Some things you should know about structural equation modeling but never thought to ask

Iacobucci (2009, 2010) covers a number of important issues in the use of structural equation modeling and in so doing provides researchers with many useful insights and sensible suggestions. This commentary focuses on three issues where our views differ somewhat from those expressed in the target articles: SEM and causal inferences, sample size, and model fit. In addressing each of these issues, our perspectives do not so much contradict the views expressed by Iacobucci as they reflect a somewhat different conceptual emphasis.     

Subordinate Influence and the Performance Evaluation Process: Test of a Model

A causal model of the performance evaluation process was proposed and tested in this paper. The proposed conceptualization incorporated social, situational, affective, and cognitive elements as they affect performance ratings, with particular emphasis on the role of subordinate influence behaviors. LISREL results demonstrated that the proposed model fit the data well, and reflected a better fit than several alternative models that were estimated. The contributions and limitations of the present study were discussed, in addition to challenges and directions for future research.     

一种新的统计方法和研究思路——结构方程建模述评

结构方程建模(SEM)是一种新的统计方法和研究思路,近年来在心理学和社会科学领域的应用日益增多。本文在非数学化的基础上,结合心理学研究实例介绍了SEM的渊源、发展、基本概念、分析过程以及相应的计算机统计软件LI-SREL。本文认为SEM有四大优点:①引进潜变量使研究更为深入,②遵循一般线性模式进行验证型分析,使研究更有意义,③妥善处理多变量间的复杂关系,④模型具有参数不变性。SEM应该引起国内心理学界的重视。     

Combining feature norms and text data with topic models

Many psychological theories of semantic cognition assume that concepts are represented by features. The empirical procedures used to elicit features from humans rely on explicit human judgments which limit the scope of such representations. An alternative computational framework for semantic cognition that does not rely on explicit human judgment is based on the statistical analysis of large text collections. In the topic modeling approach, documents are represented as a mixture of learned topics where each topic is represented as a probability distribution over words. We propose feature-topic models, where each document is represented by a mixture of learned topics as well as predefined topics that are derived from feature norms. Results indicate that this model leads to systematic improvements in generalization tasks. We show that the learned topics in the model play in an important role in the generalization performance by including words that are not part of current feature norms.     

Mediation analysis and categorical variables: Some further frontiers

Iacobucci (2012) provides a conceptually appealing, readily implemented measure to assess mediation for a far wider range of data type combinations than traditional OLS-based analyses permit. Here, we consider potential applications and extensions along several lines, particularly in terms of random utility models, simulation-based estimation, and potential nonlinearities, as well as some methodological and cultural impediments.     

单维测验合成信度三种区间估计的比较

已有许多研究建议使用合成信度来估计测验信度, 并报告其置信区间。有三种方法或途径可以计算单维测验合成信度的置信区间, 包括Bootstrap法、Delta法和直接用统计软件(如LISREL)输出的标准误进行计算。本文通过模拟研究进行比较, 发现Delta法与Bootstrap法得到的置信区间相当接近, 但用LISREL输出的标准误计算的与Bootstrap法得到的结果相差很大。推荐用Delta法估计合成信度的置信区间(使用Mplus容易实现), 但不能直接用LISREL输出的标准误来计算。举例说明了如何计算单维测验的合成信度以及用Delta法计算其置信区间。     

测验同质性系数及其区间估计

在决定将多维测验分数合并成测验总分时, 应当考虑测验同质性。如果同质性太低, 合成总分没有什么意义。同质性高低可以用同质性系数来衡量。用来计算同质性系数的模型是近年来受到关注的双因子模型(既有全局因子又有局部因子), 测验的同质性系数定义为测验分数方差中全局因子分数方差所占的比例。本文用Delta法推导出计算同质性系数的标准误公式, 进而计算其置信区间。提供了简单的计算同质性系数及其置信区间的程序。用一个例子说明如何估计同质性系数及其置信区间, 通过模拟比较了用Delta法和用Bootstrap法计算的置信区间, 发现两者差异很小。     

Observed and latent variables: Discussion of a basic LISREL paradigm

The aim of the present paper is to discuss a general paradigm of LISREL: that observed psychologocal variables are causally determined by non-observed, latent variables. An example from the LISREL manual is used to show that this basic assumption is not generally meaningful. The possibility of understanding the theoretical variables of LISREL in an instrumentalist way is also considered. But instrumentalism, it is concluded, does not provide a tenable way of defending the LISREL paradigm. For LISREL conceives latent variables as causes of observed variables, and this is not compatible with an instrumentalist understanding of theoretical terms.     

