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第544行： − − 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 − − regression. − − 回归。 − − − − The analyses of moderated mediation − − 有调节的中介分析 − − 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。 − − − 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。 − − − − − 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。 − − − Assume the model takes the form − − 假设模型采用这种形式 − − − <math> − − 《数学》 − − − \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 − − \end{align} − − 结束{ align } − − − </math> − − 数学 − − − 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: − − − <math> − − 《数学》 − − − \begin{align} − − 开始{ align } − − − NDE & = c_1 + b_0 c_3 \\ − − NDE & = c 1 + b 0 c 3 − − − NIE & = b_1 c_2 \\ − − 1 c 2 − − − TE & = c_1 + b_0 c_3 + b_1(c_2 + c_3) \\ − − TE & = c1 + b0 c3 + b1(c2 + c3) − − − & = NDE + NIE + b_1 c_3. − − & = NDE + NIE + b 1 c 3. − − − \end{align} − − 结束{ align } − − − </math> − − 数学 − −
→Moderated mediation
==Moderated mediation==
==Moderated mediation==
Mediation and [[moderation (statistics)|moderation]] can co-occur in statistical models. It is possible to mediate moderation and moderate mediation.
Mediation and [[moderation (statistics)|moderation]] can co-occur in statistical models. It is possible to mediate moderation and moderate mediation.
[[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>
[[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>
===Models of moderated mediation===
===Models of moderated mediation===
There are five possible models of moderated mediation, as illustrated in the diagrams below.<ref name="Muller" />
There are five possible models of moderated mediation, as illustrated in the diagrams below.<ref name="Muller" />
# In the first model the independent variable also moderates the relationship between the mediator and the dependent variable.
# 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).
# The second possible model of moderated mediation involves a new variable which moderates the relationship between the independent variable and the mediator (the ''A'' path).
# The third model of moderated mediation involves a new moderator variable which moderates the relationship between the mediator and the dependent variable (the ''B'' path).
# The third model of moderated mediation involves a new moderator variable which moderates the relationship between the mediator and the dependent variable (the ''B'' path).
# Moderated mediation can also occur when one moderating variable affects both the relationship between the independent variable and the mediator (the ''A'' path) and the relationship between the mediator and the dependent variable (the ''B'' path).
# Moderated mediation can also occur when one moderating variable affects both the relationship between the independent variable and the mediator (the ''A'' path) and the relationship between the mediator and the dependent variable (the ''B'' path).
# The fifth and final possible model of moderated mediation involves two new moderator variables, one moderating the ''A'' path and the other moderating the ''B'' path.
# 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.
{|
{|
| [[File:Mediated moderation model 1.png|centre|thumb|
| [[File:Mediated moderation model 1.png|centre|thumb|
First option: independent variable moderates the ''B'' path.]]
First option: independent variable moderates the ''B'' path.]]
| [[File:Mediated moderation model 2.png|centre|thumb|
| [[File:Mediated moderation model 2.png|centre|thumb|
Second option: fourth variable moderates the ''A'' path.]]
Second option: fourth variable moderates the ''A'' path.]]
| [[File:Mediated moderation model 3.png|centre|thumb|
| [[File:Mediated moderation model 3.png|centre|thumb|
Third option: fourth variable moderates the ''B'' path.]]
Third option: fourth variable moderates the ''B'' path.]]
| [[File:Mediated moderation model 4.png|centre|thumb|
| [[File:Mediated moderation model 4.png|centre|thumb|
Fourth option: fourth variable moderates both the ''A'' path and the ''B'' path.]]
Fourth option: fourth variable moderates both the ''A'' path and the ''B'' path.]]
| [[File:Mediated moderation model 5.png|centre|thumb|
| [[File:Mediated moderation model 5.png|centre|thumb|
Fifth option: fourth variable moderates the ''A'' path and a fifth variable moderates the ''B'' path.]]
Fifth option: fourth variable moderates the ''A'' path and a fifth variable moderates the ''B'' path.]]
|}
|}
==Mediated moderation==
==Mediated moderation==