Model Implied Instrumental Variables (MIIVs): An Alternative Orientation to Structural Equation Modeling

Few dispute that our models are approximations to reality. Yet when it comes to structural equation models (SEMs), we use estimators that assume true models (e.g. maximum likelihood) and that can create biased estimates when the model is inexact. This article presents an overview of the Model Implied Instrumental Variable (MIIV) approach to SEMs from Bollen (1996). The MIIV estimator using Two Stage Least Squares (2SLS), MIIV-2SLS, has greater robustness to structural misspecifications than system wide estimators. In addition, the MIIV-2SLS estimator is asymptotically distribution free. Furthermore, MIIV-2SLS has equation-based overidentification tests that can help pinpoint misspecifications. Beyond these features, the MIIV approach has other desirable qualities. MIIV methods apply to higher order factor analyses, categorical measures, growth curve models, dynamic factor analysis, and nonlinear latent variables. Finally, MIIV-2SLS permits researchers to estimate and test only the latent variable model or any other subset of equations. In addition, other MIIV estimators beyond 2SLS are available. Despite these promising features, research is needed to better understand its performance under a variety of conditions that represent empirical applications. Empirical and simulation examples in the article illustrate the MIIV orientation to SEMs and highlight an R package MIIVsem that implements MIIV-2SLS.     

Abstract: Parameter Influence In Structural Equation Models

In applications of SEM, investigators obtain and interpret parameter estimates that are computed so as to produce optimal model fit in the sense that the obtained model fit would deteriorate to some degree if any of those estimates were changed. This property raises a question: to what extent would model fit deteriorate if parameter estimates were changed? And which parameters have the greatest influence on model fit? This is the idea of parameter influence. The present paper will cover two approaches to quantifying parameter influence. Both are based on the principle of likelihood displacement (LD), which quantifies influence as the discrepancy between the likelihood under the original model and the likelihood under the model in which a minor perturbation is imposed (Cook, 1986 Cook, R. D. 1986. Assessment of local influence. Journal of the Royal Statistical Society. Series B (Methodological)., 48: 133–169. [Crossref], [Web of Science ®] , [Google Scholar]). One existing approach for quantifying parameter influence is a vector approach (Lee &; Wang, 1996 Lee, S-Y. and Wang, S. J. 1996. Sensitivity analysis of structural equation models. Psychometrika, 61: 93–108. [Crossref], [Web of Science ®] , [Google Scholar]) that determines a vector in the parameter space such that altering parameter values simultaneously in this direction will cause maximum change in LD. We propose a new approach, called influence mapping for single parameters, that determines the change in model fit under perturbation of a single parameter holding other parameter estimates constant. An influential parameter is defined as one that produces large change in model fit under minor perturbation. Figure 1 illustrates results from this procedure for three different parameters in an empirical application. Flatter curves represent less influential parameters. Practical implications of the results are discussed. The relationship with statistical power in structural equation models is also discussed.

Abstract: Parameter Influence In Structural Equation Models

All authors

Taehun Lee &; Robert MacCallum

https://doi.org/10.1080/00273170802640491

Published online:

19 December 2008

FIGURE 1 Influence mapping for single parameters.     

3.

Abstract: Evaluation of Test Statistics for Robust Structural Equation Modeling With Nonnormal Missing Data     

Xin Tong  Zhiyong Zhang  Ke-Hai Yuan 《Multivariate behavioral research》2013,48(6)

Traditional structural equation modeling (SEM) techniques have trouble dealing with incomplete and/or nonnormal data that are often encountered in practice. Yuan and Zhang (2011a) developed a two-stage procedure for SEM to handle nonnormal missing data and proposed four test statistics for overall model evaluation. Although these statistics have been shown to work well with complete data, their performance for incomplete data has not been investigated in the context of robust statistics.

Focusing on a linear growth curve model, a systematic simulation study is conducted to evaluate the accuracy of the parameter estimates and the performance of five test statistics including the naive statistic derived from normal distribution based maximum likelihood (ML), the Satorra-Bentler scaled chi-square statistic (RML), the mean- and variance-adjusted chi-square statistic (AML), Yuan-Bentler residual-based test statistic (CRADF), and Yuan-Bentler residual-based F statistic (RF). Data are generated and analyzed in R using the package rsem (Yuan & Zhang, 2011b).

