20programs/indirect.htm |title=SPSS and SAS Macro for Bootstrapping Specific Indirect Effects in Multiple Mediation Models |publisher=Comm.ohio-state.edu |access-date=2012-05-16}}</ref> 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 <ref>[http://davidakenny.net/cm/mediate.htm "Mediation"]. ''davidakenny.net''. Retrieved April 25, 2012.</ref> or the [[Sobel test]]. 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.<ref name=Hayes/>
<math>NDE = E [Y(1,M(0)) - Y(0,M(0))] </math>
[ math > NDE = e [ y (1，m (0)-y (0，m (0)]
(d) Natural indirect effect
(d)自然间接影响
==Approaches to mediation==
<math> NIE = E [Y(0,M(1)) - Y(0,M(0))] </math>
[ math > NIE = e [ y (0，m (1))-y (0，m (0)]
Where E[ ] stands for expectation taken over the error terms.
其中 e []表示期望取代了错误项。
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<ref name="Robins">{{cite journal | last1 = Robins | first1 = J. M. | author-link = James Robins | author-link2 = Sander Greenland | last2 = Greenland | first2 = S. | year = 1992 | title = Identifiability and exchangeability for direct and indirect effects | journal = Epidemiology | volume = 3 | issue = 2| pages = 143–55 | doi = 10.1097/00001648-199203000-00013 | pmid = 1576220 }}</ref><ref name="Kaufman">{{cite journal|pmc=526390|doi=10.1186/1742-5573-1-4|year=2004|last1=Kaufman|first1=J. S.|title=A further critique of the analytic strategy of adjusting for covariates to identify biologic mediation|journal=Epidemiologic Perspectives & Innovations |volume=1|issue=1|pages=4|last2=MacLehose|first2=R. F.|last3=Kaufman|first3=S|pmid=15507130}}</ref><ref name="Bullock">{{cite journal|pmid=20307128|url=http://www2.psych.ubc.ca/~schaller/528Readings/BullockGreenHa2010.pdf|year=2010|last1=Bullock|first1=J. G.|title=Yes, but what's the mechanism? (don't expect an easy answer)|journal=Journal of Personality and Social Psychology|volume=98|issue=4|pages=550–8|last2=Green|first2=D. P.|last3=Ha|first3=S. E.|doi=10.1037/a0018933}}
</ref> and interpreted formally.<ref name="Pearl-01">[[Judea Pearl|Pearl, J.]] (2001) [http://ftp.cs.ucla.edu/pub/stat_ser/R273-U.pdf "Direct and indirect effects"]. Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, [[Morgan Kaufmann]], 411–420.</ref>
These effects have the following interpretations:
这些影响有以下解释:
(1) Experimental-causal-chain design
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 relationship.
(2) Measurement-of-mediation design
A controlled version of the indirect effect does not
间接效应的受控版本则不会
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, but only involves measurement.<ref>{{cite journal|pmid=16393019|url=http://www2.psych.ubc.ca/~schaller/528Readings/SpencerZannaFong2005.pdf|year=2005|last1=Spencer|first1=S. J.|title=Establishing a causal chain: Why experiments are often more effective than mediational analyses in examining psychological processes|journal=Journal of Personality and Social Psychology|volume=89|issue=6|pages=845–51|last2=Zanna|first2=M. P.|last3=Fong|first3=G. T.|doi=10.1037/0022-3514.89.6.845}}
exist because there is no way of disabling the
因为没有办法禁用
</ref>
direct effect by fixing a variable to a constant.
把一个变量固定在一个常数上的直接效果。
==Criticisms of mediation measurement==
According to these definitions the total effect can be decomposed as a sum
根据这些定义，总效应可以分解为总和
<math>TE = NDE - NIE_r </math>
<math>TE = NDE - NIE_r </math>
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.
where NIE<sub>r</sub> stands for the reverse transition, from
其中 NIE < sub > r </sub > 代表反向过渡，从
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.
X = 1 to X = 0; it becomes additive in linear systems,
1 to x = 0; 它成为线性系统的可加性,
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:<ref name=CCWA/>
where reversal of transitions entails sign reversal.
转变的逆转导致了标志的逆转。
(1) Temporal precedence. 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.
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.
这些定义的力量在于它们的普遍性，它们适用于任意非线性相互作用的模型，干扰之间的任意依赖，以及连续变量和分类变量。
(2) Nonspuriousness and/or no confounds. 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 below.
