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.     

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

A 2-stage robust procedure as well as an R package, rsem, were recently developed for structural equation modeling with nonnormal missing data by Yuan and Zhang (2012). Several test statistics that have been used for complete data analysis are employed to evaluate model fit in the 2-stage robust method. However, properties of these statistics under robust procedures for incomplete nonnormal data analysis have never been studied. This study aims to systematically evaluate and compare 5 test statistics, including a test statistic derived from normal-distribution-based maximum likelihood, a rescaled chi-square statistic, an adjusted chi-square statistic, a corrected residual-based asymptotical distribution-free chi-square statistic, and a residual-based F statistic. These statistics are evaluated under a linear growth curve model by varying 8 factors: population distribution, missing data mechanism, missing data rate, sample size, number of measurement occasions, covariance between the latent intercept and slope, variance of measurement errors, and downweighting rate of the 2-stage robust method. The performance of the test statistics varies and the one derived from the 2-stage normal-distribution-based maximum likelihood performs much worse than the other four. Application of the 2-stage robust method and of the test statistics is illustrated through growth curve analysis of mathematical ability development, using data on the Peabody Individual Achievement Test mathematics assessment from the National Longitudinal Survey of Youth 1997 Cohort.     

Examining the Missing Completely at Random Mechanism in Incomplete Data Sets: A Multiple Testing Approach

A multiple testing procedure for examining implications of the missing completely at random (MCAR) mechanism in incomplete data sets is discussed. The approach uses the false discovery rate concept and is concerned with testing group differences on a set of variables. The method can be used for ascertaining violations of MCAR and disproving this mechanism in empirical behavioral and social research. The procedure can also be employed when locating violations of MCAR in observed measures is of interest. The outlined approach is illustrated with data from a cognitive intervention study.     

统计模型中误差方差的均方误差的区间估计

本文研究了线性统计模型(Ⅰ)—(Ⅳ)中参数σ^2的估计量σL^2或σH^2的均方误差MSE(σL^2)或MSE(σH^2),并分别给出了其1-α的置信区间。     

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.     

Using the Standardized Root Mean Squared Residual (SRMR) to Assess Exact Fit in Structural Equation Models

We examine the accuracy of p values obtained using the asymptotic mean and variance (MV) correction to the distribution of the sample standardized root mean squared residual (SRMR) proposed by Maydeu-Olivares to assess the exact fit of SEM models. In a simulation study, we found that under normality, the MV-corrected SRMR statistic provides reasonably accurate Type I errors even in small samples and for large models, clearly outperforming the current standard, that is, the likelihood ratio (LR) test. When data shows excess kurtosis, MV-corrected SRMR p values are only accurate in small models (p = 10), or in medium-sized models (p = 30) if no skewness is present and sample sizes are at least 500. Overall, when data are not normal, the MV-corrected LR test seems to outperform the MV-corrected SRMR. We elaborate on these findings by showing that the asymptotic approximation to the mean of the SRMR sampling distribution is quite accurate, while the asymptotic approximation to the standard deviation is not.     

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.     

Fit for a Bayesian: An Evaluation of PPP and DIC for Structural Equation Modeling

Despite its importance to structural equation modeling, model evaluation remains underdeveloped in the Bayesian SEM framework. Posterior predictive p-values (PPP) and deviance information criteria (DIC) are now available in popular software for Bayesian model evaluation, but they remain underutilized. This is largely due to the lack of recommendations for their use. To address this problem, PPP and DIC were evaluated in a series of Monte Carlo simulation studies. The results show that both PPP and DIC are influenced by severity of model misspecification, sample size, model size, and choice of prior. The cutoffs PPP < 0.10 and ?DIC > 7 work best in the conditions and models tested here to maintain low false detection rates and misspecified model selection rates, respectively. The recommendations provided in this study will help researchers evaluate their models in a Bayesian SEM analysis and set the stage for future development and evaluation of Bayesian SEM fit indices.     