Based on the simulation study, we can observe the following: (a) The traditional normal distribution-based method cannot yield accurate parameter estimates for nonnormal data, whereas the robust method obtains much more accurate model parameter estimates for nonnormal data and performs almost as well as the normal distribution based method for normal distributed data. (b) With the increase of sample size, or the decrease of missing rate or the number of outliers, the parameter estimates are less biased and the empirical distributions of test statistics are closer to their nominal distributions. (c) The ML test statistic does not work well for nonnormal or missing data. (d) For nonnormal complete data, CRADF and RF work relatively better than RML and AML. (e) For missing completely at random (MCAR) missing data, in almost all the cases, RML and AML work better than CRADF and RF. (f) For nonnormal missing at random (MAR) missing data, CRADF and RF work better than AML. (g) The performance of the robust method does not seem to be influenced by the symmetry of outliers.     

4.

Revisiting the Empirical Distinction Between Hedonic and Eudaimonic Aspects of Well-Being Using Exploratory Structural Equation Modeling     

Mohsen?JoshanlooEmail author 《Journal of Happiness Studies》2016,17(5):2023-2036

The distinction between hedonic (i.e., subjective well-being) and eudaimonic (i.e., psycho-social functioning) components of well-being is questioned by some researchers on the grounds that these two aspects of well-being are highly correlated. However, I argue that previous research has relied on confirmatory factor analysis (CFA), which is likely to overestimate interfactor correlations, because cross-loadings are constrained to be zero in CFA. In contrast, the new method of exploratory structural equation modeling (ESEM) does not constrain cross-ladings to zero, which results in more accurate factor intercorrelations. The present study used ESEM to reinvestigate the relationship between hedonic and eudaimonic aspects of well-being in a sample of 3986 American adults. The results showed that the ESEM model fitted the data better than the CFA model. As expected, interfactor correlations obtained with ESEM were substantially smaller than those obtained with CFA, indicating greater factor distinctiveness. These results suggest that hedonic and eudaimonic factors are correlated yet largely independent from each other. The results also suggest that ESEM is a more appropriate method than CFA in the study of multi-dimensional constructs, such as mental well-being.     

5.

Predicting Health-related Quality of Life: Testing the Contextual Model Using Structural Equation Modeling     

Kimlin T. Ashing-Giwa  Jung-Won Lim 《Applied research in quality of life》2008,3(3):215-230

This study aims to investigate the utility of the Contextual Model of Health-Related Quality of Life (HRQOL) to explain the relationship among the domains of HRQOL with a diverse, population-based sample of breast cancer survivors (BCS). We employed a cross-sectional design to investigate HRQOL among 703 multiethnic, population-based BCS. The study methodology was guided by the Contextual Model of HRQOL. Structural Equation Modeling (SEM) was conducted to assess the hypothesized model. SEM identified significant relationships among the bio-psychological domain (general health status, cancer-related factors, and psychological factors), the cultural-socio-ecological domain (health care satisfaction, socio-ecological factor, and socio-economic status), and HRQOL. The best fitting model indicates direct pathways from ‘general health status’, ‘years since diagnosis’, ‘health care satisfaction’ and ‘socio-ecological factor’ to ‘HRQOL’ variables. Additionally, ‘socio-ecological factor’ and ‘socio-economic status’ variables were indirectly associated with HRQOL through ‘general health status’. Findings suggest that the Contextual Model of HRQOL adds valid factors to explain overall HRQOL and increases our understanding of the socio-ecological dimensions predicting HRQOL outcomes. The revelation of inter-relations among the dimensions of HRQOL may inform the translational and clinical utility of the HRQOL construct.

Jung-Won Lim (Corresponding author)Email:

---

Dr. Kimlin T. Ashing-Giwa   is professor and director of the Center of Community Alliance for Research and Education (CCARE) at City of Hope. She received her doctorate in clinical psychology from the University of Colorado-Boulder. Her scholarship and life work is to understand and investigate how culture, ethnicity, ecological and systemic context influence health outcomes. Currently, she is developing and implementing community participatory interventions to reduce the risk and burden of chronic illness, in particular cancer. Dr. Jung-won Lim    is a research fellow of the CCARE at City of Hope. She received her doctorate from the University of Southern California, School of Social Work. Her research focuses on adjustment and quality of life among patients with chronic physical illness and their family. She is currently conducting studies related to health beliefs, health behaviors, and quality of life among breast cancer survivors.     

6.

Structural Equation Modeling: A Second Course     

《Personnel Psychology》2007,60(2):536-539

     

7.

