零假设显著性检验无法说明效应的实际大小。因此，很多方法学家、期刊编辑和审稿人等都推荐研究者在显著性检验结果的基础上补充报告效应量及其置信区间以弥补显著性检验的不足。中介效应分析是社会科学中最受欢迎的统计方法之一。为衡量中介效应的实际大小，已经有研究者提出了一些中介效应量指标。其中，数量最多的一类为R² 类型指标，包括R_med²、SOS、R_4.6²、R_4.7²、R_DH² 和υ 等。这类指标类似于回归分析中的R² ，试图衡量因变量的方差中被自变量和中介变量共同解释部分的大小。然而，已有的R²类型指标存在两个主要局限：（1）基本均只适用于观测变量简单中介模型（即仅含三个观测变量的中介模型），难以拓展到更复杂的模型中；（2）多数指标（如R_4.6²、R_4.7²、R_DH²、SOS）都很难解释，不能表示方差被解释的比例。这些局限大大削弱了它们的应用价值。

为克服这些局限，本文提出了一个新的中介效应量指标Δ。根据中介变量在模型中的作用机制将其拆分为与自变量有关和无关的两部分，在此基础上，从中介模型中将与中介效应无关的部分剥离出来构成一个新模型（称为剔除模型），将Δ定义为完整中介模型与剔除模型中因变量的决定系数的差值。它反映了因变量的方差中被感兴趣的中介效应所解释的比例。本文首先基于观测变量简单中介模型提出Δ，然后将它拓展到一系列更复杂的中介模型（具体包括潜变量中介模型、并行中介模型和链式中介模型）中，提出了在不同模型下定义和估计Δ的通用流程和方法，并用模拟研究全面考察了不同模型下Δ的估计（点估计和区间估计）表现。本文共包含五个研究，各研究的主要内容和结果如下。

研究一基于观测变量简单中介模型开展。首先，提出了Δ，详细阐述了定义Δ的基本思想。然后，解决了Δ的估计问题，一方面为Δ构造了恰当的样本估计量，另一方面提出用bootstrap法估计Δ置信区间的思路。最后，通过一个模拟研究评估观测变量简单中介模型中Δ的估计表现，考察不同样本量和路径系数大小的条件下Δ点估计值的偏差和均方根误差（RMSE），并比较三种不同bootstrap区间估计方法（百分位法、偏差校正法、偏差校正及加速法）的表现。模拟研究结果表明，在绝大多数模拟条件下，Δ估计值的偏差和RMSE都很小，且均随样本量的增大而减小。此外，对于区间估计，百分位bootstrap法的表现最好，后续研究将使用该方法估计Δ的置信区间。

研究二将Δ指标拓展到潜变量中介模型中，提出了在潜变量简单中介模型中定义Δ的思路与步骤，并通过提出一种模拟生成数据的新方法，重点解决了潜变量模型中Δ的样本估计值难以计算的问题。此外，研究二也设计了一个模拟研究，用于考察在潜变量简单中介模型中Δ的点估计值和置信区间的估计表现，以验证所提出的模拟生成数据法的准确性。模拟研究重点考察了不同样本量、路径系数大小及潜变量信度条件下，Δ点估计值的偏差和RMSE，以及置信区间的覆盖率、宽度和不平衡度。结果发现，在除样本量小、潜变量信度同时也低的条件外，其余多数条件下效应量的估计偏差和RMSE都较小，估计准确性较高，并且偏差和RMSE均随样本量及潜变量信度的增大而减小；从置信区间覆盖率、宽度和不平衡度结果看，百分位bootstrap方法仍可用于估计Δ的置信区间。

研究三将Δ指标进一步拓展到观测变量并行中介模型和潜变量并行中介模型中，提出了相应的中介效应量指标定义和估计的思路与步骤，并重点解决了如何为感兴趣的单个中介变量或中介变量集合分别构造中介效应量的问题。通过两个模拟研究，分别在观测变量并行中介模型和潜变量并行中介模型中，考察Δ的点估计和区间估计的表现。模拟研究中考察的影响因素为样本量、路径系数大小和中介变量信度（仅在潜变量模型中考察）。结果发现，无论是观测变量还是潜变量并行中介模型，在几乎所有条件下Δ估计值的偏差和RMSE都很小，且均随样本量的增大而减小。在潜变量模型中，偏差和RMSE还随中介变量信度的增大而减小。此外，在两类模型下，Δ的百分位bootstrap置信区间的表现均较好。

