Digital ITEMS Module 2: Scale Reliability in Structural Equation Modeling

In this ITEMS module, we frame the topic of scale reliability within a confirmatory factor analysis and structural equation modeling (SEM) context and address some of the limitations of Cronbach's α. This modeling approach has two major advantages: (1) it allows researchers to make explicit the relation between their items and the latent variables representing the constructs those items intend to measure, and (2) it facilitates a more principled and formal practice of scale reliability evaluation. Specifically, we begin the module by discussing key conceptual and statistical foundations of the classical test theory model and then framing it within an SEM context; we do so first with a single item and then expand this approach to a multi‐item scale. This allows us to set the stage for presenting different measurement structures that might underlie a scale and, more importantly, for assessing and comparing those structures formally within the SEM context. We then make explicit the connection between measurement model parameters and different measures of reliability, emphasizing the challenges and benefits of key measures while ultimately endorsing the flexible McDonald's ω over Cronbach's α. We then demonstrate how to estimate key measures in both a commercial software program (Mplus) and three packages within an open‐source environment (R). In closing, we make recommendations for practitioners about best practices in reliability estimation based on the ideas presented in the module.     

Exploratory Structural Equation Modeling

This article examines the problem of specification error in 2 models for categorical latent variables; the latent class model and the latent Markov model. Specification error in the latent class model focuses on the impact of incorrectly specifying the number of latent classes of the categorical latent variable on measures of model adequacy as well as sample reallocation to latent classes. The results show that the clarity of remaining latent classes, as measured by the entropy statistic depends on the number of observations in the omitted latent class—but this statistic is not reliable. Specification error in the latent Markov model focuses on the transition probabilities when a longitudinal Guttman process is incorrectly specified. The findings show that specifying a longitudinal Guttman process that is not true in the population impacts other transition probabilities through the covariance matrix of the logit parameters used to calculate those probabilities.     

Lower Level Mediation Effect Analysis in Two-Level Studies: A Note on a Multilevel Structural Equation Modeling Approach

This article presents a didactic discussion of a multilevel covariance structure modeling approach to estimation of lowest level mediation effect indexes in two-level studies. The procedure is useful when addressing questions about relations among total and indirect effects between variables of interest while accounting for the hierarchical structure of analyzed data. The discussed method also permits interval estimation and hypothesis tests with respect to related quantities of relevance when evaluating mediated effects with clustered data, and is illustrated on a two-level data set.     

基于结构方程模型的在线开放课程使用影响因素研究

通过研究使用在线开放课程的相关成果,结合信息系统成功模型和技术采纳模型等模型,建构大学生使用在线开放课程研究模型。研究结果表明,感知易用性、感知有用性均不同程度地对感知质量和学生满意度形成正向影响,进而影响学生实际使用在线开放课程,并对模型进行验证分析。     

结构方程与中国农村儿童入学的决定因素

中国农村儿童的入学率和辍学率到底是多少？哪些因素导致儿童辍学？家庭、社区和学生个人等诸方面因素作用辍学的路径是什么？使用2006年中西部地区20个县908名儿童的截面数据,运用SEM方法,考察教育供给、家庭教育支持、儿童在校表现和儿童失学之间的关系。结果发现,教育供给和儿童在校表现显著影响儿童失学,家庭教育支持对儿童失学不存在直接影响。通过儿童在校表现这一中介变量,教育供给和家庭教育支持同时间接作用于儿童失学。     

Multiplicity Control in Structural Equation Modeling

Abstract

Researchers conducting structural equation modeling analyses rarely, if ever, control for the inflated probability of Type I errors when evaluating the statistical significance of multiple parameters in a model. In this study, the Type I error control, power and true model rates of famsilywise and false discovery rate controlling procedures were compared with rates when no multiplicity control was imposed. The results indicate that Type I error rates become severely inflated with no multiplicity control, but also that familywise error controlling procedures were extremely conservative and had very little power for detecting true relations. False discovery rate controlling procedures provided a compromise between no multiplicity control and strict familywise error control and with large sample sizes provided a high probability of making correct inferences regarding all the parameters in the model.     

Modeling Dynamic Functional Neuroimaging Data Using Structural Equation Modeling

The aims of this study were to present a method for developing a path analytic network model using data acquired from positron emission tomography. Regions of interest within the human brain were identified through quantitative activation likelihood estimation meta-analysis. Using this information, a “true” or population path model was then developed using Bayesian structural equation modeling. To evaluate the impact of sample size on parameter estimation bias, proportion of parameter replication coverage, and statistical power, a 2 group (clinical/control) × 6 (sample size: N = 10, N = 15, N = 20, N = 25, N = 50, N = 100) Markov chain Monte Carlo study was conducted. Results indicate that using a sample size of less than N = 15 per group will produce parameter estimates exhibiting bias greater than 5% and statistical power below .80.     

