Using Fixed Thresholds with Grouped Data in Structural Equation Modeling

Valuable methods have been developed for incorporating ordinal variables into structural equation models using a latent response variable formulation. However, some model parameters, such as the means and variances of latent factors, can be quite difficult to interpret because the latent response variables have an arbitrary metric. This limitation can be particularly problematic in growth models, where the means and variances of the latent growth parameters typically have important substantive meaning when continuous measures are used. However, these methods are often applied to grouped data, where the ordered categories actually represent an interval-level variable that has been measured on an ordinal scale for convenience. The method illustrated in this article shows how category threshold values can be incorporated into the model so that interpretation is more meaningful, with particular emphasis given to the application of this technique with latent growth models.     

Variance Estimation Using Replication Methods in Structural Equation Modeling With Complex Sample Data

This article discusses replication sampling variance estimation techniques that are often applied in analyses using data from complex sampling designs: jackknife repeated replication, balanced repeated replication, and bootstrapping. These techniques are used with traditional analyses such as regression, but are currently not used with structural equation modeling (SEM) analyses. This article provides an extension of these methods to SEM analyses, including a proposed adjustment to the likelihood ratio test, and presents the results from a simulation study suggesting replication estimates are robust. Finally, a demonstration of the application of these methods using data from the Early Childhood Longitudinal Study is included. Secondary analysts can undertake these more robust methods of sampling variance estimation if they have access to certain SEM software packages and data management packages such as SAS, as shown in the article.     

Analyzing Mixed-Dyadic Data Using Structural Equation Models

Mixed-dyadic data, collected from distinguishable (nonexchangeable) or indistinguishable (exchangeable) dyads, require statistical analysis techniques that model the variation within dyads and between dyads appropriately. The purpose of this article is to provide a tutorial for performing structural equation modeling analyses of cross-sectional and longitudinal models for mixed independent variable dyadic data, and to clarify questions regarding various dyadic data analysis specifications that have not been addressed elsewhere. Artificially generated data similar to the Newlywed Project and the Swedish Adoption Twin Study on Aging were used to illustrate analysis models for distinguishable and indistinguishable dyads, respectively. Due to their widespread use among applied researchers, the AMOS and Mplus statistical analysis software packages were used to analyze the dyadic data structural equation models illustrated here. These analysis models are presented in sufficient detail to allow researchers to perform these analyses using their preferred statistical analysis software package.     

Modeling Latent Growth Curves With Incomplete Data Using Different Types of Structural Equation Modeling and Multilevel Software

This article offers different examples of how to fit latent growth curve (LGC) models to longitudinal data using a variety of different software programs (i.e., LISREL, Mx, Mplus, AMOS, SAS). The article shows how the same model can be fitted using both structural equation modeling and multilevel software, with nearly identical results, even in the case of models of latent growth fitted to incomplete data. The general purpose of this article is to provide a demonstration that integrates programming features from different software. The most immediate goal is to help researchers implement these LGC models as a useful way to test hypotheses of growth.     

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.     

Comparisons of Structural Equation Modeling and Hierarchical Linear Modeling Approaches to Couples' Data

This article compares 2 statistical approaches for the analysis of data obtained from married couples. The article summarizes a current multilevel (or hierarchical) model that has demonstrated considerable utility in marital research; it also extends this formulation in several respects. This model is then respecified into a more familiar structural equation modeling (SEM) formulation, highlighting the similarities and the differences in the 2 approaches. Cross-sectional data on 348 American married couples is used to examine the influence of age, duration of marriage, and number of children on marital satisfaction. Results of the 2 sets of analyses yielded nearly identical findings. The strengths and possible extensions of the SEM approach are discussed.     

Structural Equation Modeling Diagnostics Using R Package semdiag and EQS

Yuan and Hayashi (2010) Yuan, K.-H. and Hayashi, K. 2010. Fitting data to model: Structural equation modeling diagnosis using two scatter plots. Psychological Methods, 15: 335–351. [Crossref], [Web of Science ®] , [Google Scholar] introduced 2 scatter plots for model and data diagnostics in structural equation modeling (SEM). However, the generation of the plots requires in-depth understanding of their underlying technical details. This article develops and introduces an R package semdiag for easily drawing the 2 plots. With a model specified in EQS syntax, one only needs to supply as few as 2 parameters to generate the 2 plots using the semdiag package. Two examples are provided to illustrate the use of the package. Multiple figures are used to explain the elements of data and model diagnostics. Advice on selecting proper estimation methods following the diagnostics is also given.     

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.     

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.     

Investigating the Unique Predictors of Word-Problem Solving Using Meta-Analytic Structural Equation Modeling

The purpose of the present study is to clarify the contributions of cognitive skills (nonverbal reasoning, language comprehension, working memory, attention, processing speed) and academic skills (mathematics facts retrieval, mathematics computation, mathematics vocabulary, reading comprehension) in performing mathematics word problems among elementary school students. With the two-stage meta-analytic structural equation modeling approach, I synthesized 112 correlation matrices from 98 empirical studies (N?=?111,346) and fitted the hypothesized partial mediation model. Overall, path analysis indicated that language comprehension, working memory, attention, mathematics vocabulary, and mathematics computation were unique predictors of word-problem solving. Subgroup analysis demonstrated different unique predictors for younger and older students to perform word problems (K-2nd grades versus 3rd–5th grades). Implications, limitations, and future directions are discussed.

     

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.     

Testing Time-Invariance of Variable Specificity in Repeated Measure Designs Using Structural Equation Modeling

A structural equation modeling method for examining time-invariance of variable specificity in longitudinal studies with multiple measures is outlined, which is developed within a confirmatory factor-analytic framework. The approach represents a likelihood ratio test for the hypothesis of stability in the specificity part of the residual term associated with repeated administration of each measure. The procedure can be used in the search for parsimonious versions of multiwave multiple-indicator models, to test for variable specificity in them, and to examine assumptions underlying particular parameter estimation procedures in repeated measure designs. The outlined method is illustrated with empirical data.     

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.     

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.     

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.     

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。     

基于实验数据的航空发动机动态建模

针对基于部件级航空发动机动态建模过程中完整、准确的航空发动机部件特性数据往往难以获取、建模时间长等现象,提出使用实验数据进行辨识建模的方法。为了建立航空发动机的动态模型,通过对某轻型飞机实验台的飞行实验数据进行分析整理,提出使用BP神经网络对发动机重要参数进行建模,同时使用粒子群优化算法(Particle swarm optimization,PSO)对BP神经网络的权值和阈值进行优化,使用改进粒子群优化算法(Improved particle swarm optimization algorithm,IPSO)对传统粒子群优化算法进行改进,仿真结果表明IPSO-BP网络建立的发动机模型精度和稳定性更高。