研究四将Δ指标进一步拓展到观测变量链式中介模型和潜变量链式中介模型中，提出了相应的中介效应量指标定义和估计的思路与步骤，并重点解决了当存在中介链时，如何构造剔除模型的问题。研究四包含两个模拟研究，分别用于考察观测变量和潜变量链式中介模型中，Δ的点估计值和置信区间估计的实际表现。模拟研究考虑的影响因素与研究三相同。研究结果也与研究三类似：在几乎所有条件下Δ估计值的偏差和RMSE都很小，且样本量和中介变量信度的提高均有利于Δ的估计。此外，在两类模型下Δ的百分位bootstrap置信区间的表现也均较好。

研究五在研究一至四的基础上进一步解决了中介效应量指标Δ的实现和应用的问题。一方面，开发了一个简单易用的R软件包（“MediationES”）。MediationES包适用于结构方程模型框架下大多数常用的中介模型，可用于计算新指标Δ的估计值和置信区间。另一方面，还基于实际数据，呈现了多个实证分析案例，详细演示了应用MediationES包计算新指标的估计值及置信区间的过程，以及在实际研究中解释新指标估计结果的方式，可以为应用研究者提供实践指导。

在理论层面上，本文创新地提出了一种可拓展性很强的构造中介效应量的思想，并对其进行了全面地拓展，提炼总结了在多类中介模型中定义和估计中介效应量的思路；在实践层面上，本文开发设计了简单易用的计算中介效应量及其置信区间的工具，并提供了多个实证案例。本文提出的中介效应量指标具备诸多优良性质，较好地克服了已有中介效应量（尤其是R2类型效应量）的局限，有望成为受欢迎的中介效应量。

The null hypothesis significance test has been criticized for not providing information about the size of effects. To compensate for this limitation, researchers are advised by methodologists, journal editors, and reviewers to report effect sizes and their corresponding confidence intervals (CI) in addition to the results of significance tests. Mediation analysis has become one of the most popular statistical methods in the social sciences. To quantify the size of the mediation effect, several effect-size measures have been proposed. The most numerous category of effect-size measures for mediation is the R² effect-size measures, which mainly includes measures such as R_med² , SOS , R_4.6² 、R_4.7² , R_DH² , and υ . Like the R² commonly used in regression analysis, these measures are intended to quantify the amount of variance in the outcome jointly explained by the predictor and the mediator. However, the currently available R²-type measures have two main limitations. First, almost all of them are only applicable to the simplest mediation model with three observed variables. Second, most of them are difficult to interpret and cannot be interpreted on a standardized proportion metric. These limitations greatly restrict their use.

To address these limitations, this article proposes a new effect-size measure for mediation analysis, denoted as Δ. The central idea of this new measure is to decompose the mediator into two parts based on its influence mechanism within the model: one that is related to the predictor and another that is unrelated. Then, by stripping out the components that are unrelated to the mediation effect based on the decomposition of the mediator, an excluding model is constructed. Δ is defined as the difference between the coefficient of determination of the outcome in the complete mediation model and the excluding model. It quantifies the proportion of variance in the outcome explained by the mediation effect of interest. This article proposes Δ based on the simple mediation model with three observed variables and then extends it to several types of more complex mediation models (i.e., latent variable mediation models, parallel mediation models, and sequential mediation models). For each type of mediation model, the procedure and method for defining and estimating Δ are proposed, and simulation studies are conducted to comprehensively examine the actual estimation performance of Δ. This article contains five studies, and the main contents and results of each study are as follows.

