Some contributions to efficient statistics in structural models: Specification and estimation of moment structures

Current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments (e.g., means and covariances), and to distribution theory based on multivariate normality. In psychometrics the multinormality assumption is often incorrect, so that statistical tests on parameters, or model goodness of fit, will frequently be incorrect as well. It is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary. Structural representations are developed for generalizations of the Bentler-Weeks, Jöreskog-Keesling-Wiley, and factor analytic models. Some asymptotically distribution-free efficient estimators for such arbitrary structural models are developed. Limited information estimators are obtained as well. The special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail. The argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory, which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds. Many open research areas are described.     

Relationships between linear systems theory and covarian ce structure modeling

It is shown that an important subset of linear systems theory (LST) can be represented as a special case of covariace structure modeling (CSM). Overviews of both LST and CSM are presented, along with an explanation and illustration of their relationship. Possible modifications and extensions of LST are described based on the more general framework of CSM. An LST model where all inputs, state variables, and outputs are latent variables is proposed. The potential use of CSM methodology to carry out model fitting, parameter estimation, and hypothesis testing for certain LST models is discussed.     

Item factor analysis: current approaches and future directions

The rationale underlying factor analysis applies to continuous and categorical variables alike; however, the models and estimation methods for continuous (i.e., interval or ratio scale) data are not appropriate for item-level data that are categorical in nature. The authors provide a targeted review and synthesis of the item factor analysis (IFA) estimation literature for ordered-categorical data (e.g., Likert-type response scales) with specific attention paid to the problems of estimating models with many items and many factors. Popular IFA models and estimation methods found in the structural equation modeling and item response theory literatures are presented. Following this presentation, recent developments in the estimation of IFA parameters (e.g., Markov chain Monte Carlo) are discussed. The authors conclude with considerations for future research on IFA, simulated examples, and advice for applied researchers.     

Structural analysis of covariance and correlation matrices

A general approach to the analysis of covariance structures is considered, in which the variances and covariances or correlations of the observed variables are directly expressed in terms of the parameters of interest. The statistical problems of identification, estimation and testing of such covariance or correlation structures are discussed.Several different types of covariance structures are considered as special cases of the general model. These include models for sets of congeneric tests, models for confirmatory and exploratory factor analysis, models for estimation of variance and covariance components, regression models with measurement errors, path analysis models, simplex and circumplex models. Many of the different types of covariance structures are illustrated by means of real data.1978 Psychometric Society Presidential Address.This research has been supported by the Bank of Sweden Tercentenary Foundation under the project entitledStructural Equation Models in the Social Sciences, Karl G. Jöreskog, project director.     

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。     

General causality orientations are distinct from but related to dispositional traits

This study examines overlaps and distinctions between concepts of individual differences in the five-factor model and self-determination theory. Participants were 223 Danish adults (age M = 43.74; 60.09% women) originating in a national probability sample. Participants completed questionnaires of personality traits (NEO-FFI) and general causality orientations (GCOS). Distinct and overlapping latent models were tested using structural equation modeling, statistical re-sampling, and confirmatory factor analysis. Results indicate that all three causality orientations are distinct from but related to traits. From a perspective of integrative personality psychology, general causality orientations can be conceived of as characteristic adaptations.     

Social psychology of mental health: the social structure and personality perspective

Previous research has revealed a persistent association between social structure and mental health. However, most researchers have focused only on the psychological and psychosocial aspects of that relationship. The present paper indicates the need to include the social and structural bases of distress in our theoretical models. Starting from a general social and psychological model, our research considered the role of several social, environmental, and structural variables (social position, social stressors, and social integration), psychological factors (self-esteem), and psychosocial variables (perceived social support). The theoretical model was tested working with a group of Spanish participants (N = 401) that covered a range of social positions. The results obtained using structural equation modeling support our model, showing the relevant role played by psychosocial, psychological and social, and structural factors. Implications for theory and intervention are discussed.     

The relationship of engagement and job satisfaction in working samples

The present study explored the factor structure of engagement and its relationship with job satisfaction. The authors hypothesize that work engagement comprises 3 constructs: vigor, dedication, and absorption. Using structural equation modeling, the authors analyze data from 3 archival data sets to determine the factor structure of engagement. In addition, they examine the hypothesis that engagement and job satisfaction are separate but related constructs, using structural equation modeling and hierarchical regression. The authors test models in which engagement and job satisfaction items loaded onto a single latent variable and 1 in which they loaded onto 2 separate variables. Results from the confirmatory factor analysis indicate engagement has 3 factors. In addition, confirmatory factor analysis and hierarchical regressions indicate engagement and job satisfaction are separate constructs. Last, hierarchical regressions demonstrated the constructs have different relationships with the areas of work-life scale. Implications for theory and research are discussed.     

