Multilevel SEM Strategies for Evaluating Mediation in Three-Level Data

Strategies for modeling mediation effects in multilevel data have proliferated over the past decade, keeping pace with the demands of applied research. Approaches for testing mediation hypotheses with 2-level clustered data were first proposed using multilevel modeling (MLM) and subsequently using multilevel structural equation modeling (MSEM) to overcome several limitations of MLM. Because 3-level clustered data are becoming increasingly common, it is necessary to develop methods to assess mediation in such data. Whereas MLM easily accommodates 3-level data, MSEM does not. However, it is possible to specify and estimate some 3-level mediation models using both single- and multilevel SEM. Three new alternative approaches are proposed for fitting 3-level mediation models using single- and multilevel SEM, and each method is demonstrated with simulated data. Discussion focuses on the advantages and disadvantages of these approaches as well as directions for future research.     

有调节的多层中介效应分析

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。     

基于结构方程模型的多层中介效应分析

近年社科领域常见使用多层线性模型进行多层中介研究。尽管多层线性模型区分了多层中介的组间和组内效应, 仍然存在抽样误差和测量误差。比较好的方法是, 将多层线性模型整合到结构方程模型中, 在多层结构方程模型框架下设置潜变量和多指标, 可有效校正抽样误差和测量误差、得到比较准确的中介效应值, 还能适用于更多种类的多层中介分析并提供模型的拟合指数。在介绍新方法后, 总结出一套多层中介的分析流程, 通过一个例子来演示如何用MPLUS软件进行多层中介分析。最后展望了多层结构方程和多层中介研究的拓展方向。     

A practical guide to multilevel modeling

Collecting data from students within classrooms or schools, and collecting data from students on multiple occasions over time, are two common sampling methods used in educational research that often require multilevel modeling (MLM) data analysis techniques to avoid Type-1 errors. The purpose of this article is to clarify the seven major steps involved in a multilevel analysis: (1) clarifying the research question, (2) choosing the appropriate parameter estimator, (3) assessing the need for MLM, (4) building the level-1 model, (5) building the level-2 model, (6) multilevel effect size reporting, and (7) likelihood ratio model testing. The seven steps are illustrated with both a cross-sectional and a longitudinal MLM example from the National Educational Longitudinal Study (NELS) dataset. The goal of this article is to assist applied researchers in conducting and interpreting multilevel analyses and to offer recommendations to guide the reporting of MLM analysis results.     

新世纪20年国内心理统计方法研究回顾

新世纪头20年, 国内心理学11本专业期刊一共发表了213篇统计方法研究论文。研究范围主要包括以下10类(按论文篇数排序)：结构方程模型、测验信度、中介效应、效应量与检验力、纵向研究、调节效应、探索性因子分析、潜在类别模型、共同方法偏差和多层线性模型。对各类做了简单的回顾与梳理。结果发现, 国内心理统计方法研究的广度和深度都不断增加, 研究热点在相互融合中共同发展; 但综述类论文比例较大, 原创性研究论文比例有待提高, 研究力量也有待加强。     

基于结构方程模型的多层调节效应

使用多层线性模型进行调节效应分析在社科领域已常有应用。尽管多层线性模型区分了层1自变量的组间和组内效应、实现了多层调节效应的分解, 仍然存在抽样误差和测量误差。建议在多层结构方程模型框架下, 设置潜变量和多指标来有效校正抽样误差和测量误差。在介绍多层调节SEM分析的随机系数预测法和潜调节结构方程法后, 总结出一套多层调节的SEM分析流程, 通过一个例子来演示如何用Mplus软件进行多层调节SEM分析。随后评述了多层调节效应分析方法在国内心理学的应用现状, 并展望了多层结构方程和多层调节研究的拓展方向。     

