A Scaled F Distribution as an Approximation to the Distribution of Test Statistics in Covariance Structure Analysis

When the assumption of multivariate normality is violated or when a discrepancy function other than (normal theory) maximum likelihood is used in structural equation models, the null distribution of the test statistic may not be χ² distributed. Most existing methods to approximate this distribution only match up to 2 moments. In this article, we propose 2 additional approximation methods: a scaled F distribution that matches 3 moments simultaneously and a direct Monte Carlo–based weighted sum of i.i.d. χ² variates. We also conduct comprehensive simulation studies to compare the new and existing methods for both maximum likelihood and nonmaximum likelihood discrepancy functions and to separately evaluate the effect of sampling uncertainty in the estimated weights of the weighted sum on the performance of the approximation methods.     

三种参数估计方法的比较与启示

对回归模型进行参数估计时,常用的两种重要方法是普通最小二乘法和最大似然法。随着社会的发展,普通最小二乘法的不足之处日益显现,另一种新的参数估计方法——累积法的推广和运用,为我们提供了新的研究思路。本文通过对这三种参数估计方法进行分析与比较,得出了一些新的启示。     

Should Regularization Replace Simple Structure Rotation in Exploratory Factor Analysis?

Exploratory factor analysis (EFA) is an important tool when the measurement structure of psychological constructs is uncertain. Typically, factor rotation is applied to obtain interpretable results resembling a simple structure. However, an overwhelming multitude of rotation techniques is available of which none is unequivocally superior. Recently, regularization has been suggested as an alternative to factor rotation. In two simulation studies, we addressed the question if regularized EFA is a suitable alternative for rotated EFA. We compared their performance in recovering predefined factor loading patterns with varying amounts of cross-loadings. Elastic net regularized EFA yielded estimates comparable to rotated EFA. For complex loading patterns, both rotated and regularized EFA tended to underestimate cross-loadings and inflate factor correlations, but regularized EFA was able to recover loading patterns as long as a subset of items followed a simple structure. We conclude that regularization is a suitable alternative to factor rotation for psychometric applications.     

基于稳健估计的混凝土抗压强度测试分析

应用基于稳健估计和基于最小二乘法的三次多项式曲线模型,分析混凝土在养护28 d期间抗压强度的变化规律,相比传统最小二乘法,稳健估计能够减小数据误差对拟合曲线的影响,从而达到与实际测量相吻合的效果,较准确地预测出混凝土在不同养护时期的抗压强度值。     

Maximum Likelihood Dynamic Factor Modeling for Arbitrary N and T Using SEM

This article has 3 objectives that build on each other. First, we demonstrate how to obtain maximum likelihood estimates for dynamic factor models (the direct autoregressive factor score model) with arbitrary T and N by means of structural equation modeling (SEM) and compare the approach to existing methods. Second, we go beyond standard time series analysis (T large and N = 1) and conventional SEM (N large and T = 1 or small) by integrating both approaches. The resulting combined model offers a variety of new modeling options including a direct test of the ergodicity hypothesis, according to which the factorial structure of an individual observed at many time points is identical to the factorial structure of a group of individuals observed at a single point in time. Third, we illustrate the flexibility of SEM time series modeling by extending the approach to account for complex error structures. We end with a discussion of current limitations and future applications of SEM-based time series modeling for arbitrary T and N.     

软件Mathematica在线性回归分析中的应用

文章在提出线性回归问题的基础上,用最小二乘法求回归方程。通过实例应用软件Mathematica进行分析求解,两种方法的比较可以看出,Mathematica在求解线性回归问题中可大大地提高办公效率。     

具有部分缺失数据时两个威布尔分布的估计和检验

文中讨论了部分缺失数据两威布尔总体的参数估计和关于总体相同的似然比检验．证明估计的强相合性和渐近正态性,给出似然比检验统计量的极限分布,并探讨了基于精确分布的检验问题．     

Book review

Analyzing social & political change: A casebook of methods. Angela Dale and Richard B. Davies (Eds.), Thousand Oaks, CA: Sage, 1994, x+229 pages.     

Exploratory Graph Analysis for Factor Retention: Simulation Results for Continuous and Binary Data

Exploratory graph analysis (EGA) is a commonly applied technique intended to help social scientists discover latent variables. Yet, the results can be influenced by the methodological decisions the researcher makes along the way. In this article, we focus on the choice regarding the number of factors to retain: We compare the performance of the recently developed EGA with various traditional factor retention criteria. We use both continuous and binary data, as evidence regarding the accuracy of such criteria in the latter case is scarce. Simulation results, based on scenarios resulting from varying sample size, communalities from major factors, interfactor correlations, skewness, and correlation measure, show that EGA outperforms the traditional factor retention criteria considered in most cases in terms of bias and accuracy. In addition, we show that factor retention decisions for binary data are preferably made using Pearson, instead of tetrachoric, correlations, which is contradictory to popular belief.     