探索性结构方程建模(ESEM):EFA和CFA的整合     

麦玉娇  温忠麟 《心理科学进展》2013,21(5):934-939

探索性结构方程建模(ESEM)是在测量模型部分使用了类似于EFA模型的SEM.作为一种高级统计方法,ESEM整合了EFA和CFA两种因子分析方法的功能和优点.通过ESEM,研究者既可以灵活地探索因子结构,又可以系统地验证因子模型,为潜变量的关系分析提供更适宜的测量模型.ESEM已经在某些社科领域的研究中得到应用,是一种值得推介的因子分析方法.ESEM的具体应用问题,例如因子旋转方法的选用、测验信度评价等,仍有待探讨.     

8.

Quantifying Parsimony in Structural Equation Modeling     

《Multivariate behavioral research》2013,48(3):227-259

Fitting propensity (FP) is defined as a model's average ability to fit diverse data patterns, all else being equal. The relevance of FP to model selection is examined in the context of structural equation modeling (SEM). In SEM it is well known that the number of free model parameters influences FP, but other facets of FP are routinely excluded from consideration. It is shown that models possessing the same number of free parameters but different structures may exhibit different FPs. The consequences of this fact are demonstrated using illustrative examples and models culled from published research. The case is made that further attention should be given to quantifying FP in SEM and considering it in model selection. Practical approaches are suggested.     

9.

Postselection Inference in Structural Equation Modeling     

Po-Hsien Huang 《Multivariate behavioral research》2020,55(3):344-360

Abstract

Most statistical inference methods were established under the assumption that the fitted model is known in advance. In practice, however, researchers often obtain their final model by some data-driven selection process. The selection process makes the finally fitted model random, and it also influences the sampling distribution of the estimator. Therefore, implementing naive inference methods may result in wrong conclusions—which is probably a prime source of the reproducibility crisis in psychological science. The present study accommodates three valid state-of-the-art postselection inference methods for structural equation modeling (SEM) from the statistical literature: data splitting (DS), postselection inference (PoSI), and the polyhedral (PH) method. A simulation is conducted to compare the three methods with the commonly used naive procedure under selection events made by L₁-penalized SEM. The results show that the naive method often yields incorrect inference, and that the valid methods control the coverage rate in most cases with their own pros and cons. Real world data examples show the practical use of the valid inference methods.     

10.

Abstract: Modeling Change in a Correlation Over Time Within an SEM Framework     

Jonathan L. Helm  Emilio Ferrer 《Multivariate behavioral research》2013,48(1)

     

11.

Evaluating Small Sample Approaches for Model Test Statistics in Structural Equation Modeling     

《Multivariate behavioral research》2013,48(3):439-478

Through Monte Carlo simulation, small sample methods for evaluating overall data-model fit in structural equation modeling were explored. Type I error behavior and power were examined using maximum likelihood (ML), Satorra-Bentler scaled and adjusted (SB; Satorra & Bentler, 1988, 1994), residual-based (Browne, 1984), and asymptotically distribution free (ADF; Browne, 1982, 1984) test statistics. To accommodate small sample sizes the ML and SB statistics were adjusted using a k-factor correction (Bartlett, 1950); the residual-based and ADF statistics were corrected using modified x² and F statistics (Yuan & Bentler, 1998, 1999). Design characteristics include model type and complexity, ratio of sample size to number of estimated parameters, and distributional form. The k-factor-corrected SB scaled test statistic was especially stable at small sample sizes with both normal and nonnormal data. Methodologists are encouraged to investigate its behavior under a wider variety of models and distributional forms.     

12.

Abstract: Case Diagnostics in Structural Equation Models: Illustrations and Issues     

Jolynn Pek  Robert C. MacCallum 《Multivariate behavioral research》2013,48(6)

     

13.

管理胜任力特征分析:结构方程模型检验   总被引：171，自引：0，他引：171  

王重鸣  陈民科 《心理科学》2002,25(5):513-516

管理胜任力特征分析是人事选拔与评价的重要内容之一。本研究在运用基于胜任力的职位分析并总结国内外有关文献的基础上,编制了管理综合素质评价量表,并运用此量表调查了220名中高层管理者,采用因素分析和结构方程模型检验企业高级管理者胜任力特征的结构。结果表明,管理胜任力特征结构由管理素质和管理技能等两个维度构成,但在维度要素及其关键度上,职位层次间存在显著差异。本研究为管理职位的测评选拔提供了新的理论依据。     

14.

