A Primer on Multilevel Modeling

Multilevel modeling (MLM) is growing in use throughout the social sciences. Although daunting from a mathematical perspective, MLM is relatively easy to employ once some basic concepts are understood. In this article, I present a primer on MLM, describing some of these principles and applying them to the analysis of a multilevel data set on doctor–patient communication during medical consultations.     

Multilevel modeling: overview and applications to research in counseling psychology

Multilevel modeling (MLM) is rapidly becoming the standard method of analyzing nested data, for example, data from students within multiple schools, data on multiple clients seen by a smaller number of therapists, and even longitudinal data. Although MLM analyses are likely to increase in frequency in counseling psychology research, many readers of counseling psychology journals have had only limited exposure to MLM concepts. This paper provides an overview of MLM that blends mathematical concepts with examples drawn from counseling psychology. This tutorial is intended to be a first step in learning about MLM; readers are referred to other sources for more advanced explorations of MLM. In addition to being a tutorial for understanding and perhaps even conducting MLM analyses, this paper reviews recent research in counseling psychology that has adopted a multilevel framework, and it provides ideas for MLM approaches to future research in counseling psychology.     

基于多层结构方程模型的情境效应分析—— 兼与多层线性模型比较

多层(嵌套)数据的变量关系研究, 必须借助多层模型来实现。两层模型中, 层一自变量Xij按组均值中心化, 并将组均值 置于层2截距方程式中, 可将Xij对因变量Yij的效应分解为组间和组内部分, 二者之差被称为情境效应, 称为情境变量。多层结构方程模型(MSEM)将多层线性模型(MLM)和结构方程模型(SEM)相结合, 通过设置潜变量和多指标的方法校正了MLM在情境效应分析中出现的抽样误差和测量误差, 同时解决了数据的多层(嵌套)结构和潜变量的估计问题。除了分析原理的说明, 还以班级平均竞争氛围对学生竞争表现的情境效应为例进行分析方法的示范, 并比较MSEM和MLM的异同, 随后展望了MSEM情境效应模型、情境效应无偏估计方法和情境变量研究的拓展方向。     

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.     

多水平项目反应理论模型在测验发展中的应用

作者简要介绍了多水平项目反应模型,对多水平项目反应理论与通常项目反应理论之间的关系进行了探讨,得到了多水平项目反应模型参数与通常项目反应模型参数之间的关系,并讨论了多水平项目反应模型的推广模型。通过一个实际例子,用多水平项目反应模型对测验中项目的特征进行分析;检验个体水平和组水平预测变量对能力参数的影响;对项目功能差异进行分析。最后文章就多水平项目反应理论模型的优势与不足进行了讨论     

Centering predictor variables in cross-sectional multilevel models: a new look at an old issue

Appropriately centering Level 1 predictors is vital to the interpretation of intercept and slope parameters in multilevel models (MLMs). The issue of centering has been discussed in the literature, but it is still widely misunderstood. The purpose of this article is to provide a detailed overview of grand mean centering and group mean centering in the context of 2-level MLMs. The authors begin with a basic overview of centering and explore the differences between grand and group mean centering in the context of some prototypical research questions. Empirical analyses of artificial data sets are used to illustrate key points throughout. The article provides a number of practical recommendations designed to facilitate centering decisions in MLM applications.     

The relationship between multilevel models and non‐parametric multilevel mixture models: Discrete approximation of intraclass correlation,random coefficient distributions,and residual heteroscedasticity

Multilevel data structures are common in the social sciences. Often, such nested data are analysed with multilevel models (MLMs) in which heterogeneity between clusters is modelled by continuously distributed random intercepts and/or slopes. Alternatively, the non‐parametric multilevel regression mixture model (NPMM) can accommodate the same nested data structures through discrete latent class variation. The purpose of this article is to delineate analytic relationships between NPMM and MLM parameters that are useful for understanding the indirect interpretation of the NPMM as a non‐parametric approximation of the MLM, with relaxed distributional assumptions. We define how seven standard and non‐standard MLM specifications can be indirectly approximated by particular NPMM specifications. We provide formulas showing how the NPMM can serve as an approximation of the MLM in terms of intraclass correlation, random coefficient means and (co)variances, heteroscedasticity of residuals at level 1, and heteroscedasticity of residuals at level 2. Further, we discuss how these relationships can be useful in practice. The specific relationships are illustrated with simulated graphical demonstrations, and direct and indirect interpretations of NPMM classes are contrasted. We provide an R function to aid in implementing and visualizing an indirect interpretation of NPMM classes. An empirical example is presented and future directions are discussed.     

