Abstract: In recent years, multilevel mediation and multilevel moderation have been frequently used in social sciences, respectively. However, if they are integrated together, there are totally 12 kinds of multilevel moderated mediation models: 2 (multilevel mediation type) ×2 (level of moderator) ×3 (moderated mediation path). First, there are two types of multilevel mediation when two-level data is involved. One type is 1-1-1 multilevel mediation in which all variables are measured at Level 1, and the model includes between-cluster and within-cluster mediating effects. The other type has at least one variable at Level 2 (e.g., 2-1-1 multilevel mediation), and the model includes between-cluster mediating effect only. Second, there are two types of moderators. One is the moderator at Level 1, and the other is the moderator at Level 2. Third, there are three types of moderated paths: the first-stage (i.e., independent variable→mediator), the second-stage (i.e., mediator→dependent variable) and the dual-stage, which includes the paths of the two stages. All of the above-mentioned multilevel moderated mediation models are briefed in this paper, so that empirical researchers could know which kind of multilevel moderated mediation model meets their need and how to analyze it. It is worth noting that all predict variables of Level 1 are centered at the cluster mean, and then observed cluster mean is used as a Level-2 predictor. In this way, the effect of the predict variable of Level 1 can be divided into within-cluster and between-cluster effects. However, using observed cluster means as the proxy of the true cluster mean might result in a bias of mediating effect, and a multilevel structural equation model (MSEM) is more precise. In MSEM, a variable measured at Level 1 is orthogonally decomposed into a Level-1 latent variable and a Level-2 latent variable. There are four methods with regard to modeling moderated mediation in MSEM: the orthogonal partition (OP) method，random coefficient prediction (RCP) method，latent moderated structural (LMS) equations method, and Bayesian plausible values (BPV) method. The core issue of these four methods is how to deal with the latent interaction term. In the OP method, the interaction term is manually calculated. In the RCP method, the random slope at Level 1 is considered a latent variable at Level 2, and the latent variable is used as an outcome variable to test the interaction effect. In the LMS method, the joint distribution of the indicators is approximated by a finite mixture distribution, and the expectation maximization algorithm is applied to maximization of the log-likelihood function of this distribution, which results in maximum likelihood interaction estimates. In BPV method, the key to this estimation is that it allows generating a Bayesian analog of factor scores for latent variables by sampling from their posterior distribution some number of times. When the sample size is large enough (i.e., the number of groups is over 200 and the group size is over 30), LMS method is recommended to analyze the multilevel moderated mediation; otherwise, Bayesian plausible values method is preferred. An empirical example is employed to demonstrate how to conduct multilevel moderated mediation analysis with multilevel models and BPV method by Mplus.

Key words: Multilevel model, Multilevel structural equation model, Multilevel moderated mediation, Centering

摘要： 多层中介和多层调节效应分析在社科领域已常有应用，但如果将多层中介和调节整合在一起，可以产生2（多层中介类型）×2（调节变量的层次）×3（调节的中介路径）共12种有调节的多层中介模型。面对有调节的多层中介效应分析，研究者往往束手无策。详述了基于多层线性模型的12种有调节的多层中介的分析方法和基于多层结构方程模型的4类有调节的多层中介分析方法，包括正交分割法，随机系数预测法，潜调节结构方程法和贝叶斯合理值法。这四类方法的核心议题在于如何处理潜调节项。当样本量足够大时，建议选择潜调节结构方程法；当样本量不足时，建议选择贝叶斯合理值法。随后用一个实际例子演示如何进行有调节的多层中介效应分析并有相应的Mplus程序。最后展望了有调节的多层中介效应分析研究的拓展方向。

关键词: 多层线性模型, 多层结构方程模型, 有调节的多层中介, 中心化