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.     

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 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.     

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.

主观幸福感三成分结构的结构方程模型分析

主观幸福感指个体对生活的情绪反应和认知评价,其包括积极情感、消极情感和生活满意度三个主要成分。依据主观幸福感的多维结构概念,本研究采用结构方程模型方法分析比较了主观幸福感的三成分结构,即三独立成分模型、层次构念模型、因果系统模型和成分合成模型。用470名被试的横向数据分析主观幸福感三成分的关联性和独立性以及相关变量对主观幸福感的预测效应。结果发现:三独立成分模型和成分合成模型不能充分地解释主观幸福感三成分结构概念;层次构念模型可以较好地解释主观幸福感三成分结构概念;因果系统模型也能较好解释主观幸福感的三成分结构概念,且可以在横向研究中用以预测生活满意度。研究结果表明主观幸福感的每一种结构模型各有优劣,对结果也有着不同的解释。     

从结构方程模型看教育与心理统计学的新发展

目前，已有多种新一代统计方法问世，其中最突出、最具代表性的是结构方程模型的发展与应用。本文以结构方程模型为代表，兼顾其它新的统计方法，从统计方法的特点以及研究方法论两方面，阐述新一代统计方法与传统统计方法之间的重要区别。     

Investigating the Multidimensionality of Need Fulfillment: A Bifactor Exploratory Structural Equation Modeling Representation

This article assesses the multidimensionality of the Basic Psychological Need Satisfaction and Frustration Scale (BPNSFS) using bifactor exploratory structural equation modeling (bifactor ESEM). The first study relies on a sample of community adults (N = 2,301), and revealed the superiority of a bifactor ESEM representation, supporting the 6-factor structure of BPNSFS ratings, and the presence of a single continuum of need fulfillment relative to 2 distinct dimensions reflecting need satisfaction and frustration. These results were replicated in a second representative sample of the Hungarian adult population (N = 504), as well as across gender, and found no evidence of differential item functioning as a function of age. Relative to males, females presented higher levels of relatedness satisfaction and lower levels of competence satisfaction. Finally, autonomy frustration decreased with age, whereas competence satisfaction and frustration presented opposite curvilinear tendencies, showing that the fulfillment of this need increased sharply for younger participants, a tendency that became less pronounced with age.