Predicting Response to Intensive Multimodal Inpatient Treatment: A Comparison of Single- and Multiple-Class Growth Modeling Approaches

In a modest body of research, personality functioning assessed via performance-based instruments has been found to validly predict treatment outcome and, to some extent, differential response to treatment. However, state-of-the-science longitudinal and mixture modeling techniques, which are common in many areas of clinical psychology, have rarely been used. In this article, we compare multilevel growth curve modeling (MLM) and latent class growth modeling (LCGM) approaches with the same data set to illustrate the different research questions that can be addressed by each method. Global Assessment of Functioning (GAF) scores collected at 6 points during the course of a long-term multimodal inpatient treatment of 58 severely and persistently mentally ill adults were used to model the trajectory of treatment outcome. Pretreatment Rorschach-based markers of personality functioning and other markers of psychiatric severity were examined as covariates in each modeling approach. The results of both modeling approaches generally indicated that more psychologically impaired clients responded less favorably to treatment. The LCGM approach revealed 2 unique trajectories of improvement (a persistently low group and a higher starting, improving group). Personality functioning and baseline psychiatric variables significantly predicted group membership and the rate of change within the groups. A side-by-side examination of these 2 methods was found to be useful in predicting differential treatment response with personality functioning variables.     

On the Multilevel Nature of Meta-Analysis: A Tutorial,Comparison of Software Programs,and Discussion of Analytic Choices

The term “multilevel meta-analysis” is encountered not only in applied research studies, but in multilevel resources comparing traditional meta-analysis to multilevel meta-analysis. In this tutorial, we argue that the term “multilevel meta-analysis” is redundant since all meta-analysis can be formulated as a special kind of multilevel model. To clarify the multilevel nature of meta-analysis the four standard meta-analytic models are presented using multilevel equations and fit to an example data set using four software programs: two specific to meta-analysis (metafor in R and SPSS macros) and two specific to multilevel modeling (PROC MIXED in SAS and HLM). The same parameter estimates are obtained across programs underscoring that all meta-analyses are multilevel in nature. Despite the equivalent results, not all software programs are alike and differences are noted in the output provided and estimators available. This tutorial also recasts distinctions made in the literature between traditional and multilevel meta-analysis as differences between meta-analytic choices, not between meta-analytic models, and provides guidance to inform choices in estimators, significance tests, moderator analyses, and modeling sequence. The extent to which the software programs allow flexibility with respect to these decisions is noted, with metafor emerging as the most favorable program reviewed.     

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.     

Person‐specific versus multilevel autoregressive models: Accuracy in parameter estimates at the population and individual levels

This paper compares the multilevel modelling (MLM) approach and the person‐specific (PS) modelling approach in examining autoregressive (AR) relations with intensive longitudinal data. Two simulation studies are conducted to examine the influences of sample heterogeneity, time series length, sample size, and distribution of individual level AR coefficients on the accuracy of AR estimates, both at the population level and at the individual level. It is found that MLM generally outperforms the PS approach under two conditions: when the sample has a homogeneous AR pattern, namely, when all individuals in the sample are characterized by AR processes with the same order; and when the sample has heterogeneous AR patterns, but a multilevel model with a sufficiently high order (i.e., an order equal to or higher than the maximum order of individual AR patterns in the sample) is fitted and successfully converges. If a lower‐order multilevel model is chosen for heterogeneous samples, the higher‐order lagged effects are misrepresented, resulting in bias at the population level and larger prediction errors at the individual level. In these cases, the PS approach is preferable, given sufficient measurement occasions (T ≥ 50). In addition, sample size and distribution of individual level AR coefficients do not have a large impact on the results. Implications of these findings on model selection and research design are discussed.     

Coupling Longitudinal Data and Multilevel Modeling to Examine the Antecedents and Consequences of Jealousy Experiences in Romantic Relationships: A Test of the Relational Turbulence Model

We used longitudinal data and multilevel modeling to examine how intimacy, relational uncertainty, and failed attempts at interdependence influence emotional, cognitive, and communicative responses to romantic jealousy, and how those experiences shape subsequent relationship characteristics. The relational turbulence model ( Solomon & Knobloch, 2004 ) highlights how intimacy, relational uncertainty, and interference from partners influence and reflect reactions to events that occur within romantic relationships. Drawing from the theory, we predicted that (a) relational uncertainty and interference from partners are positively associated with cognitive and emotional jealousies; (b) the intensity of romantic jealousy, relational intimacy, and a partner’s interference is positively associated with the directness of communication about jealousy; (c) relational uncertainty is negatively associated with communicative directness; and (d) cognitive jealousy, emotional jealousy, and the directness of communicative responses to jealousy influence subsequent relationship characteristics. The results of the multilevel modeling revealed mixed support for our predictions. We explore the implications of this study for research on the relational turbulence model, relationship development, and jealousy.     

Attentional control in depression: A translational affective neuroscience approach

Translational research refers to the application of basic science to address clinical problems and acquire knowledge that can be used to guide and refine clinical practice. This special issue of Cognitive, Affective, & Behavioral Neuroscience seeks to explore and integrate some of the most promising findings offered by recent cognitive and affective neuroscience studies in hopes of filling the gap between basic and applied research, thereby heightening our understanding of vulnerability for depression. The studies presented in this special issue focus specifically on attentional processes. We solicited contributions from leading researchers involved in basic cognitive and neuroscience research investigating processes underlying depression-related disturbances in emotion processing. In this introductory article, we present an integrative overview to demonstrate how these specific contributions might be valuable for translational research.     