Formulation of the indirect effect
间接效应的表述
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 (statistics)|moderation]].
In linear analysis, all effects are determined by sums
在线性分析中，所有的影响都是由和决定的
==Other third variables==
of products of structural coefficients, giving
结构系数的乘积，给出
<math>
《数学》
(1) Confounding:
\begin{align}
开始{ align }
TE & = C + AB \\
等于 c + AB
: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.
CDE(m) & = NDE = C, \text{ independent of } m\\
CDE (m) & = NDE = c，文本{独立于} m
NIE & = AB.
和 = AB。
[[File:Mediation model with two covariates.jpg|thumb|Mediation model with two covariates]]
\end{align}
结束{ align }
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.
</math>
数学
Therefore, all effects are estimable whenever the model
因此，无论何时模型都可以估计所有的影响
(2) Suppression:
is identified. In non-linear systems, more stringent
被识别出来。在非线性系统中，更为严格
conditions are needed for estimating the
我们需要一些条件来估计
: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 (''C''), which 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.
direct and indirect effects
直接和间接影响
.
.
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.
For example, if no confounding exists,
例如，如果不存在混淆,
(i.e., ε<sub >1</sub>, ε<sub>2</sub>, and ε<sub>3</sub> are mutually independent) the
(即 ε < sub > 1 </sub > ，ε < sub > 2 </sub > ，ε < sub > 3 </sub > 是相互独立的)
(3) Moderators:
following formulas can be derived:
可以推导出以下公式:
and have become the target of estimation in many studies of mediation. They give
并成为许多中介研究评价的对象。他们给予
:Other important third variables are moderators. 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 ''X'' and ''Y''. A moderating relationship can be thought of as an [[interaction effect|interaction]]. It occurs when the relationship between variables A and B depends on the level of C. See [[moderation (statistics)|moderation]] for further discussion.
distribution-free expressions for direct and indirect
直接和间接的分布-自由表达式
effects and demonstrate that, despite the arbitrary nature of
尽管我们的研究结果具有随意性
==Moderated mediation==
the error distributions and the functions f, g, and h,
误差分布和函数 f，g，h,
mediated effects can nevertheless be estimated from data using
然而，我们可以通过使用数据来估计中介效应
Mediation and [[moderation (statistics)|moderation]] can co-occur in statistical models. It is possible to mediate moderation and moderate mediation.
regression.
回归。
The analyses of moderated mediation
有调节的中介分析
[[Moderated mediation]] is when the effect of the treatment ''A'' on the mediator and/or the partial effect ''B'' 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 moderated by different levels of another variable (i.e., a moderator). This definition has been outlined by Muller, Judd, and Yzerbyt (2005)<ref name="Muller">{{cite journal | last1 = Muller | first1 = D. | last2 = Judd | first2 = C. M. | last3 = Yzerbyt | first3 = V. Y. | year = 2005 | title = When moderation is mediated and mediation is moderated | journal = Journal of Personality and Social Psychology | volume = 89 | issue = 6| pages = 852–863 | doi = 10.1037/0022-3514.89.6.852 | pmid = 16393020 }}</ref> and Preacher, Rucker, and Hayes (2007).<ref name="Preacher">Preacher, K. J., Rucker, D. D. & Hayes, A. F. (2007). Assessing moderated mediation hypotheses: Strategies, methods, and prescriptions. Multivariate Behavioral Research, 42, 185–227.</ref>
and mediating moderators fall as special cases of the causal mediation
和调解人作为因果调解的特殊案例下降
analysis, and the mediation formulas identify how various interactions coefficients contribute to the necessary and sufficient components of mediation.
分析，以及调解公式确定各种相互作用系数如何有助于调解的必要和充分的组成部分。
===Models of moderated mediation===
There are five possible models of moderated mediation, as illustrated in the diagrams below.<ref name="Muller" />
A serial mediation model with two mediator variables.
一个具有两个中介变量的串行中介模型。
# In the first model the independent variable also moderates the relationship between the mediator and the dependent variable.
# 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).
A conceptual diagram that depicts a parallel mediation model with two mediator variables.
描述具有两个中介变量的并行中介模型的概念图。
# 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).
Assume the model takes the form
假设模型采用这种形式
# 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).
<math>
《数学》
# 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.
\begin{align}
开始{ align }
X & = \varepsilon_1 \\
1
{|
M & = b_0 + b_1X + \varepsilon_2 \\
0 + b 1x + varepsilon 2
Y & = c_0 + c_1X + c_2M + c_3XM + \varepsilon_3
Y & = c _ 0 + c _ 1x + c _ 2m + c _ 3xm + varepsilon _ 3
| [[File:Mediated moderation model 1.png|centre|thumb|
\end{align}
结束{ align }
First option: independent variable moderates the ''B'' path.]]