Number of Subjects and Time Points Needed for Multilevel Time-Series Analysis: A Simulation Study of Dynamic Structural Equation Modeling

Dynamic structural equation modeling (DSEM) is a novel, intensive longitudinal data (ILD) analysis framework. DSEM models intraindividual changes over time on Level 1 and allows the parameters of these processes to vary across individuals on Level 2 using random effects. DSEM merges time series, structural equation, multilevel, and time-varying effects models. Despite the well-known properties of these analysis areas by themselves, it is unclear how their sample size requirements and recommendations transfer to the DSEM framework. This article presents the results of a simulation study that examines the estimation quality of univariate 2-level autoregressive models of order 1, AR(1), using Bayesian analysis in Mplus Version 8. Three features are varied in the simulations: complexity of the model, number of subjects, and number of time points per subject. Samples with many subjects and few time points are shown to perform substantially better than samples with few subjects and many time points.     

Handling Missing Data in the Modeling of Intensive Longitudinal Data

Myriad approaches for handling missing data exist in the literature. However, few studies have investigated the tenability and utility of these approaches when used with intensive longitudinal data. In this study, we compare and illustrate two multiple imputation (MI) approaches for coping with missingness in fitting multivariate time-series models under different missing data mechanisms. They include a full MI approach, in which all dependent variables and covariates are imputed simultaneously, and a partial MI approach, in which missing covariates are imputed with MI, whereas missingness in the dependent variables is handled via full information maximum likelihood estimation. We found that under correctly specified models, partial MI produces the best overall estimation results. We discuss the strengths and limitations of the two MI approaches, and demonstrate their use with an empirical data set in which children’s influences on parental conflicts are modeled as covariates over the course of 15 days (Schermerhorn, Chow, & Cummings, 2010).     

非线性方程几种数值解法的MATLAB程序

研究非线性方程数值解,给出了二分法、简单迭代法、牛顿迭代法在MATLAB的程序,并进行了近似计算,可知牛顿迭代法收敛最快.     

结构方程模型在公共部门公众满意度测评中的应用

随着政府绩效评价工作的深入开展,公共部门公众满意度测评研究受到越来越多的关注。公众满意度测评涉及到对公众期望等较难直接测量的潜变量之间关系的分析,这对用于测评的工具提出了较高的要求,而结构方程模型正是能够满足这类要求的多元数据分析工具。由于用于私人部门的顾客满意度模型在经过了大量的调研实践和反复的数据验证基础上已经形成了较为完善的指标体系,所以公众满意度的结构方程模型可以在此基础上结合公共产品/服务的特点加以改进而形成,在运用中还要注意构建模型要有正确的理论基础等问题。     

Bayesian Model Averaging Over Directed Acyclic Graphs With Implications for the Predictive Performance of Structural Equation Models

This article examines Bayesian model averaging as a means of addressing predictive performance in Bayesian structural equation models. The current approach to addressing the problem of model uncertainty lies in the method of Bayesian model averaging. We expand the work of Madigan and his colleagues by considering a structural equation model as a special case of a directed acyclic graph. We then provide an algorithm that searches the model space for submodels and obtains a weighted average of the submodels using posterior model probabilities as weights. Our simulation study provides a frequentist evaluation of our Bayesian model averaging approach and indicates that when the true model is known, Bayesian model averaging does not yield necessarily better predictive performance compared to nonaveraged models. However, our case study using data from an international large-scale assessment reveals that the model-averaged submodels provide better posterior predictive performance compared to the initially specified model.     