The multilevel latent covariate model: a new, more reliable approach to group-level effects in contextual studies

In multilevel modeling (MLM), group-level (L2) characteristics are often measured by aggregating individual-level (L1) characteristics within each group so as to assess contextual effects (e.g., group-average effects of socioeconomic status, achievement, climate). Most previous applications have used a multilevel manifest covariate (MMC) approach, in which the observed (manifest) group mean is assumed to be perfectly reliable. This article demonstrates mathematically and with simulation results that this MMC approach can result in substantially biased estimates of contextual effects and can substantially underestimate the associated standard errors, depending on the number of L1 individuals per group, the number of groups, the intraclass correlation, the sampling ratio (the percentage of cases within each group sampled), and the nature of the data. To address this pervasive problem, the authors introduce a new multilevel latent covariate (MLC) approach that corrects for unreliability at L2 and results in unbiased estimates of L2 constructs under appropriate conditions. However, under some circumstances when the sampling ratio approaches 100%, the MMC approach provides more accurate estimates. Based on 3 simulations and 2 real-data applications, the authors evaluate the MMC and MLC approaches and suggest when researchers should most appropriately use one, the other, or a combination of both approaches.     

Introduction to the Special Issue on Advances in the Psychology of Workplace Coaching

This article introduces a special issue of Applied Psychology: An International Review that focuses on recent advances in the psychology of workplace coaching. To begin with, we briefly describe the current state of workplace coaching research, and we then outline the aims and objectives that had driven our motivation in editing this special issue. We set out two objectives for this special issue. First, to ensure that each of the contributions started with the relevant theoretical framework, and secondly, that the papers in this special issue utilized rigorous research design and methodology. We then provide an overview of each of the five articles making up the special issue, detailing their respective contributions to advancing workplace coaching research and theory. We conclude with recommendations for future workplace coaching research, building on the contributions in this special issue. We propose scholars should focus on three key areas: future coaching research should adopt a “start with theory” approach; that rigorous research design and methodology is prioritized, specifically in relation to utilizing multiple data sources and increasing the range of objective (hard) data as coaching outcome measures; and for coaching scholars to pay attention to and explore non-significant effects.     

Communicating the Risk of Violent and Offending Behavior: Review and Introduction to this Special Issue

How to communicate risk of recidivism in correctional and forensic contexts has been a subject of scholarly discussion for two decades. This emerging literature, however, is sparse compared with studies on the assessment of risk for violent and offending behavior. In this special issue of Behavioral Sciences and the Law, we have gathered together empirical and review papers exemplifying promising directions and methodologies. We begin with a review of the state of the field, and lessons that can be drawn from research into medical risk assessment and risk communication, finding that many of the same principles apply to the forensic context. How risks are framed, and how numerate assessors are, affects how risk information is understood and applied. We discuss the existing research bearing on these issues, as well as the conceptual, practical, empirical, and legal implications of communicating risk using numerical or categorical risk terms. Along with the seven articles in this volume, we suggest directions for future research on measuring and communicating change, understanding and managing the statistical literacy of those who use and communicate risk assessments, and developing a theoretical framework for forensic risk communication research. We hope this volume will help integrate and invigorate research into forensic risk communication. Copyright © 2015 John Wiley & Sons, Ltd.     

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。     

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。     

Incorporating Mobility in Growth Modeling for Multilevel and Longitudinal Item Response Data

Multilevel data often cannot be represented by the strict form of hierarchy typically assumed in multilevel modeling. A common example is the case in which subjects change their group membership in longitudinal studies (e.g., students transfer schools; employees transition between different departments). In this study, cross-classified and multiple membership models for multilevel and longitudinal item response data (CCMM-MLIRD) are developed to incorporate such mobility, focusing on students' school change in large-scale longitudinal studies. Furthermore, we investigate the effect of incorrectly modeling school membership in the analysis of multilevel and longitudinal item response data. Two types of school mobility are described, and corresponding models are specified. Results of the simulation studies suggested that appropriate modeling of the two types of school mobility using the CCMM-MLIRD yielded good recovery of the parameters and improvement over models that did not incorporate mobility properly. In addition, the consequences of incorrectly modeling the school effects on the variance estimates of the random effects and the standard errors of the fixed effects depended upon mobility patterns and model specifications. Two sets of large-scale longitudinal data are analyzed to illustrate applications of the CCMM-MLIRD for each type of school mobility.     

Interpersonal Mistreatment of Women in the Workplace

The purpose of this paper is to introduce the work included in the special issue: Interpersonal Mistreatment of Women in the Workplace. In doing so, the authors develop a multilevel conceptual model, illustrating how the research included in the special issue address causes and consequences of interpersonal mistreatment at the micro, meso, and macro-level of analysis. In addition, the integrated model demonstrates how factors at different levels both influence and are influenced by those at other levels of analysis. Based on this collective work, the authors encourage researchers interested in addressing the mistreatment and marginalization of less powerful groups to consider the multilevel causes and consequences of such behavior. It is only through holistic examinations that researchers can we fully understand this insidious problem and encourage people—whether likely targets of mistreatment or not—to take a stand to end this treatment in workplaces and other society as a whole.