密集追踪数据分析：模型及其应用

在心理学、教育学和临床医学等领域, 越来越多的研究者开始关注个体内部的行为、心理、临床效果等随时间而产生的动态变化, 重视针对个体的差异化建模。密集追踪是一种在短时间内对个体进行多个时间节点密集追踪测量的方法, 更适合用于研究个体内部心理过程等的动态变化及其作用机制。近年来, 密集追踪成为心理学研究的一大热点, 但许多密集追踪的研究分析仍停留在较为传统的方法。方法学领域已涌现出较多用于密集追踪数据分析的模型方法, 较为主流的模型包括以动态结构方程模型(Dynamic Structural Equation Model, DSEM)为代表的自上而下的建模方法, 以及以组迭代多模型估计(Group Iterative Multiple Model Estimation, GIMME)为代表的自下而上的建模方法。二者均可以方便地对密集追踪数据中的自回归及交叉滞后效应进行建模。     

Capturing the interplay among within- and between-person processes using multilevel modeling techniques

Multilevel modeling is an excellent way to analyze nested or clustered data of the type commonly collected through investigations into the linkages between psychological functioning and relationship processes. This article describes two especially relevant applications of multilevel modeling. The first application, growth curve analysis, is already familiar to many researchers and involves modeling individuals’ change trajectories over time and relating the derived change parameters to person-level characteristics or phenomena. The purpose of this paper is to emphasize a second application, multilevel process analysis, which involves modeling within-subject characteristics other than change over a representation of time. Multilevel analysis of within-subject processes is particularly well-suited for hypotheses common to clinical psychology investigations, yet has received substantially less attention in the literature than its growth curve counterpart. Types of research questions and methodologies that can be addressed within the multilevel process analysis framework are described. Finally, aspects of multilevel process analysis are demonstrated with daily diary data collected from wives who reported on their marital happiness and depressed mood for 3 weeks.     

A Cross-Classified CFA-MTMM Model for Structurally Different and Nonindependent Interchangeable Methods

Multirater (multimethod, multisource) studies are increasingly applied in psychology. Eid and colleagues (2008) proposed a multilevel confirmatory factor model for multitrait-multimethod (MTMM) data combining structurally different and multiple independent interchangeable methods (raters). In many studies, however, different interchangeable raters (e.g., peers, subordinates) are asked to rate different targets (students, supervisors), leading to violations of the independence assumption and to cross-classified data structures. In the present work, we extend the ML-CFA-MTMM model by Eid and colleagues (2008) to cross-classified multirater designs. The new C4 model (Cross-Classified CTC[M-1] Combination of Methods) accounts for nonindependent interchangeable raters and enables researchers to explicitly model the interaction between targets and raters as a latent variable. Using a real data application, it is shown how credibility intervals of model parameters and different variance components can be obtained using Bayesian estimation techniques.     

Multilevel Factor Analysis and Structural Equation Modeling of Daily Diary Coping Data: Modeling Trait and State Variation

This study used multilevel modeling of daily diary data to model within-person (state) and between-person (trait) components of coping variables. This application included the introduction of multilevel factor analysis (MFA) and a comparison of the predictive ability of these trait/state factors. Daily diary data were collected on a large (n = 366) multiethnic sample over the course of 5 days. Intraclass correlation coefficient for the derived factors suggested approximately equal amounts of variability in coping usage at the state and trait levels. MFAs showed that Problem-Focused Coping and Social Support emerged as stable factors at both the within-person and between-person levels. Other factors (Minimization, Emotional Rumination, Avoidance, Distraction) were specific to the within-person or between-person levels but not both. Multilevel structural equation modeling (MSEM) showed that the prediction of daily positive and negative affect differed as a function of outcome and level of coping factor. The Discussion section focuses primarily on a conceptual and methodological understanding of modeling state and trait coping using daily diary data with MFA and MSEM to examine covariation among coping variables and predicting outcomes of interest.     

