A Bootstrap Generalization of Modified Parallel Analysis for IRT Dimensionality Assessment

This article introduces a bootstrap generalization to the Modified Parallel Analysis (MPA) method of test dimensionality assessment using factor analysis. This methodology, based on the use of Marginal Maximum Likelihood nonlinear factor analysis, provides for the calculation of a test statistic based on a parametric bootstrap using the MPA methodology for generation of synthetic datasets. Performance of the bootstrap test was compared with the likelihood ratio difference test and the DIMTEST procedure using a Monte Carlo simulation. The bootstrap test was found to exhibit much better control of the Type I error rate than the likelihood ratio difference test, and comparable power to DIMTEST under most conditions. A major conclusion to be taken from this research is that under many real-world conditions, the bootstrap MPA test presents a useful alternative for practitioners using Marginal Maximum Likelihood factor analysis to test for multidimensional testing data.     

Confidence Intervals of Fit Indexes by Inverting a Bootstrap Test

Fit indexes are an important tool in the evaluation of model fit in structural equation modeling (SEM). Currently, the newest confidence interval (CI) for fit indexes proposed by Zhang and Savalei (2016) is based on the quantiles of a bootstrap sampling distribution at a single level of misspecification. This method, despite a great improvement over naive and model-based bootstrap methods, still suffers from unsatisfactory coverage. In this work, we propose a new method of constructing bootstrap CIs for various fit indexes. This method directly inverts a bootstrap test and produces a CI that involves levels of misspecification that would not be rejected in a bootstrap test. Similar in rationale to a parametric CI of root mean square error of approximation (RMSEA) based on a noncentral χ2 distribution and a profile-likelihood CI of model parameters, this approach is shown to have better performance than the approach of Zhang and Savalei (2016), with more accurate coverage and more efficient widths.     

模拟偏差对自助法估计的影响探讨

文中探讨了模拟偏差对自助法均值估计的影响.首先,从分布N（1,12）中产生样本数据,利用自助法,得到自助法均值的估计.然后讨论了样本数据均值和总体分布均值的偏差对自助法估计的影响.结果表明,当偏差的绝对值小于等于0.54时,模拟结果较好,当偏差的绝对值大于等于0.56时,模拟结果很差.     

An Introduction to the Bootstrap

This article presents bootstrap methods for estimation, using simple arguments. Minitab macros for implementing these methods are given.     

互补对称功率放大电路中自举电容作用仿真分析

理论分析互补对称功率放大电路中自举电容的作用，给出用EDA软件Multisim2001仿真分析该电路的方法，仿真分析与理论分析结果一致，为获得该类电路的分析设计提供了EDA手段和实验依据。     

Standard Errors of IRT Parameter Scale Transformation Coefficients: Comparison of Bootstrap Method,Delta Method,and Multiple Imputation Method

The present study evaluated the multiple imputation method, a procedure that is similar to the one suggested by Li and Lissitz (2004), and compared the performance of this method with that of the bootstrap method and the delta method in obtaining the standard errors for the estimates of the parameter scale transformation coefficients in item response theory (IRT) equating in the context of the common‐item nonequivalent groups design. Two different estimation procedures for the variance‐covariance matrix of the IRT item parameter estimates, which were used in both the delta method and the multiple imputation method, were considered: empirical cross‐product (XPD) and supplemented expectation maximization (SEM). The results of the analyses with simulated and real data indicate that the multiple imputation method generally produced very similar results to the bootstrap method and the delta method in most of the conditions. The differences between the estimated standard errors obtained by the methods using the XPD matrices and the SEM matrices were very small when the sample size was reasonably large. When the sample size was small, the methods using the XPD matrices appeared to yield slight upward bias for the standard errors of the IRT parameter scale transformation coefficients.     