Latent variables should remain as such: Evidence from a Monte Carlo study

Use of subject scores as manifest variables to assess the relationship between latent variables produces attenuated estimates. This has been demonstrated for raw scores from classical test theory (CTT) and factor scores derived from factor analysis. Conclusions on scores have not been sufficiently extended to item response theory (IRT) theta estimates, which are still recommended for estimation of relationships between latent variables. This is because IRT estimates appear to have preferable properties compared to CTT, while structural equation modeling (SEM) is often advised as an alternative to scores for estimation of the relationship between latent variables. The present research evaluates the consequences of using subject scores as manifest variables in regression models to test the relationship between latent variables. Raw scores and three methods for obtaining theta estimates were used and compared to latent variable SEM modeling. A Monte Carlo study was designed by manipulating sample size, number of items, type of test, and magnitude of the correlation between latent variables. Results show that, despite the advantage of IRT models in other areas, estimates of the relationship between latent variables are always more accurate when SEM models are used. Recommendations are offered for applied researchers.     

A tutorial on methods for the modeling and analysis of social network data

This article provides a tutorial review of some fundamental ideas and important methods for the modeling of empirical social network data. It describes basic concepts from graph theory and central elements from social network theory. It presents models for the network degree distribution and for network roles and positions, as well as algebraic approaches, before reviewing recent work on statistical methods to analyze social networks, including boot-strap procedures for testing the prevalence of network structures, basic edge- and dyad-independent statistical models, and more recent statistical network models that assume dependence, exponential random graph models and dynamic stochastic actor oriented models. Network social influence models are reviewed. The article concludes with a summary of new developments relating to models for time-ordered transactions.     

Structural Modeling of Measurement Error in Generalized Linear Models with Rasch Measures as Covariates

This paper proposes a structural analysis for generalized linear models when some explanatory variables are measured with error and the measurement error variance is a function of the true variables. The focus is on latent variables investigated on the basis of questionnaires and estimated using item response theory models. Latent variable estimates are then treated as observed measures of the true variables. This leads to a two-stage estimation procedure which constitutes an alternative to a joint model for the outcome variable and the responses given to the questionnaire. Simulation studies explore the effect of ignoring the true error structure and the performance of the proposed method. Two illustrative examples concern achievement data of university students. Particular attention is given to the Rasch model.     

Structural equation modeling: reviewing the basics and moving forward

This tutorial begins with an overview of structural equation modeling (SEM) that includes the purpose and goals of the statistical analysis as well as terminology unique to this technique. I will focus on confirmatory factor analysis (CFA), a special type of SEM. After a general introduction, CFA is differentiated from exploratory factor analysis (EFA), and the advantages of CFA techniques are discussed. Following a brief overview, the process of modeling will be discussed and illustrated with an example using data from a HIV risk behavior evaluation of homeless adults (Stein & Nyamathi, 2000). Techniques for analysis of nonnormally distributed data as well as strategies for model modification are shown. The empirical example examines the structure of drug and alcohol use problem scales. Although these scales are not specific personality constructs, the concepts illustrated in this article directly correspond to those found when analyzing personality scales and inventories. Computer program syntax and output for the empirical example from a popular SEM program (EQS 6.1; Bentler, 2001) are included.     

A three-stage estimation procedure for structural equation models with polytomous variables

This paper is concerned with the analysis of structural equation models with polytomous variables. A computationally efficient three-stage estimator of the thresholds and the covariance structure parameters, based on partition maximum likelihood and generalized least squares estimation, is proposed. An example is presented to illustrate the method.This research was supported in part by a research grant DA01070 from the U.S. Public Health Service. The production assistance of Julie Speckart is gratefully acknowledged.     

Dynamic structural systems under indirect observation: identifiability and estimation aspects from a system theoretic perspective

In this—partly—expository paper the parameter identifiability and estimation of a general dynamic structural model under indirect observation will be considered from a system theoretic perspective. The general dynamic model covers (dynamic) factor analytic models, (dynamic) MIMIC models and Jöreskog's linear structural model as special cases. Its reduced form is—under a slightly different specification—known in system theory and econometrics as the stochastic, stationary version of the state-space model. By using concepts and methods from system theory, such as the observability and controllability concept, the (steady-state) Kalman filter and a general nonlinear ML_estimation procedure known as prediction-error estimation the general dynamic model will be identified. It will be shown that Jöreskog's LISREL-procedure is a special case of the prediction-error estimation procedure.     

Analysis of Interactions and Nonlinear Effects with Missing Data: A Factored Regression Modeling Approach Using Maximum Likelihood Estimation

Abstract

When estimating multiple regression models with incomplete predictor variables, it is necessary to specify a joint distribution for the predictor variables. A convenient assumption is that this distribution is a multivariate normal distribution, which is also the default in many statistical software packages. This distribution will in general be misspecified if predictors with missing data have nonlinear effects (e.g., x²) or are included in interaction terms (e.g., x·z). In the present article, we introduce a factored regression modeling approach for estimating regression models with missing data that is based on maximum likelihood estimation. In this approach, the model likelihood is factorized into a part that is due to the model of interest and a part that is due to the model for the incomplete predictors. In three simulation studies, we showed that the factored regression modeling approach produced valid estimates of interaction and nonlinear effects in regression models with missing values on categorical or continuous predictor variables under a broad range of conditions. We developed the R package mdmb, which facilitates a user-friendly application of the factored regression modeling approach, and present a real-data example that illustrates the flexibility of the software.     