Structural equation modeling of multitrait-multimethod data: different models for different types of methods

The question as to which structural equation model should be selected when multitrait-multimethod (MTMM) data are analyzed is of interest to many researchers. In the past, attempts to find a well-fitting model have often been data-driven and highly arbitrary. In the present article, the authors argue that the measurement design (type of methods used) should guide the choice of the statistical model to analyze the data. In this respect, the authors distinguish between (a) interchangeable methods, (b) structurally different methods, and (c) the combination of both kinds of methods. The authors present an appropriate model for each type of method. All models allow separating measurement error from trait influences and trait-specific method effects. With respect to interchangeable methods, a multilevel confirmatory factor model is presented. For structurally different methods, the correlated trait-correlated (method-1) model is recommended. Finally, the authors demonstrate how to appropriately analyze data from MTMM designs that simultaneously use interchangeable and structurally different methods. All models are applied to empirical data to illustrate their proper use. Some implications and guidelines for modeling MTMM data are discussed.     

基于阶层线性理论的多层级中介效应

本文介绍了三种常见的多层级中介效应模型, 并根据阶层线性理论和依次检验回归系数的方法, 详述了多层级中介效应的检验步骤以及中介效应量的估计方法, 在2-1-1和1-1-1中介效应模型中, 推荐采用对层1自变量按组均值中心化, 同时将组均值置于层2截距方程式的中心化方法, 以实现组间和组内中介效应的有效分离。本文还展望了多层级中介效应模型的拓展方向, 即多层级调节性中介模型和多层级结构方程模型; 以及检验方法的拓展, 即Sobel检验和置信区间检验。     

Collective Efficacy as a Mediator of the Trustworthiness – Performance Relationship in Computer-Mediated Team-based Contexts

The current study investigated the role of trustworthiness perceptions at the individual level and collective efficacy at the team level on team performance in computer-mediated teams using multi-level structural equation modeling (MSEM). It was hypothesized that trustworthiness perceptions and collective efficacy would predict team performance, and collective efficacy would partially mediate the trustworthiness – performance relationship in computer-mediated teams. Sixty-four teams (five participants each) engaged in a computer-mediated task across two experimental sessions. Trustworthiness measured after session 1, collective efficacy measured after sessions 1 and 2, and team performance measured of sessions 1 and 2 were used to build the MSEM. The half longitudinal model for assessing mediation was used to examine the influence of trustworthiness perceptions on performance through collective efficacy over time. Results demonstrated support for the hypothesized model, such that trustworthiness perceptions demonstrated indirect effects on performance through collective efficacy. These findings extend past research by identifying an emergent mechanism by which trustworthiness is important for team performance in computer-mediated teams.     

A Computationally More Efficient and More Accurate Stepwise Approach for Correcting for Sampling Error and Measurement Error

Over the last decade or two, multilevel structural equation modeling (ML-SEM) has become a prominent modeling approach in the social sciences because it allows researchers to correct for sampling and measurement errors and thus to estimate the effects of Level 2 (L2) constructs without bias. Because the latent variable modeling software Mplus uses maximum likelihood (ML) by default, many researchers in the social sciences have applied ML to obtain estimates of L2 regression coefficients. However, one drawback of ML is that covariance matrices of the predictor variables at L2 tend to be degenerate, and thus, estimates of L2 regression coefficients tend to be rather inaccurate when sample sizes are small. In this article, I show how an approach for stabilizing covariance matrices at L2 can be used to obtain more accurate estimates of L2 regression coefficients. A simulation study is conducted to compare the proposed approach with ML, and I illustrate its application with an example from organizational research.     

Multilevel factor analysis and structural equation modeling of daily diary coping data: Modeling trait and state variation

The current study used multilevel modeling of daily diary data to model within-person (state) and between-person (trait) components of coping variables. This application included the introduction of multilevel factor analysis (MFA) and a comparison of the predictive ability of these trait/state factors. Daily diary data was collected on a large (n = 366) multiethnic sample over the course of five days. Intraclass correlation coefficient for the derived factors suggested approximately equal amounts of variability in coping usage at the state and trait levels. MFAs showed that Problem-Focused Coping and Social Support emerged as stable factors at both the within-person and between-person levels. Other factors (Minimization, Emotional Rumination, Avoidance, Distraction) were specific to the within-person or between-person levels, but not both. Multilevel structural equation modeling (MSEM) showed that the prediction of daily positive and negative affect differed as a function of outcome and level of coping factor. The Discussion section focuses primarily on a conceptual and methodological understanding of modeling state and trait coping using daily diary data with MFA and MSEM to examine covariation among coping variables and predicting outcomes of interest.     