</math>
数学
| [[File:Mediated moderation model 2.png|centre|thumb|
where the parameter <math>c_3</math> quantifies the degree to which M modifies the effect of X on Y. Even when all parameters are estimated from data, it is still not obvious what combinations of parameters measure the direct and indirect effect of X on Y, or, more practically, how to assess the fraction of the total effect <math>TE</math> that is explained by mediation and the fraction of <math>TE</math> that is owed to mediation. In linear analysis, the former fraction is captured by the product <math>b_1 c_2 / TE</math>, the latter by the difference <math>(TE - c_1)/TE</math>, 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:
其中参数 c _ 3 </math > 量化了 m 修改 x 对 y 影响的程度。即使所有的参数都是从数据中估计出来的，仍然不清楚哪些参数组合可以衡量 x 对 y 的直接和间接影响，或者更实际地说，如何评估调解和归因于调解的“数学”“数学”“数学”所占总影响的比例。在线性分析中，前者由乘积 < math > b1c2/TE </math > 获得，后者由差 < math > (TE-c1)/TE </math > 获得，两个量重合。然而，在存在相互作用的情况下，每个部分都需要按照调解公式进行单独分析，分析结果如下:
Second option: fourth variable moderates the ''A'' path.]]
<math>
《数学》
| [[File:Mediated moderation model 3.png|centre|thumb|
\begin{align}
开始{ align }
Third option: fourth variable moderates the ''B'' path.]]
NDE & = c_1 + b_0 c_3 \\
NDE & = c 1 + b 0 c 3
| [[File:Mediated moderation model 4.png|centre|thumb|
NIE & = b_1 c_2 \\
1 c 2
Fourth option: fourth variable moderates both the ''A'' path and the ''B'' path.]]
TE & = c_1 + b_0 c_3 + b_1(c_2 + c_3) \\
TE & = c1 + b0 c3 + b1(c2 + c3)
| [[File:Mediated moderation model 5.png|centre|thumb|
& = NDE + NIE + b_1 c_3.
& = NDE + NIE + b 1 c 3.
Fifth option: fourth variable moderates the ''A'' path and a fifth variable moderates the ''B'' path.]]
\end{align}
结束{ align }
|}
</math>
数学
==Mediated moderation==
Thus, the fraction of output response for which mediation would be sufficient is
因此，输出响应中中介足够的部分是
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.<ref name="Muller" />
<math> \frac{NIE}{TE} = \frac{b_1 c_2}{c_1 + b_0 c_3 + b_1 (c_2 + c_3)}, </math>
1 + b _ 0 c _ 3 + b _ 1(c _ 2 + c _ 3) ，</math >
In order to establish mediated moderation, one must first establish [[Moderation (statistics)|moderation]], meaning that the direction and/or the strength of the relationship between the independent and dependent variables (path ''C'') 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 ''A'') or between the moderator and the dependent variable (path ''C'').
while the fraction for which mediation would be necessary is
而调解的必要部分是
'''Example'''
<math> 1- \frac{NDE}{TE} = \frac{b_1 (c_2 +c_3)}{c_1 + b_0c_3 + b_1 (c_2 + c_3)}. </math>
1-frac { NDE }{ TE } = frac { b _ 1(c _ 2 + c _ 3)}{ c _ 1 + b _ 0c _ 3 + b _ 1(c _ 2 + c _ 3)}.数学
The following is a published example of mediated moderation in psychological research.<ref>{{cite journal | last1 = Smeesters | first1 = D. | last2 = Warlop | first2 = L. | last3 = Avermaet | first3 = E. V. | last4 = Corneille | first4 = O. | last5 = Yzerbyt | first5 = V. | year = 2003 | title = Do not prime hawks with doves: The interplay of construct activation and consistency of social value orientation on cooperative behavior | journal = Journal of Personality and Social Psychology | volume = 84 | issue = 5| pages = 972–987 | doi = 10.1037/0022-3514.84.5.972 | pmid = 12757142 }}</ref>
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 [[Prisoner's dilemma|Prisoner's Dilemma Game]] (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, [[Social value orientations|social value orientation]] (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).