结构方程建模中的题目打包策略   总被引：2，自引：0，他引：2  

吴艳  温忠麟 《心理科学进展》2011,19(12):1859-1867

结构方程建模中题目打包法的优缺点包括：指标数据质量变好、模型拟合程度提高; 估计偏差不大, 可校正; 估计稳定, 但降低了敏感性与可证伪性。打包法的前提条件是单维、同质, 适合结构模型分析, 不适合测量模型分析。对于单维测验, 给出了一个打包流程。对于通常的多个子量表(多维结构)测验, 推荐在子量表内打包, 每个子量表打包成1个指标或者3个指标, 用于结构方程建模。     

15.

项目组合在结构方程模型中的应用   总被引：8，自引：0，他引：8  

卞冉  车宏生  阳辉 《心理科学进展》2007,15(3):567-576

项目组合（itemparceling）是对同一量表中的若干项目进行整合并形成新的观测指标的过程。虽然一直以来它都是一个有争议的议题,但随着其在结构方程模型中的应用日益广泛,它越来越受到研究者重视。文章从项目组合的基本逻辑、优缺点以及具体方法等方面对项目组合的研究进行了概括,并在此基础上提出了使用的具体建议：（1）根据研究的目的与具体情境选择是否需要组合;（2）组合之前必须首先确定概念的维度性;（3）项目组合最好建立在一定的理论基础上等等。未来的研究可以深入探讨各种组合方法对模型拟合以及参数估计的影响以及项目组合在一些SEM高阶应用中的效果,并进一步与项目反应理论等测量理论相结合     

16.

OpenMx 2.0: Extended Structural Equation and Statistical Modeling     

Michael C. Neale  Michael D. Hunter  Joshua N. Pritikin  Mahsa Zahery  Timothy R. Brick  Robert M. Kirkpatrick  Ryne Estabrook  Timothy C. Bates  Hermine H. Maes  Steven M. Boker 《Psychometrika》2016,81(2):535-549

The new software package OpenMx 2.0 for structural equation and other statistical modeling is introduced and its features are described. OpenMx is evolving in a modular direction and now allows a mix-and-match computational approach that separates model expectations from fit functions and optimizers. Major backend architectural improvements include a move to swappable open-source optimizers such as the newly written CSOLNP. Entire new methodologies such as item factor analysis and state space modeling have been implemented. New model expectation functions including support for the expression of models in LISREL syntax and a simplified multigroup expectation function are available. Ease-of-use improvements include helper functions to standardize model parameters and compute their Jacobian-based standard errors, access to model components through standard R $ mechanisms, and improved tab completion from within the R Graphical User Interface.     

17.

Structural Equation Modeling with Small Samples: Test Statistics     

《Multivariate behavioral research》2013,48(2):181-197

Structural equation modeling is a well-known technique for studying relationships among multivariate data. In practice, high dimensional nonnormal data with small to medium sample sizes are very common, and large sample theory, on which almost all modeling statistics are based, cannot be invoked for model evaluation with test statistics. The most natural method for nonnormal data, the asymptotically distribution free procedure, is not defined when the sample size is less than the number of nonduplicated elements in the sample covariance. Since normal theory maximum likelihood estimation remains defined for intermediate to small sample size, it may be invoked but with the probable consequence of distorted performance in model evaluation. This article studies the small sample behavior of several test statistics that are based on maximum likelihood estimator, but are designed to perform better with nonnormal data. We aim to identify statistics that work reasonably well for a range of small sample sizes and distribution conditions. Monte Carlo results indicate that Yuan and Bentler's recently proposed F-statistic performs satisfactorily.     

18.

Reexamining Nonlinear Structural Equation Modeling Procedures: The Effect of Parallel and Congeneric Measures     

Karina Rdz-Navarro  Jesús M. Alvarado 《Multivariate behavioral research》2013,48(6):645-661

The current study examines the performance of the extended unconstrained approach (EXUC) and the latent moderated structural equation modeling procedure (LMS) in situations where quadratic and interaction terms are tested simultaneously and investigates their limitations with regard to the employment of parallel and congeneric measures, relatively low indicator reliabilities, and relatively large numbers of indicators. By means of a Monte Carlo study, we found LMS to be the best option for testing multiple nonlinear effects given sufficient sample size (n ≥ 500) and normally distributed exogenous variables. Its advantages became more prominent when indicator reliabilities were heterogeneous and small. The EXUC was a viable option for estimating the model when indicators were parallel and exhibited large indicator reliabilities. An empirical example of the results is provided, and the relevance of measurement model characteristics to assess nonlinear relationships is discussed.     