一种提高室内定位精度的模糊逻辑方法

超宽带技术由于其精确的定时分辨率,在视距（LOS）和非视距（NLOS）混合环境中应用前景广阔。为提高跟踪精确度、消除与UWB跟踪系统测距数据集异常值,构建合适的误差抑制方法,提出一种误差抑制方法。首先对环境进行建模,分析LOS和NLOS环境中的信号参数;然后,采用基于模糊逻辑的两步自适应定位算法,分析和选择最佳测距数据,用于计算被跟踪设备的位置;使用模糊加权最小二乘估计（FWLSE）方法对非视距（NLOS）混合环境中的实际数据进行测试。实验结果表明,与其它已知算法相比,该方法定位精度显著提高18.28%,且在实际应用中易于实现。     

权回归模型下几种估计性能的比较

在给定的权回归模型下,讨论了最小二乘估计、最优加权最小二乘估计和线性无偏最小方差估计的性能比较,得出了在随机误差方差矩阵可逆条件下,可算出最优加权最小二乘估计与线性无偏最小方差估计误差方差阵的差表达式,并在一定条件下,两者趋于一致。     

Identifying Aberrant Data in Structural Equation Models With IRLS-ADF

In structural equation models, outliers could result in inaccurate parameter estimates and misleading fit statistics when using traditional methods. To robustly estimate structural equation models, iteratively reweighted least squares (IRLS; Yuan & Bentler, 2000) has been proposed, but not thoroughly examined. We explore the large-sample properties of IRLS and its effect on parameter recovery, model fit, and aberrant data identification. A parametric bootstrap technique is proposed to determine the tuning parameters of IRLS, which results in improved Type I error rates in aberrant data identification, for data sets generated from homogenous populations. Scenarios concerning (a) simulated data, (b) contaminated data, and (c) a real data set are studied. Results indicate good parameter recovery, model fit, and aberrant data identification when noisy observations are drawn from a real data set, but lackluster parameter recovery and identification of aberrant data when the noise is parametrically structured. Practical implications and further research are discussed.     

连续型幂律分布的参数估计

文章探索连续型幂律分布的参数估计,主要研究参数的极大似然估计和有效估计.给出了参数的一个渐近有效估计,并且证明了不存在参数的有效无偏估计。     

约束条件下的广义最小二乘估计

本文仿造约束最小二乘估计和广义最小二乘估计的推导方法．给出约束条件下的广义最小二乘估计。     

Factor Retention in Exploratory Factor Analysis With Missing Data

Determining the number of factors in exploratory factor analysis is arguably the most crucial decision a researcher faces when conducting the analysis. While several simulation studies exist that compare various so-called factor retention criteria under different data conditions, little is known about the impact of missing data on this process. Hence, in this study, we evaluated the performance of different factor retention criteria—the Factor Forest, parallel analysis based on a principal component analysis as well as parallel analysis based on the common factor model and the comparison data approach—in combination with different missing data methods, namely an expectation-maximization algorithm called Amelia, predictive mean matching, and random forest imputation within the multiple imputations by chained equations (MICE) framework as well as pairwise deletion with regard to their accuracy in determining the number of factors when data are missing. Data were simulated for different sample sizes, numbers of factors, numbers of manifest variables (indicators), between-factor correlations, missing data mechanisms and proportions of missing values. In the majority of conditions and for all factor retention criteria except the comparison data approach, the missing data mechanism had little impact on the accuracy and pairwise deletion performed comparably well as the more sophisticated imputation methods. In some conditions, especially small-sample cases and when comparison data were used to determine the number of factors, random forest imputation was preferable to other missing data methods, though. Accordingly, depending on data characteristics and the selected factor retention criterion, choosing an appropriate missing data method is crucial to obtain a valid estimate of the number of factors to extract.     

The Weird World,and Equally Weird Measurement Models: Reactive Indicators and the Validity Revolution

Researchers using structural equation modeling (SEM) aspire to learn about the world by seeking models with causal specifications that match the causal forces extant in the world. This quest for a model matching existing worldly causal forces constitutes an ontology that orients, or perhaps reorients, thinking about measurement validity. This article illustrates several ways the seemingly innocuous quest for structural equation models that mirror “the world beyond” confronts entrenched notions of measurement validity. The article begins by considering simple measurement models and ends by “discovering” a new class of indicators called reactive indicators. Reactive indicators act as both the cause and effect of an underlying latent variable. The identifiability of a simple model containing a reactive indicator is proven and a research example illustrating the use of a reactive indicator is provided. However, the real challenge is to understand how an indicator can be both a cause and effect of the latent it measures. The understanding does not come from complying with the traditional rules for reliability and validity, but from focusing on the quest to make the structural equation model match the structuring of the worldly forces we seek to understand. Valid measurement in the context of a weirdly structured world requires an equally weird structural equation model.     

推广的最优加权最小二乘估计解的一个结果

文章根据加权最小二乘估计解，存在权系数，在估计误差方差矩阵最小意义下，得出了推广的最优加权最小二乘估计解的一个结果。     

Software review

STATISTICA 5.0. StatSoft, 2325 East 13th Street, Tulsa, OK 74104, (918) 583–4149. $995 retail, academic site license—$2,000 for 10 copies. Requirements: 386 or better, 4 Meg RAM, Microsoft Windows 3.1 or 95.     

泊松分布中参数的经典估计与Bayes估计的相等关系

文中证明了泊松分布中未知参数的矩估计和最大似然估计,一定存在一个先验分布,使其贝叶斯估计就是该经典估计的结论.     

等价限制线性模型中极大似然估计的稳健性

稳健性分析是判断估计值与真实值之间差异是否重要的一种方法。限制线性模型下的极大似然估计的稳健性是当前大家比较感兴趣的一个问题。笔者在前人的基础上,给出限制线性模型中极大似然估计对随机误差协方差矩阵的稳健性统计量,并对其进行分析,得出限制线性模型中极大似然估计对随机误差协方差矩阵不敏感。