These fractions involve non-obvious combinations
这些分数包含不明显的组合
of the model's parameters, and can be constructed
模型的参数，可以构造出
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’ [[Social value orientations|social value orientation]] 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 with their partner and cooperate with the authorities. In contrast, participants with a pro-self social value orientation always acted competitively.
mechanically with the help of the Mediation Formula. Significantly, due to interaction, a direct effect can be sustained even when the parameter <math>c_1</math> 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 separately.
借助调解公式机械地进行调解。值得注意的是，由于相互作用，即使参数 c _ 1 </math > 消失，直接影响也可以持续，而且，即使直接和间接影响消失，总体影响也可以持续。这表明，孤立地估计参数并不能告诉我们有关调解效果的信息，更普遍地说，调解和调节是相互交织的，不能单独进行评估。
==Regression equations for moderated mediation and mediated moderation==
Muller, Judd, and Yzerbyt (2005)<ref name="Muller"/> outline three fundamental models that underlie both moderated mediation and mediated moderation. ''Mo'' represents the moderator variable(s), ''Me'' represents the mediator variable(s), and ''ε<sub>i</sub>'' represents the measurement error of each regression equation.
Notes
注释
[[File:Mediation.jpg|434px|right|A simple statistical mediation model.]]
Bibliography
参考书目
'''Step 1''': Moderation of the relationship between the independent variable (X) and the dependent variable (Y), also called the overall treatment effect (path ''C'' in the diagram).
: <math>Y=\beta_{40} +\beta_{41}X +\beta_{42}Mo +\beta_{43}XMo + \varepsilon_4</math>
| last = Preacher
| last = Preacher
* To establish overall moderation, the ''β''<sub>43</sub> regression weight must be significant (first step for establishing mediated moderation).
| first = Kristopher J.
第一，克里斯托弗 j。
* Establishing moderated mediation requires that there be no moderation effect, so the ''β''<sub>43</sub> regression weight must not be significant.
| last2 = Hayes
2 = Hayes
| first2 = Andrew F.
2 = Andrew f.
'''Step 2''': Moderation of the relationship between the independent variable and the mediator (path ''A'').
| title = SPSS and SAS procedures for estimating indirect effects in simple mediation models
| title = 用于估计简单调解模型中的间接影响的 SPSS 和 SAS 程序
: <math>Me=\beta_{50} +\beta_{51}X +\beta_{52}Mo +\beta_{53}XMo + \varepsilon_5</math>
| journal = Behavior Research Methods, Instruments, and Computers
行为研究方法，仪器和计算机
* If the ''β''<sub>53</sub> regression weight is significant, the moderator affects the relationship between the independent variable and the mediator.
| volume = 36
36
| issue = 4
第四期
'''Step 3''': Moderation of both the relationship between the independent and dependent variables (path ''A'') and the relationship between the mediator and the dependent variable (path ''B'').
| pages = 717–731
| 页数 = 717-731
: <math>Y=\beta_{60} +\beta_{61}X +\beta_{62}Mo +\beta_{63}XMo +\beta_{64}Me +\beta_{65}MeMo + \varepsilon_6</math>
| url = http://www.afhayes.com/spss-sas-and-mplus-macros-and-code.html
Http://www.afhayes.com/spss-sas-and-mplus-macros-and-code.html
* If both ''β''<sub>53</sub> in step 2 and ''β''<sub>63</sub> in step 3 are significant, the moderator affects the relationship between the independent variable and the mediator (path ''A'').
| year = 2004
2004年
* If both ''β''<sub>53</sub> in step 2 and ''β<sub>65</sub>'' in step 3 are significant, the moderator affects the relationship between the mediator and the dependent variable (path ''B'').
| doi = 10.3758/BF03206553
| doi = 10.3758/BF03206553
* Either or both of the conditions above may be true.
| pmid = 15641418
15641418
| doi-access = free
免费访问
==Causal mediation analysis==
}}
}}
===Fixing versus conditioning===
| last = Preacher
| last = Preacher
| first = Kristopher J.
第一，克里斯托弗 j。
Mediation analysis quantifies the
| last2 = Hayes
2 = Hayes
extent to which a variable participates in the transmittance
| first2 = Andrew F.