19.

Abstract: Measurement and Structural Model Class Separation in Mixture-CFA     

Sarah Depaoli 《Multivariate behavioral research》2013,48(6)

     

20.

不同适应水平小学生有意义事件报告比较——小学生自我调节机制的一项研究     

李晓文  缪小春 《心理科学》2001,24(4):402-405

本研究选取发展良好与适应不良的三——五年级小学生为被试,以问卷访谈形式调查他们心目中的正性和负性意义事件。结果表明,两组被试在事件意义体验的人际亲和性、内在一外在性和丰富性方面有明显不同的反映。感受的丰富性表现在正负性意义事件两方面,某种事件负性意义感受的出现是良好适应的表现。     

Abstract: Evaluation of Test Statistics for Robust Structural Equation Modeling With Nonnormal Missing Data

Traditional structural equation modeling (SEM) techniques have trouble dealing with incomplete and/or nonnormal data that are often encountered in practice. Yuan and Zhang (2011a) developed a two-stage procedure for SEM to handle nonnormal missing data and proposed four test statistics for overall model evaluation. Although these statistics have been shown to work well with complete data, their performance for incomplete data has not been investigated in the context of robust statistics.

Focusing on a linear growth curve model, a systematic simulation study is conducted to evaluate the accuracy of the parameter estimates and the performance of five test statistics including the naive statistic derived from normal distribution based maximum likelihood (ML), the Satorra-Bentler scaled chi-square statistic (RML), the mean- and variance-adjusted chi-square statistic (AML), Yuan-Bentler residual-based test statistic (CRADF), and Yuan-Bentler residual-based F statistic (RF). Data are generated and analyzed in R using the package rsem (Yuan & Zhang, 2011b).

Based on the simulation study, we can observe the following: (a) The traditional normal distribution-based method cannot yield accurate parameter estimates for nonnormal data, whereas the robust method obtains much more accurate model parameter estimates for nonnormal data and performs almost as well as the normal distribution based method for normal distributed data. (b) With the increase of sample size, or the decrease of missing rate or the number of outliers, the parameter estimates are less biased and the empirical distributions of test statistics are closer to their nominal distributions. (c) The ML test statistic does not work well for nonnormal or missing data. (d) For nonnormal complete data, CRADF and RF work relatively better than RML and AML. (e) For missing completely at random (MCAR) missing data, in almost all the cases, RML and AML work better than CRADF and RF. (f) For nonnormal missing at random (MAR) missing data, CRADF and RF work better than AML. (g) The performance of the robust method does not seem to be influenced by the symmetry of outliers.     

Revisiting the Empirical Distinction Between Hedonic and Eudaimonic Aspects of Well-Being Using Exploratory Structural Equation Modeling

The distinction between hedonic (i.e., subjective well-being) and eudaimonic (i.e., psycho-social functioning) components of well-being is questioned by some researchers on the grounds that these two aspects of well-being are highly correlated. However, I argue that previous research has relied on confirmatory factor analysis (CFA), which is likely to overestimate interfactor correlations, because cross-loadings are constrained to be zero in CFA. In contrast, the new method of exploratory structural equation modeling (ESEM) does not constrain cross-ladings to zero, which results in more accurate factor intercorrelations. The present study used ESEM to reinvestigate the relationship between hedonic and eudaimonic aspects of well-being in a sample of 3986 American adults. The results showed that the ESEM model fitted the data better than the CFA model. As expected, interfactor correlations obtained with ESEM were substantially smaller than those obtained with CFA, indicating greater factor distinctiveness. These results suggest that hedonic and eudaimonic factors are correlated yet largely independent from each other. The results also suggest that ESEM is a more appropriate method than CFA in the study of multi-dimensional constructs, such as mental well-being.     