Factorial Structure of the Family Values Scale From a Multilevel-Multicultural Perspective

In cross-cultural research, there is a tendency for researchers to draw inferences at the country level based on individual-level data. Such action implicitly and often mistakenly assumes that both the measuring instrument and its underlying construct(s) are operating equivalently across both levels. Based on responses from 5,482 college students sampled from 27 countries, we took a structural equation modeling approach to addressing this issue of level equivalence. Purposes of the study were: (a) to validate the hypothesized two-factor structure of the Family Values Scale (FV Scale; Georgas, 1999) within a multilevel framework that took individual- and country-level information into account; (b) to test equivalence of the FV Scale across individual and country levels; and (c) to evaluate relations between the FV Scale and three possibly important covariates—gender at the individual level, and affluence and religion at the country level. Implications of findings and importance of multilevel equivalence in cross-cultural research are discussed.     

Hierarchical modeling of sequential behavioral data: examining complex association patterns in mediation models

This article presents new methods for modeling the strength of association between multiple behaviors in a behavioral sequence, particularly those involving substantively important interaction patterns. Modeling and identifying such interaction patterns becomes more complex when behaviors are assigned to more than two categories, as is the case for most observational research. The authors propose multilevel empirical Bayes methods to overcome the challenges inherent in such data. Furthermore, these methods allow the study of how variation in interaction patterns can mediate the effects of antecedents or intervention on distal outcomes. New procedures are developed to compare alternative mediation models and pinpoint which random effects operate as mediators. These models are then applied to observational data taken from a study of the behavioral interactions of 254 couples.     

The role of workaholism in the job demands-resources model

Background and Objectives: The present study tries to gain more insight in workaholism by investigating its antecedents and consequences using the job demands-resources model. Design: We hypothesized that job demands would be positively related to workaholism, particularly when job resources are low. In addition, we hypothesized that workaholism would be positively related to negative outcomes in three important life domains: health, family, and work. Methods: The research involved 617 Italian workers (employees and self-employed). To test the hypotheses we applied structural equation modeling (SEM) and moderated structural equation modeling (MSEM) using Mplus 6. Results: The results of SEM showed a good model where workload, cognitive demands, emotional demands, and customer-related social stressors were positively related to workaholism and work–family conflict (WFC) (partial mediation). Additionally, workaholism was indirectly related to exhaustion and intentions to change jobs through WFC. Moreover, MSEM analyses confirmed that job resources (job security and opportunities for development) buffered the relationship between job demands and workaholism. Particularly, the interaction effects were statistically significant in five out of eight combinations. Conclusions: These findings suggest that workaholism is a function of a suboptimal work environment and predicts unfavorable employee outcomes. We discuss the theoretical and practical implications of these findings.     

Friendship Dissolution Within Social Networks Modeled Through Multilevel Event History Analysis

A social network perspective can bring important insight into the processes that shape human behavior. Longitudinal social network data, measuring relations between individuals over time, has become increasingly common—as have the methods available to analyze such data. A friendship duration model utilizing discrete-time multilevel survival analysis with a multiple membership random effect structure is developed and applied here to study the processes leading to undirected friendship dissolution within a larger social network. While the modeling framework is introduced in terms of understanding friendship dissolution, it can be used to understand microlevel dynamics of a social network more generally. These models can be fit with standard generalized linear mixed-model software, after transforming the data to a pair-period data set. An empirical example highlights how the model can be applied to understand the processes leading to friendship dissolution between high school students, and a simulation study is used to test the use of the modeling framework under representative conditions that would be found in social network data. Advantages of the modeling framework are highlighted, and potential limitations and future directions are discussed.