基于结构方程模型的多层调节效应

使用多层线性模型进行调节效应分析在社科领域已常有应用。尽管多层线性模型区分了层1自变量的组间和组内效应、实现了多层调节效应的分解, 仍然存在抽样误差和测量误差。建议在多层结构方程模型框架下, 设置潜变量和多指标来有效校正抽样误差和测量误差。在介绍多层调节SEM分析的随机系数预测法和潜调节结构方程法后, 总结出一套多层调节的SEM分析流程, 通过一个例子来演示如何用Mplus软件进行多层调节SEM分析。随后评述了多层调节效应分析方法在国内心理学的应用现状, 并展望了多层结构方程和多层调节研究的拓展方向。     

SEM with simplicity and accuracy

Professor Iacobucci has provided a useful introduction to the computer program LISREL, as well as to several technical topics in structural equation modeling (SEM). However, SEM has not been synonymous with LISREL for several decades, and focusing on LISREL's 13 Greek matrices and vectors is not the most intuitive way to learn SEM. It is possible today to do model specification via a path diagram without any need for filling in matrix elements. The simplest alternative is based on the Bentler–Weeks model, whose basic concepts are reviewed. Selected additional SEM topics are discussed, including some recent developments and their practical implications. New simulation results on model fit under null and alternative hypotheses are also presented that are consistent with statistical theory but in part seem to contradict those reported by Iacobucci.     

Multilevel modeling: current and future applications in personality research

Traditional statistical analyses can be compromised when data are collected from groups or multiple observations are collected from individuals. We present an introduction to multilevel models designed to address dependency in data. We review current use of multilevel modeling in 3 personality journals showing use concentrated in the 2 areas of experience sampling and longitudinal growth. Using an empirical example, we illustrate specification and interpretation of the results of series of models as predictor variables are introduced at Levels 1 and 2. Attention is given to possible trends and cycles in longitudinal data and to different forms of centering. We consider issues that may arise in estimation, model comparison, model evaluation, and data evaluation (outliers), highlighting similarities to and differences from standard regression approaches. Finally, we consider newer developments, including 3-level models, cross-classified models, nonstandard (limited) dependent variables, multilevel structural equation modeling, and nonlinear growth. Multilevel approaches both address traditional problems of dependency in data and provide personality researchers with the opportunity to ask new questions of their data.     

Nested models of relative judgment: Applications to a similarity averaging model

A theoretical analysis of the Eisler and Ekman (1959) model of similarity judgments for unidimensional continua is presented, based on a general model of relative judgment. This general model assumes that judgments are mediated by perceived relations of pairs of stimuli, that there exists a transformation of the judgmental response that is a function of the sensory ratio of the two stimuli, and that response bias operates in a multiplicative manner. Three structural conditions are presented, each imposing constraints on the structure of observed judgments. The structural conditions define threenested models of relative judgment, with the second a weakened version of the first, and the third a weakened version of the second. The special virtue of the general model is that it is applicable to a variety of judgmental tasks (e.g., ratio estimation, similarity, pair comparison), the key being derivation of theresponse transformation conforming to the structural conditions. The structural conditions thus constitute necessary conditions for several different judgmental models. The theory was first applied with success to ratio estimation judgments (Fagot, 1978), and this paper applies the general model to the Eisler and Ekman similarity “averaging” model. Empirical tests were carried out on published data for pitch, darkness, visual area, and heaviness judgments. Although the strong form of the model presented by Eisler and Ekman was rejected, weakened versions were generally supported by the data. These results were similar to those obtained for ratio estimation (Fagot, 1978), and are interpreted to be very promising for the general model of relative judgment.     

SEM with Missing Data and Unknown Population Distributions Using Two-Stage ML: Theory and Its Application

This article provides the theory and application of the 2-stage maximum likelihood (ML) procedure for structural equation modeling (SEM) with missing data. The validity of this procedure does not require the assumption of a normally distributed population. When the population is normally distributed and all missing data are missing at random (MAR), the direct ML procedure is nearly optimal for SEM with missing data. When missing data mechanisms are unknown, including auxiliary variables in the analysis will make the missing data mechanism more likely to be MAR. It is much easier to include auxiliary variables in the 2-stage ML than in the direct ML. Based on most recent developments for missing data with an unknown population distribution, the article first provides the least technical material on why the normal distribution-based ML generates consistent parameter estimates when the missing data mechanism is MAR. The article also provides sufficient conditions for the 2-stage ML to be a valid statistical procedure in the general case. For the application of the 2-stage ML, an SAS IML program is given to perform the first-stage analysis and EQS codes are provided to perform the second-stage analysis. An example with open- and closed-book examination data is used to illustrate the application of the provided programs. One aim is for quantitative graduate students/applied psychometricians to understand the technical details for missing data analysis. Another aim is for applied researchers to use the method properly.