2 = Andrew f.
of change from a cause to its effect. It is inherently a causal
| title = Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models
| title = 评估和比较多重介质模型中间接影响的渐近和重采样策略
notion, hence it cannot be defined in statistical terms. Traditionally,
| journal = Behavior Research Methods
行为研究方法
however, the bulk of mediation analysis has been conducted
| volume = 40
40
within the confines of linear regression, with statistical
| issue = 3
第三期
terminology masking the causal character of the
| pages = 879–891
879-891
relationships involved. This led to difficulties,
| url = http://www.afhayes.com/spss-sas-and-mplus-macros-and-code.html
Http://www.afhayes.com/spss-sas-and-mplus-macros-and-code.html
biases, and limitations that have been alleviated by
| year = 2008
2008年
modern methods of causal analysis, based on causal diagrams
| doi = 10.3758/BRM.40.3.879
| doi = 10.3758/BRM. 40.3.879
and counterfactual logic.
| pmid = 18697684
18697684
| doi-access = free
免费访问
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
| last = Preacher
| last = Preacher
epiphenomena which sometimes accompany mediation but,
| first = K. J.
| 第一 = k. j。
in general, fail to capture the causal relationships that
| last2 = Zyphur
2 = Zyphur
mediation analysis aims to quantify.
| first2 = M. J.
2 = m. j.
| last3 = Zhang
3 = Zhang
The basic premise of the causal approach is that it is
| first3 = Z.
3 = z.
not always appropriate to "control" for the mediator ''M''
| title = A general multilevel SEM framework for assessing multilevel mediation
| title = 用于评估多层次调解的通用多层次结构方程模型框架
when we seek to estimate the direct effect of ''X'' on ''Y''
| journal = Psychological Methods
心理学方法
(see the Figure above).
| volume = 15
15
The classical rationale for "controlling" for ''M''"
| issue = 3
第三期
is that, if we succeed in preventing ''M'' from changing, then
| pages = 209–233
| pages = 209-233
whatever changes we measure in Y are attributable solely
| year = 2010
2010年
to variations in ''X'' and we are justified then in proclaiming the
| doi = 10.1037/a0020141
| doi = 10.1037/a0020141
effect observed as "direct effect of ''X'' on ''Y''." Unfortunately,
| pmid = 20822249
20822249
"controlling for ''M''" does not physically prevent ''M'' from changing;
| citeseerx = 10.1.1.570.7747
10.1.1.570.7747
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 only operator probability provides is "Conditioning"
which is what we do when we "control" for ''M'',
or add ''M'' as a regressor in the equation for ''Y''.
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,<ref>{{cite journal|last1=Robins|first1=J.M.|last2=Greenland|first2=S.|title=Identifiability and exchangeability for direct and indirect effects|journal=Epidemiology|date=1992|volume=3|issue=2|pages=143–155|doi=10.1097/00001648-199203000-00013|pmid=1576220}}</ref><ref name="pearl1994" >{{cite journal|last1=Pearl|first1=Judea|editor1-last=Lopez de Mantaras|editor1-first=R.|editor2-last=Poole|editor2-first=D.|title=A probabilistic calculus of actions|journal=Uncertainty in Artificial Intelligence 10|volume=1302|date=1994|pages=454–462|publisher=[[Morgan Kaufmann]]|location=San Mateo, CA|bibcode=2013arXiv1302.6835P|arxiv=1302.6835}}</ref> except in the case of no omitted variables.
To illustrate, assume that the error terms of ''M'' and ''Y''
are correlated. Under such conditions, the
structural coefficient ''B'' and ''A'' (between ''M'' and ''Y'' and between ''Y'' and ''X'')
can no longer be estimated by regressing ''Y'' on ''X'' and ''M''.
In fact, the regression slopes may both be nonzero
even when ''C'' is zero.<ref>{{cite journal|pmid=24885338|year=2014|last1=Pearl|first1=J|title=Interpretation and identification of causal mediation|journal=Psychological Methods|volume=19|issue=4|pages=459–81|doi=10.1037/a0036434|url=ftp://ftp.cs.ucla.edu/pub/stat_ser/r389-imai-etal-commentary-r421-reprint.pdf}}</ref> This has two
consequences. First, new strategies must be devised for
estimating the structural coefficients ''A,B'' and ''C''. Second,
the basic definitions of direct and indirect effects
must go beyond regression analysis, and should
invoke an operation that mimics "fixing ''M''",
rather than "conditioning on ''M''."
Category:Statistical models
类别: 统计模型
Category:Independence (probability theory)
类别: 独立概率论
===Definitions===
Category:Psychometrics
类别: 心理测量学
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