Sensitivity Analysis in Structural Equation Models: Cases and Their Influence

The detection of outliers and influential observations is routine practice in linear regression. Despite ongoing extensions and development of case diagnostics in structural equation models (SEM), their application has received limited attention and understanding in practice. The use of case diagnostics informs analysts of the uncertainty of model estimates under different subsets of the data and highlights unusual and important characteristics of certain cases. We present several measures of case influence applicable in SEM and illustrate their implementation, presentation, and interpretation with two empirical examples: (a) a common factor model on verbal and visual ability (Holzinger &; Swineford, 1939 Holzinger, K. and Swineford, F. 1939. A study in factor analysis: The stability of a bi-factor solution. Chicago, IL: University of Chicago..  [Google Scholar]) and (b) a general structural equation model assessing the effect of industrialization on democracy in a mediating model using country-level data (Bollen, 1989 Bollen, K. A. 1989. Structural equation models with latent variables New York, NY: Wiley.. [Crossref] , [Google Scholar]; Bollen &; Arminger, 1991 Bollen, K. A. and Arminger, G. 1991. Observational residuals in factor analysis and structural equation models. Sociological Methodology, 21: 235–262. [Crossref], [Web of Science ®] , [Google Scholar]). Throughout these examples, three issues are emphasized. First, cases may impact different aspects of results as identified by different measures of influence. Second, the important distinction between outliers and influential cases is highlighted. Third, the concept of good and bad cases is introduced—these are influential cases that improve/worsen overall model fit based on their presence in the sample. We conclude with a discussion on the utility of detecting influential cases in SEM and present recommendations for the use of measures of case influence.     

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。     

自发走神和有意走神及其与元认知的关系

走神包括有意走神和自发走神两种类型,元认知对二者的影响可能不同。研究使用两维度走神量表和元认知-30量表,对国内部分高校学生的走神和元认知(元认知信念、元认知加工和认知自信判断)进行调查,结果显示:(1)走神可以划分为有意走神和自发走神;(2)失控和危险感既能预测自发走神也能预测有意走神,但认知自信只能预测自发走神,认知的自我意识只能预测有意走神。说明元认知对自发走神和有意走神的影响存在差异。     

西方哲学心智转向对心理学的影响

心智哲学是20世纪中末期西方哲学所发生的继语言(义)学转向和语用学转向之后的一次重要转向,它为心理学提供了新的元理论和方法论。(1)为心理学提供了"心智-语言-世界"新的世界观;(2)从哲学角度对人的心理进行了探讨,促进了哲学与心理学的结合并互哺;(3)促使人们对"人是什么"重新审视与理解;(4)引发了对以往心理学尤其是主流心理学的基石——身心二元论的质疑;(5)催生了第二代认知科学、活动主义、情境认知等新取向的兴起。它对心理学有很大启示:第一,人工智能、动物研究等研究是有限度的;第二,应重视身体的作用;第三,应重视人的意向性,注重隐喻分析;第四,应关注人的存在,尤其是生命的意义。     

The Specific Analysis of Structural Equation Models

Conventional structural equation modeling fits a covariance structure implied by the equations of the model. This treatment of the model often gives misleading results because overall goodness of fit tests do not focus on the specific constraints implied by the model. An alternative treatment arising from Pearl's directed acyclic graph theory checks identifiability and lists and tests the implied constraints. This approach is complete for Markov models, but has remained incomplete for models with correlated disturbances. Some new algebraic results overcome the limitations of DAG theory and give a specific form of structural equation analysis that checks identifiability, tests the implied constraints, equation by equation, and gives consistent estimators of the parameters in closed form from the equations. At present the method is limited to recursive models subject to exclusion conditions. With further work, specific structural equation modeling may yield a complete alternative to the present, rather unsatisfactory, global covariance structure analysis.     

Equivalent Structural Equation Models and Group Equality Constraints

This article is concerned with equivalent structural equation models that have been extended to multigroup models. It is shown that imposing cross-group equality constraints upon (a) no parameters or all parameters, or (b) any number of parameters in which the models are identical, preserves the model equivalence property. Alternatively, constraining for equality across groups some of those parameters in which the models differ can yield nonequivalent multiple-group models. The results are illustrated on two-group cognitive intervention data.     

多项式加工树模型在社会心理学中的应用

多项式加工树（multinomial processing tree, MPT）从理论模型出发,使用多项式模型来拟合行为数据并估计理论模型中各个加工过程发生的可能性。该模型能够有效分离和量化不同心理过程,被广泛应用于社会认知研究之中,如态度、刻板印象等。本文首先介绍该模型的基本原理及其实现,并以道德判断为例说明其在社会心理学中的最新应用。最后,总结其对社会心理学研究的意义,即可以作为一种方法提高研究的效度和精度,具有较高的实用价值,并指出其潜在不足。     

How to Generate Non-normal Data for Simulation of Structural Equation Models

A procedure for generating non-normal data for simulation of structural equation models is proposed. A simple transformation of univariate random variables is used for the generation of data on latent and error variables under some restrictions for the elements of the covariance matrices for these variables. Data on the observed variables is then computed from latent and error variables according to the model. It is shown that by controlling univariate skewness and kurtosis on pre-specified random latent and error variables, observed variables can be made to have a relatively wide range of univariate skewness and kurtosis characteristics according to the pre-specified model. Univariate distributions are used for the generation of data which enables a user to choose from a large number of different distributions. The use of the proposed procedure is illustrated for two different structural equation models and it is shown how PRELIS can be used to generate the data.     

