Book Review of Basics of Structural Equation Modeling,by Geoffrey M. Maruyama

Confirmatory factor analysis (CFA) is a statistical procedure frequently used to test the fit of data to measurement models. Published CFA studies typically report factor pattern coefficients. Few reports, however, also present factor structure coefficients, which can be essential for the accurate interpretation of CFA results. The interpretation errors that can arise when CFA results are interpreted without considering structure coefficients are described, and some examples from current literature illustrating these errors are also presented.     

Introduction to Structural Equation Modeling: Issues and Practical Considerations

Structural equation modeling (SEM) is a versatile statistical modeling tool. Its estimation techniques, modeling capacities, and breadth of applications are expanding rapidly. This module introduces some common terminologies. General steps of SEM are discussed along with important considerations in each step. Simple examples are provided to illustrate some of the ideas for beginners. In addition, several popular specialized SEM software programs are briefly discussed with regard to their features and availability. The intent of this module is to focus on foundational issues to inform readers of the potentials as well as the limitations of SEM. Interested readers are encouraged to consult additional references for advanced model types and more application examples.     

A Second-Order Longitudinal Model for Binary Outcomes: Item Response Theory Versus Structural Equation Modeling

Measuring academic growth, or change in aptitude, relies on longitudinal data collected across multiple measurements. The National Educational Longitudinal Study (NELS:88) is among the earliest, large-scale, educational surveys tracking students’ performance on cognitive batteries over 3 years. Notable features of the NELS:88 data set, and of almost all repeated measures educational assessments, are (a) the outcome variables are binary or at least categorical in nature; and (b) a set of different items is given at each measurement occasion with a few anchor items to fix the measurement scale. This study focuses on the challenges related to specifying and fitting a second-order longitudinal model for binary outcomes, within both the item response theory and structural equation modeling frameworks. The distinctions between and commonalities shared between these two frameworks are discussed. A real data analysis using the NELS:88 data set is presented for illustration purposes.     

A Systematic Evaluation and Comparison Between Exploratory Structural Equation Modeling and Bayesian Structural Equation Modeling

In this study, we contrast two competing approaches, not previously compared, that balance the rigor of CFA/SEM with the flexibility to fit realistically complex data. Exploratory SEM (ESEM) is claimed to provide an optimal compromise between EFA and CFA/SEM. Alternatively, a family of three Bayesian SEMs (BSEMs) replace fixed-zero estimates with informative, small-variance priors for different subsets of parameters: cross-loadings (CL), residual covariances (RC), or CLs and RCs (CLRC). In Study 1, using three simulation studies, results showed that (1) BSEM-CL performed more closely to ESEM; (2) BSEM-CLRC did not provide more accurate model estimation compared with BSEM-CL; (3) BSEM-RC provided unstable estimation; and (4) different specifications of targeted values in ESEM and informative priors in BSEM have significant impacts on model estimation. The real data analysis (Study 2) showed that the differences in estimation between different models were largely consistent with those in Study1 but somewhat smaller.     

Effects of Missing Data Methods in Structural Equation Modeling With Nonnormal Longitudinal Data

The purpose of this study is to investigate the effects of missing data techniques in longitudinal studies under diverse conditions. A Monte Carlo simulation examined the performance of 3 missing data methods in latent growth modeling: listwise deletion (LD), maximum likelihood estimation using the expectation and maximization algorithm with a nonnormality correction (robust ML), and the pairwise asymptotically distribution-free method (pairwise ADF). The effects of 3 independent variables (sample size, missing data mechanism, and distribution shape) were investigated on convergence rate, parameter and standard error estimation, and model fit. The results favored robust ML over LD and pairwise ADF in almost all respects. The exceptions included convergence rates under the most severe nonnormality in the missing not at random (MNAR) condition and recovery of standard error estimates across sample sizes. The results also indicate that nonnormality, small sample size, MNAR, and multicollinearity might adversely affect convergence rate and the validity of statistical inferences concerning parameter estimates and model fit statistics.     

A Regularized GLS for Structural Equation Modeling

Ill conditioning of covariance and weight matrices used in structural equation modeling (SEM) is a possible source of inadequate performance of SEM statistics in nonasymptotic samples. A maximum a posteriori (MAP) covariance matrix is proposed for weight matrix regularization in normal theory generalized least squares (GLS) estimation. Maximum likelihood (ML), GLS, and regularized GLS test statistics (RGLS and rGLS) are studied by simulation in a 15-variable, 3-factor model with 15 levels of sample size varying from 60 to 100,000. A key result showed that in terms of nominal rejection rates, RGLS outperformed ML at all sample sizes below 500, and GLS at most sample sizes below 500. In larger samples, their performance was equivalent. The second regularization methodology (rGLS) performed well asymptotically, but poorly in small samples. Regularization in SEM deserves further study.     

英语学习动机与自我认同变化——-对五所高校跟踪研究的结构方程模型分析

本文是大学生英语学习动机与自我认同跟踪项目的一部分, 考察动机类型与自我认同变化的关系。研究材料是同一问卷在四年中五次施测获得的定量数据, 对象为北京五所高校1300 余名学生。结构方程模型检验发现, 英语学习动机类型与自我认同变化相互影响, 前者对后者的影响更大。随着时间的推移, 动机对自我认同的影响具有下降趋势, 而认同对动机的影响先降后升。此外, 学习成绩动机与情境动机、出国动机与削减性认同变化始终显著相关。     

A Note on Structural Equation Modeling Estimates of Reliability

Reliability can be estimated using structural equation modeling (SEM). Two potential problems with this approach are that estimates may be unstable with small sample sizes and biased with misspecified models. A Monte Carlo study was conducted to investigate the quality of SEM estimates of reliability by themselves and relative to coefficient alpha. The SEM approach showed minimal bias when the model was correctly specified if items were relatively well defined by their underlying factor(s). They tended to demonstrate somewhat greater bias when the model was misspecified, particularly underspecified. Overall, SEM estimates were more stable than anticipated. Researchers are more likely to obtain accurate estimates of reliability using SEM by conducting large-sample studies with well-constructed scales and critically assessing model fit.     

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.     

基于结构方程模型的保险意识测度

文章采用福州市居民保险意识调查的样本数据,用因子分析法探究了影响居民保险意识的主要因素,用结构方程模型研究了各因素内部及相互间的关系,建立了居民保险意识指数的三级测量指标体系,测度出了居民保险意识的单项指数、影响因子指数和总指数。研究发现：居民保险意识由风险意识、保险认知、保险替代和保险情感4个因子构成,保险认知对保险意识的综合影响最大,保险情感次之,保险替代的影响稍弱,风险意识的总效应最小,表明普及保险知识和重塑行业诚信形象对民众保险意识的提高至关重要;以＂养儿防老＂为代表的传统保障模式的衰退正在成为民众保险意识提高的重要推动力量;民众风险意识不强,侥幸心理过重,将在长期内阻滞其保险意识的提高。