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.     

Assessing Model Similarity in Structural Equation Modeling

Two models can be nonequivalent, but fit very similarly across a wide range of data sets. These near-equivalent models, like equivalent models, should be considered rival explanations for results of a study if they represent plausible explanations for the phenomenon of interest. Prior to conducting a study, researchers should evaluate plausible models that are alternatives to those hypothesized to evaluate whether they are near-equivalent or equivalent and, in so doing, address the adequacy of the study’s methodology. To assess the extent to which alternative models for a study are empirically distinguishable, we propose 5 indexes that quantify the degree of similarity in fit between 2 models across a specified universe of data sets. These indexes compare either the maximum likelihood fit function values or the residual covariance matrices of models. Illustrations are provided to support interpretations of these similarity indexes.     

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.     

开源软件在教育信息化中的应用研究

阐述了OSS的现状及发展趋势,对其在教育信息化过程中的应用优势进行了分析,并对OSS的具体应用进行了实证研究,最后指出了OSS存在的一些问题。     

开源软件在高校中的应用参考

在高校中应用开源软件能节省投资、增强知识产权意识和促进知识创新。文章按照应用的层次和类别对开源软件予以划分,列出了一些有代表性且应用广泛的开源软件作为实践参考。     

Multilevel Factorial Invariance in n-Level Structural Equation Modeling (nSEM)

We present a multigroup multilevel confirmatory factor analysis (CFA) model and a procedure for testing multilevel factorial invariance in n-level structural equation modeling (nSEM). Multigroup multilevel CFA introduces a complexity when the group membership at the lower level intersects the clustered structure, because the observations in different groups but in the same cluster are not independent of one another. nSEM provides a framework in which the multigroup multilevel data structure is represented with the dependency between groups at the lower level properly taken into account. The procedure for testing multilevel factorial invariance is illustrated with an empirical example using an R package xxm2.     

Modeling Nonlinear Structural Equation Models: A Comparison of the Two-Stage Generalized Additive Models and the Finite Mixture Structural Equation Model

Researchers have devoted some time and effort to developing methods for fitting nonlinear relationships among latent variables. In particular, most of these have focused on correctly modeling interactions between 2 exogenous latent variables, and quadratic relationships between exogenous and endogenous variables. All of these approaches require prespecification of the nonlinearity by the researcher, and are limited to fairly simple nonlinear relationships. Other work has been done using mixture structural equation models (SEMM) in an attempt to fit more complex nonlinear relationships. This study expands on this earlier work by introducing the 2-stage generalized additive model (2SGAM) approach for fitting regression splines in the context of structural equation models. The model is first described and then investigated through the use of simulated data, in which it was compared with the SEMM approach. Results demonstrate that the 2SGAM is an effective tool for fitting a variety of nonlinear relationships between latent variables, and can be easily and accurately extended to models including multiple latent variables. Implications of these results are discussed.     

Improving the Root Mean Square Error of Approximation for Nonnormal Conditions in Structural Equation Modeling

In this study, the authors investigated incorporating adjusted model fit information into the root mean square error of approximation (RMSEA) fit index. Through Monte Carlo simulation, the usefulness of this adjusted index was evaluated for assessing model adequacy in structural equation modeling when the multivariate normality assumption underlying maximum likelihood estimation is violated. Adjustment to the RMSEA was considered in 2 forms: a rescaling adjustment via the Satorra-Bentler rescaled goodness-of-fit statistic and a bootstrap adjustment via the Bollen and Stine adjusted model p value. Both properly specified and misspecifed models were examined. The adjusted RMSEA was evaluated in terms of the average index value across study conditions and with respect to model rejection rates under tests of exact fit, close fit, and not-close 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。     

空间直线方程的拟合

探讨用最小二乘法解决空间直线方程的拟合问题.先拟合三个直角坐标系中的投影直线,再通过投影直线求出空间直线方程,并对拟合出来的三个不同的直线方程进行比较,选择最佳拟合方案.     

论研究生智慧型学习空间的构建意义、功能与策略——以美国大学为案例

随着教育技术的不断进步,学习空间的打造具备了多种可能性。智慧型学习空间是在全球云资源可共享的条件下,实现课堂教学、研究和实践一体化的学习模式。智慧型学习空间适应了当今研究生培养的多种需求。文章以现实案例与图示设计为基础,从满足理论学习与实践应用的双重需求及满足以职业或学术为导向等多元化的培养需求阐述研究生智慧型学习空间对研究生教育的重要意义,从课堂教学、研究与实践一体化打造个性化、翻转课堂的学习空间探讨其独特功能。中国研究生智慧空间建设可以从有效整合资源和依托各项新技术,打造多功能的、个性化的学习空间等方面推进。     