系统引导型病毒机理特征及最佳根治方法

系统引导型病毒是在系统引导加载过程中进入系统中，获得对系统的控制权。其传染性强，危害大，难以根除。本文根据系统引导型病毒机理及特征，从防范的角度出发，找到了根治系统引导型病毒的最佳方法。     

A Bootstrap Experiment on the Statistical Properties of Students' Ratings of Teaching Effectiveness

This paper examines the effects of two background variables in students' ratings of teaching effectiveness (SETs): class size and students' motivation (as surrogated by students' likelihood to respond randomly). Resampling simulation methodology has been employed to test the sensitivity of the SET scale for three hypothetical instructors (excellent, average, and poor). In an ideal scenario without confounding factors, SET statistics unmistakably distinguish the instructors. However, at different class sizes and levels of random responses, SET class averages are significantly biased. Results suggest that evaluations based on SET statistics should look at more than class averages. Resampling methodology (bootstrap simulation) is useful for SET research for scale sensitivity study, research results validation, and actual SET score analyses. Examples will be given on how bootstrap simulation can be applied to real-life SET data comparison.     

Implementing Restricted Maximum Likelihood Estimation in Structural Equation Models

Structural equation modeling (SEM) is now a generic modeling framework for many multivariate techniques applied in the social and behavioral sciences. Many statistical models can be considered either as special cases of SEM or as part of the latent variable modeling framework. One popular extension is the use of SEM to conduct linear mixed-effects modeling (LMM) such as cross-sectional multilevel modeling and latent growth modeling. It is well known that LMM can be formulated as structural equation models. However, one main difference between the implementations in SEM and LMM is that maximum likelihood (ML) estimation is usually used in SEM, whereas restricted (or residual) maximum likelihood (REML) estimation is the default method in most LMM packages. This article shows how REML estimation can be implemented in SEM. Two empirical examples on latent growth model and meta-analysis are used to illustrate the procedures implemented in OpenMx. Issues related to implementing REML in SEM are discussed.     

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.     

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.     

Item Generation for Test Development,by Sidney Irvine and Patrick Kyllonen (Eds.)

Structural Equation Modeling: A Second Course, edited by Hancock and Mueller, is an important resource for methodologists, applied researchers, and students of structural equation modeling (SEM) alike. This well-written edited volume provides coverage of a number of important issues and techniques not commonly treated in a didactic manner and specifically not covered in most introductory SEM textbooks. Indeed, the topics covered in this volume are topics for which instructors of SEM courses commonly refer students to supplemental journal article readings (Stapleton &; Leite, 2005). This book is particularly valuable in that readers are provided with relevant literature reviews and as such do not have to wrestle with integrating concepts across journal articles with different notation. It is useful in its provision of concrete examples of how to implement each data analytic strategy using common SEM software. In cases where the procedure is not implemented in widely distributed software, chapter authors make clear reference to alternative software and available macros. Hancock and Mueller are to be credited for working carefully with the chapter authors for consistent use of software for their examples, notation, and tone. As such, this volume is much more than a course pack. The following provides a review of the content of each chapter in this edited volume.     

Structural equation modeling: Back to basics

Major technological advances incorporated into structural equation modeling (SEM) computer programs now make it possible for practitioners who are basically unfamiliar with the purposes and limitations of SEM to use this tool within their research contexts. The current move by program developers to market more user friendly software packages is a welcomed trend in the social and behavioral science research community. The quest to simplify the data analysis step in the research process has—at least with regard to SEM—created a situation that allows practitioners to apply SEM but forgetting, knowingly ignoring, or most dangerously, being ignorant of some basic philosophical and statistical issues that must be addressed before sound SEM analyses should be conducted. This article focuses on some of the almost forgotten topics taken here from each step in the SEM process: model conceptualization, identification and parameter estimation, and data‐model fit assessment and model modification. The main objective is to raise awareness among researchers new to SEM of a few basic but key philosophical and statistical issues. These should be addressed before launching into any one of the new generation of SEM software packages and being led astray by the seemingly irresistible temptation to prematurely start “playing” with the data.     

Application of a new resampling method to SEM: a comparison of S-SMART with the bootstrap

Among the commonly used resampling methods of dealing with small-sample problems, the bootstrap enjoys the widest applications because it often outperforms its counterparts. However, the bootstrap still has limitations when its operations are contemplated. Therefore, the purpose of this study is to examine an alternative, new resampling method (called S-SMART) and compare the statistical performance of it with that of the bootstrap through an application of them to the most advanced modelling technique, SEM, as an example. The evaluation of the statistical performances of S-SMART and the bootstrap with respect to the standard errors of the parameter estimates was conducted through a Monte Carlo simulation study. This work, while potentially benefiting educational and behavioural research, conceivably would also provide methodological support for other research areas, such as bioinformatics, biology, geosciences, astronomy, and ecology, where large samples are hard to obtain.     

