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.     

How the 2SLS/IV estimator can handle equality constraints in structural equation models: A system‐of‐equations approach

Parameters in structural equation models are typically estimated using the maximum likelihood (ML) approach. Bollen (1996) proposed an alternative non‐iterative, equation‐by‐equation estimator that uses instrumental variables. Although this two‐stage least squares/instrumental variables (2SLS/IV) estimator has good statistical properties, one problem with its application is that parameter equality constraints cannot be imposed. This paper presents a mathematical solution to this problem that is based on an extension of the 2SLS/IV approach to a system of equations. We present an example in which our approach was used to examine strong longitudinal measurement invariance. We also investigated the new approach in a simulation study that compared it with ML in the examination of the equality of two latent regression coefficients and strong measurement invariance. Overall, the results show that the suggested approach is a useful extension of the original 2SLS/IV estimator and allows for the effective handling of equality constraints in structural equation models.     

The factor structure and factorial invariance of the 12-item General Health Questionnaire (GHQ-12) across time: evidence from two community-based samples

This study provides new knowledge about the factor structure of the 12-item General Health Questionnaire (GHQ-12; D. Goldberg, 1972) through the application of confirmatory factor analysis to longitudinal data, thereby enabling investigation of the factor structure, its invariance across time, and the rank-order stability of the factors. Two community-based longitudinal adult samples with 1-year (n = 640) and 6-year (n = 330) follow-up times were studied. As a result, the correlated 3-factor model (i.e., Anxiety/Depression, Social Dysfunction, and Loss of Confidence) showed a better fit with both samples than the alternative models. The correlated 3-factor structure was also relatively invariant across time in both samples, indicating that the scale has good construct validity. The rank-order stabilities of the factors were low across time, which suggests that the GHQ-12 measures temporal mental state.     

The Eating Attitudes Test-26 Revisited using Exploratory Structural Equation Modeling

Most previous studies have failed to replicate the original factor structure of the 26-item version of the Eating Attitudes Test (EAT-26) among community samples of adolescents. The main objective of the present series of four studies (n?=?2178) was to revisit the factor structure of this instrument among mixed gender community samples of adolescents using both exploratory structural equation modeling (ESEM) and confirmatory factor analysis (CFA). First, results from the ESEM analyses provided satisfactory goodness-of-fit statistics and reliability coefficients for a six-factor model of the EAT with 18 items (EAT-18) closely corresponding to the original seven-factor structure proposed for the 40-item version of the EAT. Second, these analyses were satisfactorily replicated among a new sample of community adolescents using CFA. The results confirmed the factor loading and intercept invariance of this model across gender and age groups (i.e., early and late adolescence), as well as the complete invariance of the EAT-18 measurement model between ethnicities (i.e., European versus African origins) and across weight categories (i.e., underweight, normal weight and overweight). Finally, the last study provided support for convergent validity of the EAT-18 with the Eating Disorder Inventory and with instruments measuring global self-esteem, physical appearance, social physique anxiety and fear of negative appearance evaluation.     

Transfer to Derived Sample-comparison Relations by Pigeons Following Many-to-one versus One-to-many Matching with Identical Training Relations

Separate groups of pigeons learned the same three sets of sample-comparison relations across two phases of conditional discrimination training. For one group, that training consisted of multiple-sample, single-comparison (A-X, B-X) matching-to-sample followed by a second matching task in which two of the original samples were matched to new comparisons (A-Y). For the other group, initial training consisted of single-sample, multiple-comparison (A-X, A-Y) matching-to-sample followed by a second task in which two of the original comparisons were matched to new samples (B-X). Both groups were then tested on the same set of derived sample-comparison relations (B-Y). Transfer to these derived relations was evident following the multiple-sample, single-comparison training sequence but not following the single-sample, multiple-comparison sequence. Apparently, the emergence of new conditional relations in pigeons depends upon the order in which the component conditional discriminations are learned—a result predictable from Hull's (1939) analysis of secondary stimulus generalization.     