Hypothesis Testing and Model Comparison in Two-level Structural Equation Models

One basic and important problem in two-level structural equation modeling is to find a good model for the observed sample data. This article demonstrates the use of the well-known Bayes factor in the Bayesian literature for hypothesis testing and model comparison in general two-level structural equation models. It is shown that the proposed methodology is flexible, and can be applied to situations with a wide variety of nonnested models. Moreover, some problems encountered in using existing methods for goodness-of-fit assessment of the proposed model can be alleviated. An illustrative example with some real data from an AIDS care study is presented.     

论证的形式模型概述及其在哲学上的应用

论证是一个用理由支持观点以及回应其所受攻击的过程。在过去的几十年里,论证已经成为哲学和人工智能研究领域中的一个重要主题。在哲学方面,十九世纪50年代和60年代图尔敏和佩雷尔曼对形式逻辑的批判,促进了非形式逻辑这一学科的产生,它研究推理和论证的非形式模型。在人工智能方面,论证的形式模型也发展成为常识推理和多主体冲突解决的基本模型。本文将讨论后一领域中所研究发展的形式模型如何能够用以澄清一些哲学领域、以及非形式逻辑领域中的理论问题和争议。本文的一个重要观点是,图尔敏和佩雷尔曼时代的形式逻辑只关注数学化的推理,但那些非数学化的推理形式其实同样也能够被形式化。     

On Insensitivity of the Chi-Square Model Test to Nonlinear Misspecification in Structural Equation Models

In this paper, we show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of nonlinear terms in the model. As an example, we consider a regression model with latent variables and interactions terms. Not only the model test has zero power against that type of misspecifications, but even the theoretical (chi-square) distribution of the test is not distorted when severe interaction term misspecification is present in the postulated model. We explain this phenomenon by exploiting results on asymptotic robustness in structural equation models. The importance of this paper is to warn against the conclusion that if a proposed linear model fits the data well according to the chi-quare goodness-of-fit test, then the underlying model is linear indeed; it will be shown that the underlying model may, in fact, be severely nonlinear. In addition, the present paper shows that such insensitivity to nonlinear terms is only a particular instance of a more general problem, namely, the incapacity of the classical chi-square goodness-of-fit test to detect deviations from zero correlation among exogenous regressors (either being them observable, or latent) when the structural part of the model is just saturated.     

潜变量交互效应建模方法演变与简化

综述了近年来加入乘积指标的潜变量交互效应建模方法, 从产生乘积指标的策略、参数约束方法、均值结构与指标中心化的关系三个方面, 讨论了建模方法的简化进程。最后总结出同类方法中比较简洁又不失精确的潜变量交互效应建模方法—— 无需均值结构的无约束方法, 并给出了建模 步骤。     

A Return to Form in the Philosophy of Mind

In recent decades philosophy of mind has undergone a number of important transformations. In the first part of this essay I review a survey of the subject provided by Daniel Dennett some twenty years ago and consider the current state of affairs. Notwithstanding the rise of physicalist causal theories, the field now displays a degree of diversity that suggests disarray. In the second part of the essay I examine three central issues: the nature of persons, of thought, and of action, and present a series of hylomorphic accounts of each.     

结构方程模型中调节效应的标准化估计

回归分析和结构方程分析中,标准化估计对解释模型和比较效应大小有重要作用。对于调节效应模型（或交互效应模型）,通常的标准化估计没有意义。虽然显变量的调节效应模型标准化估计问题已经解决,但潜变量的调节效应模型标准化估计问题复杂得多。本文先介绍回归分析中显变量调节效应模型的标准化估计,然后提出了一种通过参数的原始估计和通常标准化估计来计算潜变量调节效应模型的“标准化”估计的方法,得到的“标准化”估计是尺度不变的,说明可以用“标准化”估计来解释和比较主效应和调节效应     

Structural Equation Models in a Redundancy Analysis Framework With Covariates

A recent method to specify and fit structural equation modeling in the Redundancy Analysis framework based on so-called Extended Redundancy Analysis (ERA) has been proposed in the literature. In this approach, the relationships between the observed exogenous variables and the observed endogenous variables are moderated by the presence of unobservable composites, estimated as linear combinations of exogenous variables. However, in the presence of direct effects linking exogenous and endogenous variables, or concomitant indicators, the composite scores are estimated by ignoring the presence of the specified direct effects.

To fit structural equation models, we propose a new specification and estimation method, called Generalized Redundancy Analysis (GRA), allowing us to specify and fit a variety of relationships among composites, endogenous variables, and external covariates. The proposed methodology extends the ERA method, using a more suitable specification and estimation algorithm, by allowing for covariates that affect endogenous indicators indirectly through the composites and/or directly. To illustrate the advantages of GRA over ERA we propose a simulation study of small samples. Moreover, we propose an application aimed at estimating the impact of formal human capital on the initial earnings of graduates of an Italian university, utilizing a structural model consistent with well-established economic theory.     

Reliability of Summed Item Scores Using Structural Equation Modeling: An Alternative to Coefficient Alpha

A method is presented for estimating reliability using structural equation modeling (SEM) that allows for nonlinearity between factors and item scores. Assuming the focus is on consistency of summed item scores, this method for estimating reliability is preferred to those based on linear SEM models and to the most commonly reported estimate of reliability, coefficient alpha.