Study 1 proposes the effect size Δ based on the simple mediation model with three observed variables, elaborates on the basic idea of defining Δ, proposes an appropriate sample estimator for Δ, and proposes the idea of estimating CIs for Δ by bootstrapping. A simulation study is conducted to examine the bias and root mean square error (RMSE) of the point estimates of Δ across conditions of sample sizes and path coefficients and to compare the performance of three different bootstrap methods (percentile bootstrap, bias-corrected bootstrap, bias-corrected and accelerated bootstrap) for estimating CIs for Δ. Results indicate that both the bias and RMSE of the point estimates of Δ are small under most of the simulation conditions, and that they decrease as the sample size increase. Among the three bootstrap methods, the percentile method performs the best. Therefore, it is used in all the subsequent studies for estimating the CIs of Δ.

Study 2 extends Δ to mediation models with latent variables, elaborates on the procedure of defining Δ in the simple mediation model with latent variables, and proposes a new method of simulating the observations of variables in the structural part of the excluding model to calculate the estimates of Δ in latent variable models. A simulation study is conducted to examine the performance of the point and interval estimates of Δ in a simple mediation model with latent variables and to demonstrate the effectiveness of the proposed new method for calculating estimates of Δ. The bias and RMSE of the point estimates of Δ, as well as the coverage, width, and imbalance of the CIs are assessed across conditions of sample size, magnitude of path coefficients, and magnitude of composite reliability of latent variables. Results suggest that both the bias and RMSE of the estimates of Δ are small under most conditions except for those with small sample size and low reliability at the same time, and they both decrease with increasing sample size and reliability. Results of the coverage, width, and imbalance of the CIs suggest that the percentile bootstrap method returns proper CIs for Δ.

Study 3 further extends Δ to parallel mediation models with observed variables and with latent variables. The procedure for defining and estimating Δ is outlined, with a particular focus on addressing the issue of defining appropriate effect-size measures to quantify the mediation effect of a single mediator or a set of mediators of interest. Two simulation studies are conducted to examine the performance of point and interval estimation of Δ in a parallel mediation model with observed variables and a parallel mediation model with latent variables. The factors manipulated in the simulation studies are sample size, path coefficient, and composite reliability of the mediators (manipulated only in the latent variable model). Results show that the point estimates of Δ exhibit small bias and RMSE under most simulation conditions in both observed and latent variable parallel mediation models. Additionally, the bias and RMSE tend to decrease as the sample size increases. In the latent variable model, the bias and RMSE also decrease with increasing reliability of mediators. Furthermore, the percentile bootstrap CI of Δ performs well in both models.

Study 4 further extends Δ to sequential mediation models with observed variables and with latent variables. The definition and estimation of the new effect-size measure are elaborated, with a particular focus on addressing the issue of constructing excluding model when there is a sequential mediation chain. Two simulation studies are conducted to examine the performance of the point and interval estimates of Δ in a sequential mediation model with observed and latent variables, respectively. The factors manipulated remains the same as those in Study 3. The results are also similar to those of Study 3. Specifically, the bias and RMSE of the estimates of Δ are small under almost all conditions, and the increase in sample size and reliability favor the estimation of Δ. Additionally, the percentile bootstrap CI for Δ performs well in both types of models.

Study 5 focuses on the implementation and application of Δ based on Studies 1 to 4. An R package called "MediationES" is developed, which can be easily used and applied to most of the commonly used mediation models in the structural equation modeling framework to calculate the estimates and CIs of the new effect-size measure. Several empirical examples are provided to demonstrate how to use the MediationES package to calculate the estimates and CIs and how to interpret the new effect-size estimates in practical studies. This provides practical guidance for applied researchers

To sum up, this article proposes a novel approach to constructing effect-size measures for mediation and extends it to various types of mediation models. For each type of mediation model, the basic idea of defining the new measure and methods for estimating it are elaborated and summarized. Furthermore, to facilitate practical usage, an accessible tool for calculating point estimates and confidence intervals of the new effect-size measure has been developed. The proposed effect-size measure for mediation analysis has desirable properties and overcomes the limitations of existing measures. Hence, it is anticipated that this measure will be a popular effect-size measure for mediation analysis in the future.