结构方程模型在英语阅读语料库中的研究

该文从建立基础型英语阅读语料库(English Reading Corpus,ERC),然后采用结构方程模型(Structural EquationModeling,SEM)及语言统计学方法,从英语阅读语料库的语篇复杂度、学习者个体的信息获取水平及情感因素三方面进行了建模及相关关系的探索性研究,在数据统计和分析的基础上,找到了满足置信度及可拟合的数学模型,以期能对英语阅读教学和学习有所启示。在通过对SEM的ERC建模之后的数据进行全面、准确的统计分析,能够为提高英语阅读教学质量提供有价值的统计数据和分析资料。     

关于齐次线性方程组的一个注记

给出了命题“齐次线性方程组Ax=0(A为方阵)有非零解的充分必要条件是|A|=0”的基于行列式理论的一个证明,并探讨了这一证明在教学中的应用。     

关于代数方程根的研究的注记

利用函数的导数对方程根的存在性、惟一性及个数进行研究和归纳。     

Evaluating Interventions with Multimethod Data: A Structural Equation Modeling Approach

In many intervention and evaluation studies, outcome variables are assessed using a multimethod approach comparing multiple groups over time. In this article, we show how evaluation data obtained from a complex multitrait–multimethod–multioccasion–multigroup design can be analyzed with structural equation models. In particular, we show how the structural equation modeling approach can be used to (a) handle ordinal items as indicators, (b) test measurement invariance, and (c) test the means of the latent variables to examine treatment effects. We present an application to data from an evaluation study of an early childhood prevention program. A total of 659 children in intervention and control groups were rated by their parents and teachers on prosocial behavior and relational aggression before and after the program implementation. No mean change in relational aggression was found in either group, whereas an increase in prosocial behavior was found in both groups. Advantages and limitations of the proposed approach are highlighted.     

Bayesian Data-Model Fit Assessment for Structural Equation Modeling

Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes and illustrates key features of Bayesian approaches to model diagnostics and assessing data–model fit of structural equation models, discussing their merits relative to traditional procedures.     

Standards-Based Evaluation and Teacher Career Satisfaction: A Structural Equation Modeling Analysis

Structural equation modeling was used to assess the plausibility of a conceptual model specifying hypothesized linkages among perceptions of characteristics of standards-based evaluation, work environment mediators, and career satisfaction and other outcomes. Four comprehensive high schools located in two neighboring counties in southern California provided the data for this study. The schools’ districts had recently developed and implemented evaluation systems based on six California Standards for the Teaching Profession generated in 1997. One hundred and seventy-eight teachers responded to survey questions designed to capture the following constructs: understandable/relevant standards, satisfactory/helpful evaluation, role ambiguity, effort performance-rating linkage, work criteria autonomy, career satisfaction, organizational commitment, and perceptions of the effectiveness of the evaluation system. Confirmatory factor analysis was used to assess whether the items measuring evaluation fit two hypothesized constructs. Structural equation modeling results indicated that there are two mediators in the evaluation-career satisfaction relationship: role ambiguity and work criteria autonomy.

A Two-Stage Approach to Synthesizing Covariance Matrices in Meta-Analytic Structural Equation Modeling

A great obstacle for wider use of structural equation modeling (SEM) has been the difficulty in handling categorical variables. Two data sets with known structure between 2 related binary outcomes and 4 independent binary variables were generated. Four SEM strategies and resulting apparent validity were tested: robust maximum likelihood (ML), tetrachoric correlation matrix input followed by SEM ML analysis, SEM ML estimation for the sum of squares and cross-products (SSCP) matrix input obtained by the log-linear model that treated all variables as dependent, and asymptotic distribution-free (ADF) SEM estimation. SEM based on the SSCP matrix obtained by the log-linear model and SEM using robust ML estimation correctly identified the structural relation between the variables. SEM using ADF added an extra parameter. SEM based on tetrachoric correlation input did not specify the data generating process correctly. Apparent validity was similar for all models presented. Data transformation used in log-linear modeling can serve as an input for SEM.     

关于回归方程显著性检验的一个注记

针对多元线性回归方程的显著性检验问题,在随机误差服从任意分布的假设下,运用线性模型和随机变量二次型的相关理论,推导出总离差平方和分解式中各分量的数学期望,进而从定量的角度说明回归方程显著性检验中所取拒绝域的合理性。     

Revisiting the Model Size Effect in Structural Equation Modeling

Fitting a large structural equation modeling (SEM) model with moderate to small sample sizes results in an inflated Type I error rate for the likelihood ratio test statistic under the chi-square reference distribution, known as the model size effect. In this article, we show that the number of observed variables (p) and the number of free parameters (q) have unique effects on the Type I error rate of the likelihood ratio test statistic. In addition, the effects of p and q cannot be fully explained using degrees of freedom (df). We also evaluated the performance of 4 correctional methods for the model size effect, including Bartlett’s (1950), Swain’s (1975), and Yuan’s (2005) corrected statistics, and Yuan, Tian, and Yanagihara’s (2015) empirically corrected statistic. We found that Yuan et al.’s (2015) empirically corrected statistic generally yields the best performance in controlling the Type I error rate when fitting large SEM models.