Psychometric Methodologies and Testing

Evaluating Structural Equation Models with Unobservable Variables and Measurement Error

The statistical tests used in the analysis of structural equation models with unobservable variables and measurement error are examined. A drawback of the commonly applied chi square test, in addition to the known problems related to sample size and power, is that it may indicate an increasing correspondence between the hypothesized model and the observed data as both the measurement properties and the relationship between constructs decline. Further, and contrary to common assertion, the risk of making a Type II error can be substantial even when the sample size is large. Moreover, the present testing methods are unable to assess a model's explanatory power. To overcome these problems, the authors develop and apply a testing system based on measures of shared variance within the structural model, measurement model, and overall model.

Evaluating Structural Equation Models with Unobservable Variables and Measurement Error

The statistical tests used in the analysis of structural equation models with unobservable variables and measurement error are examined. A drawback of the commonly applied chi square test, in addit...

Structural equation modeling in practice: A review and recommended two-step approach.

In this article, we provide guidance for substantive researchers on the use of structural equation modeling in practice for theory testing and development. We present a comprehensive, two-step modeling approach that employs a series of nested models and sequential chi-square difference tests. We discuss the comparative advantages of this approach over a one-step approach. Considerations in specification, assessment of fit, and respecification of measurement models using confirmatory factor analysis are reviewed. As background to the two-step approach, the distinction between exploratory and confirmatory analysis, the distinction between complementary approaches for theory testing versus predictive application, and some developments in estimation methods also are discussed.

Principles and Practice of Structural Equation Modeling

Emphasizing concepts and rationale over mathematical minutiae, this is the most widely used, complete, and accessible structural equation modeling (SEM) text. Continuing the tradition of using real data examples from a variety of disciplines, the significantly revised fourth edition incorporates recent developments such as Pearl's graphing theory and the structural causal model (SCM), measurement invariance, and more. Readers gain a comprehensive understanding of all phases of SEM, from data collection and screening to the interpretation and reporting of the results. Learning is enhanced by exercises with answers, rules to remember, and topic boxes. The companion website supplies data, syntax, and output for the book's examples--now including files for Amos, EQS, LISREL, Mplus, Stata, and R (lavaan). New to This Edition •Extensively revised to cover important new topics: Pearl's graphing theory and the SCM, causal inference frameworks, conditional process modeling, path models for longitudinal data, item response theory, and more. •Chapters on best practices in all stages of SEM, measurement invariance in confirmatory factor analysis, and significance testing issues and bootstrapping. •Expanded coverage of psychometrics. •Additional computer tools: online files for all detailed examples, previously provided in EQS, LISREL, and Mplus, are now also given in Amos, Stata, and R (lavaan). •Reorganized to cover the specification, identification, and analysis of observed variable models separately from latent variable models. Pedagogical Features •Exercises with answers, plus end-of-chapter annotated lists of further reading. •Real examples of troublesome data, demonstrating how to handle typical problems in analyses. •Topic boxes on specialized issues, such as causes of nonpositive definite correlations. •Boxed rules to remember. •Website promoting a learn-by-doing approach, including syntax and data files for six widely used SEM computer tools.

A new criterion for assessing discriminant validity in variance-based structural equation modeling

Discriminant validity assessment has become a generally accepted prerequisite for analyzing relationships between latent variables. For variance-based structural equation modeling, such as partial least squares, the Fornell-Larcker criterion and the examination of cross-loadings are the dominant approaches for evaluating discriminant validity. By means of a simulation study, we show that these approaches do not reliably detect the lack of discriminant validity in common research situations. We therefore propose an alternative approach, based on the multitrait-multimethod matrix, to assess discriminant validity: the heterotrait-monotrait ratio of correlations. We demonstrate its superior performance by means of a Monte Carlo simulation study, in which we compare the new approach to the Fornell-Larcker criterion and the assessment of (partial) cross-loadings. Finally, we provide guidelines on how to handle discriminant validity issues in variance-based structural equation modeling.

A 12-Item Short-Form Health Survey

Regression methods were used to select and score 12 items from the Medical Outcomes Study 36-Item Short-Form Health Survey (SF-36) to reproduce the Physical Component Summary and Mental Component Summary scales in the general US population (n=2,333). The resulting 12-item short-form (SF-12) achieved multiple R squares of 0.911 and 0.918 in predictions of the SF-36 Physical Component Summary and SF-36 Mental Component Summary scores, respectively. Scoring algorithms from the general population used to score 12-item versions of the two components (Physical Components Summary and Mental Component Summary) achieved R squares of 0.905 with the SF-36 Physical Component Summary and 0.938 with SF-36 Mental Component Summary when cross-validated in the Medical Outcomes Study. Test-retest (2-week)correlations of 0.89 and 0.76 were observed for the 12-item Physical Component Summary and the 12-item Mental Component Summary, respectively, in the general US population (n=232). Twenty cross-sectional and longitudinal tests of empirical validity previously published for the 36-item short-form scales and summary measures were replicated for the 12-item Physical Component Summary and the 12-item Mental Component Summary, including comparisons between patient groups known to differ or to change in terms of the presence and seriousness of physical and mental conditions, acute symptoms, age and aging, self-reported 1-year changes in health, and recovery for depression. In 14 validity tests involving physical criteria, relative validity estimates for the 12-item Physical Component Summary ranged from 0.43 to 0.93 (median=0.67) in comparison with the best 36-item short-form scale. Relative validity estimates for the 12-item Mental Component Summary in 6 tests involving mental criteria ranged from 0.60 to 107 (median=0.97) in relation to the best 36-item short-form scale. Average scores for the 2 summary measures, and those for most scales in the 8-scale profile based on the 12-item short-form, closely mirrored those for the 36-item short-form, although standard errors were nearly always larger for the 12-item short-form.