Standardized Parameters in Misspecified Structural Equation Models: Empirical Performance in Point Estimates,Standard Errors,and Confidence Intervals

In practice, models always have misfit, and it is not well known in what situations methods that provide point estimates, standard errors (SEs), or confidence intervals (CIs) of standardized structural equation modeling (SEM) parameters are trustworthy. In this article we carried out simulations to evaluate the empirical performance of currently available methods. We studied maximum likelihood point estimates, as well as SE estimators based on the delta method, nonparametric bootstrap (NP-B), and semiparametric bootstrap (SP-B). For CIs we studied Wald CI based on delta, and percentile and BC_a intervals based on NP-B and SP-B. We conducted simulation studies using both confirmatory factor analysis and SEM models. Depending on (a) whether point estimate, SE, or CI is of interest; (b) amount of model misfit; (c) sample size; and (d) model complexity, different methods can be the one that renders best performance. Based on the simulation results, we discuss how to choose proper methods in practice.     

自举式扫描电路的时间误差

引入了时差概念 ,分析了自举式扫描电路的相对时差及其与补偿系数m、电源利用系数 η和非线性系数ε之间的关系 ,并且归纳了一个近似公式 ,简化了计算 .     

A Comparison of Method Effects in Two Confirmatory Factor Models for Structurally Different Methods

It is well known that measurement error in observable variables induces bias in estimates in standard regression analysis and that structural equation models are a typical solution to this problem. Often, multiple indicator equations are subsumed as part of the structural equation model, allowing for consistent estimation of the relevant regression parameters. In many instances, however, embedding the measurement model into structural equation models is not possible because the model would not be identified. To correct for measurement error one has no other recourse than to provide the exact values of the variances of the measurement error terms of the model, although in practice such variances cannot be ascertained exactly, but only estimated from an independent study. The usual approach so far has been to treat the estimated values of error variances as if they were known exact population values in the subsequent structural equation modeling (SEM) analysis. In this article we show that fixing measurement error variance estimates as if they were true values can make the reported standard errors of the structural parameters of the model smaller than they should be. Inferences about the parameters of interest will be incorrect if the estimated nature of the variances is not taken into account. For general SEM, we derive an explicit expression that provides the terms to be added to the standard errors provided by the standard SEM software that treats the estimated variances as exact population values. Interestingly, we find there is a differential impact of the corrections to be added to the standard errors depending on which parameter of the model is estimated. The theoretical results are illustrated with simulations and also with empirical data on a typical SEM model.     

计算机应用软件中的宏

计算机应用软件中的宏是一个执行命令，代表解决问题的一个命令序列或动作序列，用户使用时只需给出宏的名称或快捷键，计算机便可自动完成所指定的任务，宏可由语言控制或软件自动录制生成，使用宏观提高效率，并能解决一些特殊问题。     

semPlot: Unified Visualizations of Structural Equation Models

Structural equation modeling (SEM) has a long history of representing models graphically as path diagrams. This article presents the freely available semPlot package for R, which fills the gap between advanced, but time-consuming, graphical software and the limited graphics produced automatically by SEM software. In addition, semPlot offers more functionality than drawing path diagrams: It can act as a common ground for importing SEM results into R. Any result usable as input to semPlot can also be represented in any of the 3 popular SEM frameworks, as well as translated to input syntax for the R packages sem (Fox, Nie, & Byrnes, 2013) and lavaan (Rosseel, 2012). Special considerations are made in the package for the automatic placement of variables, using 3 novel algorithms that extend the earlier work of Boker, McArdle, and Neale (2002). The article concludes with detailed instructions on these node-placement algorithms.     

宏程序在模块化加工技术中的应用

随着各类CAD／CAM软件的日益普及,自动编程慢慢有取代手工编程的趋势,但手工编程毕竟是基础,各种“疑难杂症”的解决往往还是要利用手工编程,且手工编程还可以使用变量编程,即宏程序。从模块化加工角度阐述了宏程序在模块化加工技术中的应用。