Bootstrapping Confidence Intervals for Fit Indexes in Structural Equation Modeling

Bootstrapping approximate fit indexes in structural equation modeling (SEM) is of great importance because most fit indexes do not have tractable analytic distributions. Model-based bootstrap, which has been proposed to obtain the distribution of the model chi-square statistic under the null hypothesis (Bollen & Stine, 1992), is not theoretically appropriate for obtaining confidence intervals (CIs) for fit indexes because it assumes the null is exactly true. On the other hand, naive bootstrap is not expected to work well for those fit indexes that are based on the chi-square statistic, such as the root mean square error of approximation (RMSEA) and the comparative fit index (CFI), because sample noncentrality is a biased estimate of the population noncentrality. In this article we argue that a recently proposed bootstrap approach due to Yuan, Hayashi, and Yanagihara (YHY; 2007) is ideal for bootstrapping fit indexes that are based on the chi-square. This method transforms the data so that the “parent” population has the population noncentrality parameter equal to the estimated noncentrality in the original sample. We conducted a simulation study to evaluate the performance of the YHY bootstrap and the naive bootstrap for 4 indexes: RMSEA, CFI, goodness-of-fit index (GFI), and standardized root mean square residual (SRMR). We found that for RMSEA and CFI, the CIs under the YHY bootstrap had relatively good coverage rates for all conditions, whereas the CIs under the naive bootstrap had very low coverage rates when the fitted model had large degrees of freedom. However, for GFI and SRMR, the CIs under both bootstrap methods had poor coverage rates in most conditions.     

The Relation Among Fit Indexes,Power, and Sample Size in Structural Equation Modeling

The relation among fit indexes, power, and sample size in structural equation modeling is examined. The noncentrality parameter is required to compute power. The 2 existing methods of computing power have estimated the noncentrality parameter by specifying an alternative hypothesis or alternative fit. These methods cannot be implemented easily and reliably. In this study, 4 fit indexes (RMSEA, CFI, McDonald's Fit Index, and Steiger's gamma) were used to compute the noncentrality parameter and sample size to achieve certain level of power. The resulting power and sample size varied as a function of (a) choice of fit index, (b) number of variables/degrees of freedom, (c) relation among the variables, and (d) value of the fit index. However, if the level of misspecification were held constant, then the resulting power and sample size would be identical.     

开放灵活的分布式学习环境

为了帮助设计者创建开放、灵活的分布式E-Learning环境,该文提出了一个E-Learning框架模型,从八个维度列出了E-Learning设计中需要考虑的关键问题:机构,教学,技术,界面设计,评价,管理,资源支持,伦理。     

立体异构分子模型的简易制作及其应用

立体异构是有机化学课的重点教学内容，在教学实践中探索出以橡皮泥为原料制作简易立体异构分子模型的方法。结果表明：制作和应用分子模型辅助教学，培养了学生的动手能力和创新意识，建立了空间观念，收到了较好的教学效果。     

一种解释结构模型的优化算法研究

解释结构模型被广泛应用于医疗、教育等领域,但相关理论发展较为缓慢。为加快解释结构模型的计算速度,丰富解释结构模型相关理论,通过对系统各要素所对应有向图的本质关系进行分析,对该模型中的级间划分方法作更深一步解析并给出优化算法,发现有向图中若不存在回路,则有向图汇点对应的是最高级要素集合中的要素,因此汇点可以从缩减可达矩阵中直接找出,从而能对复杂系统要素更快地进行分层。对应的优化算法相比传统方法减少了一倍左右的计算量,并通过实证分析进行验证。该研究结果为解释结构模型方法优化提供了一种新诠释。     

一般状态空间模型和东亚股票指数的波动

通过一般状态空间模型和VECM验证了东亚两大经济大国之间的股价指数的波动关系,为国际分散投资提供参考.通过对上证综合指数,上证B股指数和日经股票指数分时期进行单位根检验,结果表明一阶差分平稳,是一阶单整列,可以作协整分析.并且通过对其卡尔曼滤波进行线递推计算,以自适应方式跟踪时序列变化,利用残差进行VECM的计算,其结果表明只有上证B股对日经Top-ix有单向影响.     

Banach空间中微分方程解的存在性初探

通过一个反例,说明了欧氏空间中关于微分方程解的存在性的Peano定理,对Banach空间中微分方程是不成立的.并对Peano定理进行了改进,证明了改进后的结果在Banach空间中是成立的.     

特殊子空间上矩阵方程有解的判定

利用矩阵的广义逆和Kronecker积，给出了矩阵方程AXB=C在中心对称矩阵空间中有解的充要条件.