On the Evaluation of Structural Equation Models

Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification.

This study evaluated the sensitivity of maximum likelihood (ML)-, generalized least squares (GLS)-, and asymptotic distribution-free (ADF)-based fit indices to model misspecification, under conditions that varied sample size and distribution. The effect of violating assumptions of asymptotic robustness theory also was ex-amined. Standardized root-mean-square residual (SRMR) was the most sensitive index to models with misspecified factor covariance(s), and Tucker-Lewis Index (1973; TLI), Bollen's fit index (1989; BL89), relative noncentrality index (RNI), comparative fit index (CFI), and the ML- and GLS-based gamma hat, McDonald's centrality index (1989; Me), and root-mean-square error of approximation (RMSEA) were the most sensitive indices to models with misspecified factor loadings. With ML and GLS methods, we recommend the use of SRMR, supple-mented by TLI, BL89, RNI, CFI, gamma hat, Me, or RMSEA (TLI, Me, and RMSEA are less preferable at small sample sizes). With the ADF method, we recommend the use of SRMR, supplemented by TLI, BL89, RNI, or CFI. Finally, most of the ML-based fit indices outperformed those obtained from GLS and ADF

Quality criteria were proposed for measurement properties of health status questionnaires

Structural Equation Modelling: Guidelines for Determining Model Fit

The following paper presents current thinking and research on fit indices for structural equation modelling. The paper presents a selection of fit indices that are widely regarded as the most informative indices available to researchers. As well as outlining each of these indices, guidelines are presented on their use. The paper also provides reporting strategies of these indices and concludes with a discussion on the future of fit indices.

Mixed-effects modeling with crossed random effects for subjects and items

A Beginner's Guide to Structural Equation Modeling

Noted for its crystal clear explanations, this book is considered the most comprehensive introductory text to structural equation modeling (SEM). Noted for its thorough review of basic concepts and a wide variety of models, this book better prepares readers to apply SEM to a variety of research questions. Programming details and the use of algebra are kept to a minimum to help readers easily grasp the concepts so they can conduct their own analysis and critique related research. Featuring a greater emphasis on statistical power and model validation than other texts, each chapter features key concepts, examples from various disciplines, tables and figures, a summary, and exercises. Highlights of the extensively revised 4th edition include: -Uses different SEM software (not just Lisrel) including Amos, EQS, LISREL, Mplus, and R to demonstrate applications. -Detailed introduction to the statistical methods related to SEM including correlation, regression, and factor analysis to maximize understanding (Chs. 1 – 6). -The 5 step approach to modeling data (specification, identification, estimation, testing, and modification) is now covered in more detail and prior to the modeling chapters to provide a more coherent view of how to create models and interpret results (ch. 7). -More discussion of hypothesis testing, power, sampling, effect sizes, and model fit, critical topics for beginning modelers (ch. 7). - Each model chapter now focuses on one technique to enhance understanding by providing more description, assumptions, and interpretation of results, and an exercise related to analysis and output (Chs. 8 -15). -The use of SPSS AMOS diagrams to describe the theoretical models. -The key features of each of the software packages (Ch. 1). -Guidelines for reporting SEM research (Ch. 16). -www.routledge.com/9781138811935 which provides access to data sets that can be used with any program, links to other SEM examples, related readings, and journal articles, and more. Reorganized, the new edition begins with a more detailed introduction to SEM including the various software packages available, followed by chapters on data entry and editing, and correlation which is critical to understanding how missing data, non-normality, measurement, and restriction of range in scores affects SEM analysis. Multiple regression, path, and factor models are then reviewed and exploratory and confirmatory factor analysis is introduced. These chapters demonstrate how observed variables share variance in defining a latent variables and introduce how measurement error can be removed from observed variables. Chapter 7 details the 5 SEM modeling steps including model specification, identification, estimation, testing, and modification along with a discussion of hypothesis testing and the related issues of power, and sample and effect sizes.Chapters 8 to 15 provide comprehensive introductions to different SEM models including Multiple Group, Second-Order CFA, Dynamic Factor, Multiple-Indicator Multiple-Cause, Mixed Variable and Mixture, Multi-Level, Latent Growth, and SEM Interaction Models. Each of the 5 SEM modeling steps is explained for each model along with an application. Chapter exercises provide practice with and enhance understanding of the analysis of each model. The book concludes with a review of SEM guidelines for reporting research. Designed for introductory graduate courses in structural equation modeling, factor analysis, advanced, multivariate, or applied statistics, quantitative techniques, or statistics II taught in psychology, education, business, and the social and healthcare sciences, this practical book also appeals to researchers in these disciplines. Prerequisites include an introduction to intermediate statistics that covers correlation and regression principles.

A Beginner's Guide to Structural Equation Modeling

The second edition features: a CD with all of the book's Amos, EQS, and LISREL programs and data sets; new chapters on importing data issues related to data editing and on how to report research; an updated introduction to matrix notation and programs that illustrate how to compute these calculations; many more computer program examples and chapter exercises; and increased coverage of factors that affect correlation, the 4-step approach to SEM and hypothesis testing, significance, power, and sample size issues. The new edition's expanded use of applications make this book ideal for advanced students and researchers in psychology, education, business, health care, political science, sociology, and biology. A basic understanding of correlation is assumed and an understanding of the matrices used in SEM models is encouraged.