Reporting structural equation modeling results in Psychology and Aging: some proposed guidelines.

Structural equation modeling (SEM) is now widely used in social and behavioral science research. SEM provides the possibility of fitting, and evaluating the fit, of well-specified, theoretical models to empirical data--more generally, of testing elaborated psychological theories. The options available to users of these approaches are many and varied. Popular SEM computational software packages, such as LISREL and EQS, provide a large amount of information, and there is some uncertainty as to what should be routinely reported. A series of guidelines are proposed for reporting SEM results in articles submitted to Psychology and Aging. The suggested guidelines ask authors using SEM methodology to provide important analysis information that will enable readers to evaluate the findings.     

Structural Equation Modeling With AMOS,EQS, and LISREL: Comparative Approaches to Testing for the Factorial Validity of a Measuring Instrument

Using a confirmatory factor analytic (CFA) model as a paradigmatic basis for all comparisons, this article reviews and contrasts important features related to 3 of the most widely-used structural equation modeling (SEM) computer programs: AMOS 4.0 (Arbuckle, 1999), EQS 6 (Bentler, 2000), and LISREL 8 (Joreskog & Sorbom, 1996b). Comparisons focus on (a) key aspects of the programs that bear on the specification and testing of CFA models-preliminary analysis of data, and model specification, estimation, assessment, and misspecification; and (b) other important issues that include treatment of incomplete, nonnormally-distributed, or categorically-scaled data. It is expected that this comparative review will provide readers with at least a flavor of the approach taken by each program with respect to both the application of SEM within the framework of a CFA model, and the critically important issues, previously noted, related to data under study.     

The J-Curve Hypothesis of Conforming Behavior

Abstract

We examined fear of crime in the residential environment from a theoretical and social psychological perspective by constructing a model that relates feelings of unsafety to attributions about self, the potential criminal, and the situation in which the criminal act might occur. Using data from a questionnaire field survey of 440 residents in four urban neighborhoods, the model was compared with a socio-demographic alternative (comprising such variables as gender, age, and educational level). LISREL, a relatively new method of analysis that takes measurement error into account, indicated that the model has superior explanatory power and greater in-terpretability. Multiple regression analyses confirmed these results and point to ways in which operationalization of the theoretical model might be improved.     

Structural Equation Modeling Approaches for Analyzing Partially Nested Data

Study designs involving clustering in some study arms, but not all study arms, are common in clinical treatment-outcome and educational settings. For instance, in a treatment arm, persons may be nested in therapy groups, whereas in a control arm there are no groups. Methodological approaches for handling such partially nested designs have recently been developed in a multilevel modeling framework (MLM-PN) and have proved very useful. We introduce two alternative structural equation modeling (SEM) approaches for analyzing partially nested data: a multivariate single-level SEM (SSEM-PN) and a multiple-arm multilevel SEM (MSEM-PN). We show how SSEM-PN and MSEM-PN can produce results equivalent to existing MLM-PNs and can be extended to flexibly accommodate several modeling features that are difficult or impossible to handle in MLM-PNs. For instance, using an SSEM-PN or MSEM-PN, it is possible to specify complex structural models involving cluster-level outcomes, obtain absolute model fit, decompose person-level predictor effects in the treatment arm using latent cluster means, and include traditional factors as predictors/outcomes. Importantly, implementation of such features for partially nested designs differs from that for fully nested designs. An empirical example involving a partially nested depression intervention combines several of these features in an analysis of interest for treatment-outcome studies.     

Evaluating Structural Equation Models for Categorical Outcomes: A New Test Statistic and a Practical Challenge of Interpretation

This research is concerned with two topics in assessing model fit for categorical data analysis. The first topic involves the application of a limited-information overall test, introduced in the item response theory literature, to structural equation modeling (SEM) of categorical outcome variables. Most popular SEM test statistics assess how well the model reproduces estimated polychoric correlations. In contrast, limited-information test statistics assess how well the underlying categorical data are reproduced. Here, the recently introduced C₂ statistic of Cai and Monroe (2014) is applied. The second topic concerns how the root mean square error of approximation (RMSEA) fit index can be affected by the number of categories in the outcome variable. This relationship creates challenges for interpreting RMSEA. While the two topics initially appear unrelated, they may conveniently be studied in tandem since RMSEA is based on an overall test statistic, such as C₂. The results are illustrated with an empirical application to data from a large-scale educational survey.     