新世纪20年国内心理统计方法研究回顾

新世纪头20年, 国内心理学11本专业期刊一共发表了213篇统计方法研究论文。研究范围主要包括以下10类(按论文篇数排序)：结构方程模型、测验信度、中介效应、效应量与检验力、纵向研究、调节效应、探索性因子分析、潜在类别模型、共同方法偏差和多层线性模型。对各类做了简单的回顾与梳理。结果发现, 国内心理统计方法研究的广度和深度都不断增加, 研究热点在相互融合中共同发展; 但综述类论文比例较大, 原创性研究论文比例有待提高, 研究力量也有待加强。     

Full-Time versus Part-Time Employees: Understanding the Links between Work Status, the Psychological Contract, and Attitudes

Research findings comparing the work attitudes of full-time and part-time employees have been inconsistent and inconclusive. Furthermore, empirical studies have tended to be atheoretical, and there are few convincing psychological explanations to explain differences where found. This article tests the psychological contract as an explanatory framework for attitudinal differences across work status (i.e., whether employed on a part-time or full-time basis). The model is tested across samples from two different organizations using structural equation modeling. The analysis reveals that part-time and full-time employees differed on a number of attitudes and that psychological contract fulfillment could be used to explain differences in certain attitudes (e.g., satisfaction) but not others (e.g., affective commitment). Analyses also show that the relationships between psychological contract fulfillment and outcomes were rarely moderated by work status, suggesting that part-time employees will respond in a similar way as full-time employees to adjustments in their psychological contract.     

单维项目因素分析：CCFA与IRT估计方法的比较

当观测指标变量为二分分类数据时,传统的因素分析方法不再适用。作者简要回顾了SEM框架下的分类数据因素分析模型和IRT框架下的测验题目和潜在能力的关系模型,并对两种框架下主要采用的参数估计方法进行了总结。通过两个模拟研究,比较了SEM框架下GLSc和MGLSc估计方法与IRT框架下MML/EM估计方法的差异。研究结果表明：（1）三种方法中,GLSc得到参数估计的偏差最大,MGLSc和MML/EM估计方法相差不大;（2）随着样本量增大,各种项目参数估计的精度均提高;（3）项目因素载荷和难度估计的精度受测验长度的影响;（4）项目因素载荷和区分度估计的精度受总体因素载荷（区分度）高低的影响;（5）测验项目中阈值的分布会影响参数估计的精度,其中受影响最大的是项目区分度。（6）总体来看,SEM框架下的项目参数估计精度较IRT框架下项目参数估计的精度高。此外,文章还将两种方法在实际应用中应该注意的问题提供了一些建议。     

贝叶斯结构方程模型及其研究现状

在心理学研究中结构方程模型(Structural Equation Modeling, SEM)被广泛用于检验潜变量间的因果效应, 其估计方法有频率学方法(如, 极大似然估计)和贝叶斯方法两类。近年来由于贝叶斯统计的流行及其在结构方程建模中易于处理小样本、缺失数据及复杂模型等方面的优势, 贝叶斯结构方程模型发展迅速, 但其在国内心理学领域的应用不足。主要介绍了贝叶斯结构方程模型的方法基础和优良特性, 及几类常用的贝叶斯结构方程模型及其应用现状, 旨在为应用研究者介绍新的研究工具。     

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.     

PERCEIVED JOB CHARACTERISTICS AND JOB SATISFACTION: AN EXAMINATION OF RECIPROCAL CAUSATION

The following four assumptions were tested (a) satisfaction with job/task events and perceptions of job challenge, autonomy, and importance are direct, reciprocal causes of each other; (b) job perceptions are also caused directly by situation attributes, although perceptual distortions resulting for individual dispositions must also be considered; (c) job satisfaction is also cognitively consistent with (i.e., caused by) individual dispositions, although these individual dispositions are generally different from those associated with job perceptions; and (d) individuals reply on job perceptions, and not situational attributes, for information in formulating job satisfaction attitudes. The assumptions are tested on a sample of nonsupervisory subjects ( n = 642) from divergent work environments (e.g., production-lines and a computer software department). A nonrecursive, structural equation analysis, combined with tests of logical consistency, supported the assumptions above. The results were employed to recommend changes in current perspectives regarding perceptual/affective dichotomies and unidirectional causal models and moderator models that link job perceptions to job satisfaction.     

