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第526行： − of products of structural coefficients, giving − − 结构系数的乘积，给出 − − − − <math> − − \begin{align} − TE & = C + AB \\ − − CDE(m) & = NDE = C, \text{ independent of } m\\ − − CDE (m) & = NDE = c，文本{独立于} m − − − − NIE & = AB. − − 和 = AB。 − − \end{align} − − 结束{ align } − − − </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 − − 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 − − direct and indirect effects − − 直接和间接影响 − − − − . − − . − − 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) − − 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 − − 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
→Other third variables
==Other third variables==
==Other third variables==
(1) Confounding:
(1) Confounding:
:Another model that is often tested is one in which competing variables in the model are alternative potential mediators or an unmeasured cause of the dependent variable. An additional variable in a [[causal model]] may obscure or confound the relationship between the independent and dependent variables. Potential confounders are variables that may have a causal impact on both the independent variable and dependent variable. They include common sources of measurement error (as discussed above) as well as other influences shared by both the independent and dependent variables.
: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.
[[File:Mediation model with two covariates.jpg|thumb|Mediation model with two covariates]]
[[File:Mediation model with two covariates.jpg|thumb|Mediation model with two covariates]]
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.
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.
(2) Suppression:
(2) Suppression:
: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.
: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.
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.
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.
(3) Moderators:
(3) Moderators:
: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.
: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.
==Moderated mediation==
==Moderated mediation==