Alternative Factor Structure for the Revised Self-Consciousness Scale

Confirmatory factor analysis (LISREL; Jöreskog & Sörbom, 1989) of data drawn from a sample of middle and senior school students was used to examine a variety of factor structures proposed in previous studies to underlie self-consciousness. Examination of the content of the Revised Self-Consciousness Scale (Scheier & Carver, 1985) suggested an alternative factor structure. This alternative structure comprised 2 private self-consciousness factors: Rumination on the General Self and Monitoring of Specific Aspects of Self. The public self-consciousness measure was retained as originally formulated with the exception of 1 item that was excluded from the final structure. This model of self-consciousness fit the data better than the 4 previously proposed structures.     

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。     

Goal Orientation in Organizational Research: A Conceptual and Empirical Foundation

Although some have argued that goal orientation could be beneficially integrated into organizational research, progress in this area has been impeded by several problematic conceptual issues and a lack of validated dispositional measures. This research was intended to address these issues and to provide a foundation for future organizational research in this area. We argue that goal orientation is a two-dimensional construct that has both dispostional and situational components. In each of four independent studies, LISREL VIII confirmatory factor analyses (Jöreskog & Sörbom, 1993) illustrated that a two-factor model fit a set of goal orientation items better than a single-factor model. In addition, the latent goal orientations were found to be uncorrelated in each study. Moreover, correlational analyses indicated that demographic and substantive variables exhibited differential relationships with the latent learning goal and performance goal orientation constructs. Other analyses illustrated that the dispositional and situational aspects of goal orientation are distinguishable. Collectively, the results provided ample support for the convergent and discriminant validity of eight-item measures of each goal orientation and help to define the nomological network within which the two goal orientations reside. The importance of goal orientation as a multidimensional construct is discussed and several recommendations for further research are suggested.     

A model for integrating fixed-, random-, and mixed-effects meta-analyses into structural equation modeling

Meta-analysis and structural equation modeling (SEM) are two important statistical methods in the behavioral, social, and medical sciences. They are generally treated as two unrelated topics in the literature. The present article proposes a model to integrate fixed-, random-, and mixed-effects meta-analyses into the SEM framework. By applying an appropriate transformation on the data, studies in a meta-analysis can be analyzed as subjects in a structural equation model. This article also highlights some practical benefits of using the SEM approach to conduct a meta-analysis. Specifically, the SEM-based meta-analysis can be used to handle missing covariates, to quantify the heterogeneity of effect sizes, and to address the heterogeneity of effect sizes with mixture models. Examples are used to illustrate the equivalence between the conventional meta-analysis and the SEM-based meta-analysis. Future directions on and issues related to the SEM-based meta-analysis are discussed.     

A causal model of burnout among self-managed work team members

The findings on burnout that are almost universally from research in service settings are applied to an industrial setting with self-managed work teams. Researchers formulated several hypotheses on the basis of this literature. These hypotheses were then used to develop a structural (causal) model that was tested and refined using LISREL 8. Data were collected from 320 employees concerning perceptions of several job and organization conditions, as well as the three components of burnout. Results indicated that role conflict contributed to emotional exhaustion, and participation in work teams diminished it. Job ambiguity, low co-worker support, and low job ability contributed to feelings of low personal accomplishment. These results were consistent with previous findings. When insufficient time to complete a job was removed from the workload measures, workload actually diminished burnout, a finding opposite from previous research. Other organization factors had no significant impact on burnout in this setting.     

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.     

结构方程模型统计检验力分析：原理与方法

结构方程模型是心理学、管理学、社会学等学科中重要的统计工具之一。然而, 大量使用结构方程模型的研究忽视了对该方法的统计检验力进行必要的分析和报告, 在一定程度上降低了这些研究的结果的证明效力。结构方程模型的统计检验力分析方法主要有Satorra-Saris法、MacCallum法与Monte Carlo法三类。其中Satorra-Saris法适用于备择模型清晰、检验对象相对简单、检验方法基于χ²分布的情形; MacCallum法适用于基于χ²分布的模型拟合检验且备择模型不明的情形; Monte Carlo法适用于检验对象相对复杂、采用模拟或重抽样方法进行检验的情形。在实际应用中, 研究者应当首先判断检验的目的、方法以及是否有明确的备择模型, 并根据这些信息选择具体的分析方法。