压力容器压力试验时免作强度校核的条件

压力容器在进行压力试验时，须先对在试验压力作用下的强度进行理论校核，合格后才能进行实际操作。通过综合分析和实例验证得出：在液压试验时，对碳素钢和低合金钢容器当PL≤0．19p、对高合金钢容器当PL≤0．1p时，则不必校核压力试验时的强度，可直接进行液压试验的实际操作；对作气压试验的容器，无论何种情况都不必校核压力试验时的强度，可直接进行气压试验的实际操作。     

基于SEM的高铁时代出游行为机理测度模型研究

高速铁路的大规模运行为区域旅游产业带来了新的发展契机,同时也对需求引导下的产业要素供给与优化配置提出了新的要求。根据交通行为理论,作为一种快捷、高效的交通工具,高铁所特有的"时空压缩"特性从旅游出行动机、旅游过程中的活动参与情况和旅游出行特征三个方面对游客的出游行为产生了不同程度的影响。SEM(结构方程模型)是测度行为机理的典型分析工具,据此构建的研究假设和概念模型可以为高铁驱动下的出游行为结构链条的变迁以及趋势的定性解构和定量测度与验证构建一套概念框架与逻辑思路,为进一步展开实证分析提供理论启示与操作步骤;这对完善高铁时代沿线旅游供需要素配置和配套政策也具有一定的参考价值。     

The Theory of Planned Behavior Within the Stages of the Transtheoretical Model: Latent Structural Modeling of Stage-Specific Prediction Patterns in Physical Activity

This is the first study to test whether the stages of change of the transtheoretical model are qualitatively different through exploring discontinuity patterns in theory of planned behavior (TPB) variables using latent multigroup structural equation modeling (MSEM) with AMOS. Discontinuity patterns in terms of latent means and prediction patterns for the different stage groups were examined. Adults (n = 3,462) were assessed on their physical activity stages of change and TPB variables. The TPB was separately examined within the five stage groups. The TPB measurement model fit was acceptable. Latent mean analyses with post-hoc contrast and MSEM indicated discontinuity patterns. Results underscore the qualitative differences between the stages that may guide further research and the design of interventions integrating the approaches.     

单向分类随机效应模型误差方差线性关系的一种检验

利用多元正态总体的复相关系数检验 ,给出了单向分类随机效应模型 yij=uj+αi+εij,误差方差σ21 ,σ22 ,… ,σ2 m 线性关系H0 :1ΛM =0 1×r 的一种检验 ,其中Λ =diag(σ21 ,σ22 ,… ,σ2 m) ,1=(1,1,… ,1)′,R(Mm×r) =r .     

Mediated Effects with the Parallel Process Latent Growth Model: An Evaluation of Methods for Testing Mediation in the Presence of Nonnormal Data

This Monte Carlo simulation study investigated the impact of nonnormality on estimating and testing mediated effects with the parallel process latent growth model and 3 popular methods for testing the mediated effect (i.e., Sobel’s test, the asymmetric confidence limits, and the bias-corrected bootstrap). It was found that nonnormality had little effect on the estimates of the mediated effect, standard errors, empirical Type I error, and power rates in most conditions. In terms of empirical Type I error and power rates, the bias-corrected bootstrap performed best. Sobel’s test produced very conservative Type I error rates when the estimated mediated effect and standard error had a relationship, but when the relationship was weak or did not exist, the Type I error was closer to the nominal .05 value.     

Modeling the kinetics of methane conversion in steam reforming process of coke-oven gas based on experimental data

Steam-reforming is an effective approach for upgrading methane and hydrocarbon of coke-oven gas into CO and H2, but the kinetic behavior needs more study. We investigated the conversion of methane in coke-oven gas by steam reforming process in an electric tubular flow at 14 kPa with temperature varying from 500 °C to 950 °C, and developed a kenetic model for , ignoring the effects of adsorption and diffusion. The optimal dynamic conditions for methane conversion 14 kPa are as follows:the ratio of the amount of water to the amount of methane is from 1.1 to 1.3;the reaction temperature is from 1 223 K to 1 273 K. The methane conversion rate is larger than 95% when the ratio of the amount of water to the amount of methane is 1.2 at a temperature above 1 223 K with the residence time up to 0.75 s.