Predicting Health-related Quality of Life: Testing the Contextual Model Using Structural Equation Modeling

This study aims to investigate the utility of the Contextual Model of Health-Related Quality of Life (HRQOL) to explain the relationship among the domains of HRQOL with a diverse, population-based sample of breast cancer survivors (BCS). We employed a cross-sectional design to investigate HRQOL among 703 multiethnic, population-based BCS. The study methodology was guided by the Contextual Model of HRQOL. Structural Equation Modeling (SEM) was conducted to assess the hypothesized model. SEM identified significant relationships among the bio-psychological domain (general health status, cancer-related factors, and psychological factors), the cultural-socio-ecological domain (health care satisfaction, socio-ecological factor, and socio-economic status), and HRQOL. The best fitting model indicates direct pathways from ‘general health status’, ‘years since diagnosis’, ‘health care satisfaction’ and ‘socio-ecological factor’ to ‘HRQOL’ variables. Additionally, ‘socio-ecological factor’ and ‘socio-economic status’ variables were indirectly associated with HRQOL through ‘general health status’. Findings suggest that the Contextual Model of HRQOL adds valid factors to explain overall HRQOL and increases our understanding of the socio-ecological dimensions predicting HRQOL outcomes. The revelation of inter-relations among the dimensions of HRQOL may inform the translational and clinical utility of the HRQOL construct.

探索性结构方程建模(ESEM):EFA和CFA的整合

探索性结构方程建模(ESEM)是在测量模型部分使用了类似于EFA模型的SEM.作为一种高级统计方法,ESEM整合了EFA和CFA两种因子分析方法的功能和优点.通过ESEM,研究者既可以灵活地探索因子结构,又可以系统地验证因子模型,为潜变量的关系分析提供更适宜的测量模型.ESEM已经在某些社科领域的研究中得到应用,是一种值得推介的因子分析方法.ESEM的具体应用问题,例如因子旋转方法的选用、测验信度评价等,仍有待探讨.     

Quantifying Parsimony in Structural Equation Modeling

Fitting propensity (FP) is defined as a model's average ability to fit diverse data patterns, all else being equal. The relevance of FP to model selection is examined in the context of structural equation modeling (SEM). In SEM it is well known that the number of free model parameters influences FP, but other facets of FP are routinely excluded from consideration. It is shown that models possessing the same number of free parameters but different structures may exhibit different FPs. The consequences of this fact are demonstrated using illustrative examples and models culled from published research. The case is made that further attention should be given to quantifying FP in SEM and considering it in model selection. Practical approaches are suggested.     

Postselection Inference in Structural Equation Modeling

Abstract

Most statistical inference methods were established under the assumption that the fitted model is known in advance. In practice, however, researchers often obtain their final model by some data-driven selection process. The selection process makes the finally fitted model random, and it also influences the sampling distribution of the estimator. Therefore, implementing naive inference methods may result in wrong conclusions—which is probably a prime source of the reproducibility crisis in psychological science. The present study accommodates three valid state-of-the-art postselection inference methods for structural equation modeling (SEM) from the statistical literature: data splitting (DS), postselection inference (PoSI), and the polyhedral (PH) method. A simulation is conducted to compare the three methods with the commonly used naive procedure under selection events made by L₁-penalized SEM. The results show that the naive method often yields incorrect inference, and that the valid methods control the coverage rate in most cases with their own pros and cons. Real world data examples show the practical use of the valid inference methods.     

Evaluating Small Sample Approaches for Model Test Statistics in Structural Equation Modeling

Through Monte Carlo simulation, small sample methods for evaluating overall data-model fit in structural equation modeling were explored. Type I error behavior and power were examined using maximum likelihood (ML), Satorra-Bentler scaled and adjusted (SB; Satorra & Bentler, 1988, 1994), residual-based (Browne, 1984), and asymptotically distribution free (ADF; Browne, 1982, 1984) test statistics. To accommodate small sample sizes the ML and SB statistics were adjusted using a k-factor correction (Bartlett, 1950); the residual-based and ADF statistics were corrected using modified x² and F statistics (Yuan & Bentler, 1998, 1999). Design characteristics include model type and complexity, ratio of sample size to number of estimated parameters, and distributional form. The k-factor-corrected SB scaled test statistic was especially stable at small sample sizes with both normal and nonnormal data. Methodologists are encouraged to investigate its behavior under a wider variety of models and distributional forms.     