多维测验项目参数的估计：基于SEM与MIRT方法的比较

作者简要回顾了SEM框架下分类数据因素分析(CCFA)模型和MIRT框架下测验题目和潜在能力的关系模型, 对两种框架下的主要参数估计方法进行了总结。通过模拟研究, 比较了SEM框架下WLSc和WLSMV估计方法与MIRT框架下MLR和MCMC估计方法的差异。研究结果表明：(1) WLSc得到参数估计的偏差最大, 且存在参数收敛的问题; (2)随着样本量增大, 各种项目参数估计的精度均提高, WLSMV方法与MLR方法得到的参数估计精度差异很小, 大多数情况下不比MCMC方法差; (3)除WLSc方法外, 随着每个维度测验题目的增多参数估计的精度逐渐增高; (4)测验维度对区分度参数和难度参数的影响较大, 而测验维度对项目因素载荷和阈值的影响相对较小; (5)项目参数的估计精度受项目测量维度数的影响, 只测量一个维度的项目参数估计精度较高。另外文章还对两种方法在实际应用中应该注意的问题提供了一些建议。     

On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints

The authors show how the use of inequality constraints on parameters in structural equation models may affect the distribution of the likelihood ratio test. Inequality constraints are implicitly used in the testing of commonly applied structural equation models, such as the common factor model, the autoregressive model, and the latent growth curve model, although this is not commonly acknowledged. Such constraints are the result of the null hypothesis in which the parameter value or values are placed on the boundary of the parameter space. For instance, this occurs in testing whether the variance of a growth parameter is significantly different from 0. It is shown that in these cases, the asymptotic distribution of the chi-square difference cannot be treated as that of a central chi-square-distributed random variable with degrees of freedom equal to the number of constraints. The correct distribution for testing 1 or a few parameters at a time is inferred for the 3 structural equation models mentioned above. Subsequently, the authors describe and illustrate the steps that one should take to obtain this distribution. An important message is that using the correct distribution may lead to appreciably greater statistical power.     

Misspecification in Latent Change Score Models: Consequences for Parameter Estimation,Model Evaluation,and Predicting Change

Latent change score models (LCS) are conceptually powerful tools for analyzing longitudinal data (McArdle & Hamagami, 2001). However, applications of these models typically include constraints on key parameters over time. Although practically useful, strict invariance over time in these parameters is unlikely in real data. This study investigates the robustness of LCS when invariance over time is incorrectly imposed on key change-related parameters. Monte Carlo simulation methods were used to explore the impact of misspecification on parameter estimation, predicted trajectories of change, and model fit in the dual change score model, the foundational LCS. When constraints were incorrectly applied, several parameters, most notably the slope (i.e., constant change) factor mean and autoproportion coefficient, were severely and consistently biased, as were regression paths to the slope factor when external predictors of change were included. Standard fit indices indicated that the misspecified models fit well, partly because mean level trajectories over time were accurately captured. Loosening constraint improved the accuracy of parameter estimates, but estimates were more unstable, and models frequently failed to converge. Results suggest that potentially common sources of misspecification in LCS can produce distorted impressions of developmental processes, and that identifying and rectifying the situation is a challenge.     

Bayesian latent variable models for the analysis of experimental psychology data

In this paper, we address the use of Bayesian factor analysis and structural equation models to draw inferences from experimental psychology data. While such application is non-standard, the models are generally useful for the unified analysis of multivariate data that stem from, e.g., subjects’ responses to multiple experimental stimuli. We first review the models and the parameter identification issues inherent in the models. We then provide details on model estimation via JAGS and on Bayes factor estimation. Finally, we use the models to re-analyze experimental data on risky choice, comparing the approach to simpler, alternative methods.     

Generating Nonnormal Multivariate Data Using Copulas: Applications to SEM

This article develops a procedure based on copulas to simulate multivariate nonnormal data that satisfy a prespecified variance-covariance matrix. The covariance matrix used can comply with a specific moment structure form (e.g., a factor analysis or a general structural equation model). Thus, the method is particularly useful for Monte Carlo evaluation of structural equation models within the context of nonnormal data. The new procedure for nonnormal data simulation is theoretically described and also implemented in the widely used R environment. The quality of the method is assessed by Monte Carlo simulations. A 1-sample test on the observed covariance matrix based on the copula methodology is proposed. This new test for evaluating the quality of a simulation is defined through a particular structural model specification and is robust against normality violations.     

The processing role of structural constraints on the interpretation of pronouns and anaphors

The authors report 6 self-paced word-by-word reading studies of how morphosyntactic agreement, focus status, and the structural constraints of binding theory apply and interact during the online interpretation of pronouns (e.g., him, her) and anaphors (e.g., himself, each other). Previous studies held that structural conditions on coreference work as interpretive filters that impose exceptionless limits on which antecedent candidates can be evaluated by subsequent, content-based processes. These experiments instead support an interactive-parallel-constraint model, in which multiple weighted constraints (including constraints on binding) simultaneously influence the net activation of a candidate during preselection stages of antecedent evaluation. Accordingly, structurally inaccessible candidates can interfere with antecedent selection if they are both prominent in focus structure and gender-number compatible with the pronoun or anaphor.     

Modified Distribution-Free Goodness-of-Fit Test Statistic

Covariance structure analysis and its structural equation modeling extensions have become one of the most widely used methodologies in social sciences such as psychology, education, and economics. An important issue in such analysis is to assess the goodness of fit of a model under analysis. One of the most popular test statistics used in covariance structure analysis is the asymptotically distribution-free (ADF) test statistic introduced by Browne (Br J Math Stat Psychol 37:62–83, 1984). The ADF statistic can be used to test models without any specific distribution assumption (e.g., multivariate normal distribution) of the observed data. Despite its advantage, it has been shown in various empirical studies that unless sample sizes are extremely large, this ADF statistic could perform very poorly in practice. In this paper, we provide a theoretical explanation for this phenomenon and further propose a modified test statistic that improves the performance in samples of realistic size. The proposed statistic deals with the possible ill-conditioning of the involved large-scale covariance matrices.     

On structural models for analyzing change

The recommendation to base the analysis of multi-wave data upon explicit models for change is advocated. Several univariate and multivariate models are described, which emerge from an interaction between the classical test theory and the structural equation modeling approach. The resulting structural models for analyzing change reflect in some of their parameters substantively interesting aspects of intra- and interindividual change in follow-up studies. The models are viewed as an alternative to an ANOVA-based analysis of longitudinal data, and are illustrated on data from a cognitive intervention study of old adults (Bakes et al , 1986). The approach presents a useful means of analyzing change over time, and is applicable for purposes of (latent) growth curve analysis when analysis of variance assumptions are violated (e.g., Schaie & Hertzog, 1982; Morrison, 1976).     

Examining the impact of gender on the factor structure of the Psychopathic Personality Inventory-Revised

Research on the factor structure of psychopathy has yielded mixed results, supporting anywhere from one to three factors. Additionally, most of this research has used all-male samples, and the possibility of structural invariance across gender has not been examined. Using a mixed-gender sample of 360 undergraduates, the factor structure of the Psychopathic Personality Inventory-Revised was examined using confirmatory factor analysis and multiple group analysis. One-, two-, and three-factor models were tested and compared with each other. When males and females were combined, none of the three models provided adequate fit to the data. Multiple group analyses revealed partial invariance across gender for all three models. Model comparison criteria supported use of both the one- and two-factor models, taking into account variable factor structure across gender. The importance of considering structural differences based on biological sex when assessing psychopathic traits is discussed.