管理胜任力特征分析:结构方程模型检验

管理胜任力特征分析是人事选拔与评价的重要内容之一。本研究在运用基于胜任力的职位分析并总结国内外有关文献的基础上,编制了管理综合素质评价量表,并运用此量表调查了220名中高层管理者,采用因素分析和结构方程模型检验企业高级管理者胜任力特征的结构。结果表明,管理胜任力特征结构由管理素质和管理技能等两个维度构成,但在维度要素及其关键度上,职位层次间存在显著差异。本研究为管理职位的测评选拔提供了新的理论依据。     

结构方程建模中的题目打包策略

结构方程建模中题目打包法的优缺点包括：指标数据质量变好、模型拟合程度提高; 估计偏差不大, 可校正; 估计稳定, 但降低了敏感性与可证伪性。打包法的前提条件是单维、同质, 适合结构模型分析, 不适合测量模型分析。对于单维测验, 给出了一个打包流程。对于通常的多个子量表(多维结构)测验, 推荐在子量表内打包, 每个子量表打包成1个指标或者3个指标, 用于结构方程建模。     

项目组合在结构方程模型中的应用

项目组合（itemparceling）是对同一量表中的若干项目进行整合并形成新的观测指标的过程。虽然一直以来它都是一个有争议的议题,但随着其在结构方程模型中的应用日益广泛,它越来越受到研究者重视。文章从项目组合的基本逻辑、优缺点以及具体方法等方面对项目组合的研究进行了概括,并在此基础上提出了使用的具体建议：（1）根据研究的目的与具体情境选择是否需要组合;（2）组合之前必须首先确定概念的维度性;（3）项目组合最好建立在一定的理论基础上等等。未来的研究可以深入探讨各种组合方法对模型拟合以及参数估计的影响以及项目组合在一些SEM高阶应用中的效果,并进一步与项目反应理论等测量理论相结合     

OpenMx 2.0: Extended Structural Equation and Statistical Modeling

The new software package OpenMx 2.0 for structural equation and other statistical modeling is introduced and its features are described. OpenMx is evolving in a modular direction and now allows a mix-and-match computational approach that separates model expectations from fit functions and optimizers. Major backend architectural improvements include a move to swappable open-source optimizers such as the newly written CSOLNP. Entire new methodologies such as item factor analysis and state space modeling have been implemented. New model expectation functions including support for the expression of models in LISREL syntax and a simplified multigroup expectation function are available. Ease-of-use improvements include helper functions to standardize model parameters and compute their Jacobian-based standard errors, access to model components through standard R $ mechanisms, and improved tab completion from within the R Graphical User Interface.     

Structural Equation Modeling with Small Samples: Test Statistics

Structural equation modeling is a well-known technique for studying relationships among multivariate data. In practice, high dimensional nonnormal data with small to medium sample sizes are very common, and large sample theory, on which almost all modeling statistics are based, cannot be invoked for model evaluation with test statistics. The most natural method for nonnormal data, the asymptotically distribution free procedure, is not defined when the sample size is less than the number of nonduplicated elements in the sample covariance. Since normal theory maximum likelihood estimation remains defined for intermediate to small sample size, it may be invoked but with the probable consequence of distorted performance in model evaluation. This article studies the small sample behavior of several test statistics that are based on maximum likelihood estimator, but are designed to perform better with nonnormal data. We aim to identify statistics that work reasonably well for a range of small sample sizes and distribution conditions. Monte Carlo results indicate that Yuan and Bentler's recently proposed F-statistic performs satisfactorily.     

Reexamining Nonlinear Structural Equation Modeling Procedures: The Effect of Parallel and Congeneric Measures

The current study examines the performance of the extended unconstrained approach (EXUC) and the latent moderated structural equation modeling procedure (LMS) in situations where quadratic and interaction terms are tested simultaneously and investigates their limitations with regard to the employment of parallel and congeneric measures, relatively low indicator reliabilities, and relatively large numbers of indicators. By means of a Monte Carlo study, we found LMS to be the best option for testing multiple nonlinear effects given sufficient sample size (n ≥ 500) and normally distributed exogenous variables. Its advantages became more prominent when indicator reliabilities were heterogeneous and small. The EXUC was a viable option for estimating the model when indicators were parallel and exhibited large indicator reliabilities. An empirical example of the results is provided, and the relevance of measurement model characteristics to assess nonlinear relationships is discussed.     

不同适应水平小学生有意义事件报告比较——小学生自我调节机制的一项研究

本研究选取发展良好与适应不良的三——五年级小学生为被试,以问卷访谈形式调查他们心目中的正性和负性意义事件。结果表明,两组被试在事件意义体验的人际亲和性、内在一外在性和丰富性方面有明显不同的反映。感受的丰富性表现在正负性意义事件两方面,某种事件负性意义感受的出现是良好适应的表现。