Confirmation bias in structural equation modeling

In this article, a theoretical and philosophical revision of the concept of fit in structural equation modeling and its relation to a confirmation bias is developed. The neutral character of the fit indexes regarding this issue is argued, yielding the conclusion that the creation of new indexes is not a viable protection against confirmation bias. This protection relies on the model modification strategy and the behavior of scientists, rather than on mathematical or computational statistics. The differentiation between two sets of overidentifying constraints and two dimensions for nested models is introduced, leading to a general model‐modification strategy based on the framework of Popper's view of science.     

Errors of inference in structural equation modeling

Although structural equation modeling (SEM) is one of the most comprehensive and flexible approaches to data analysis currently available, it is nonetheless prone to researcher misuse and misconceptions. This article offers a brief overview of the unique capabilities of SEM and discusses common sources of user error in drawing conclusions from these analyses. We make recommendations to guide proper analytical practices and appropriate inferences and provide references for more advanced study. © 2007 Wiley Periodicals, Inc. Psychol Schs 44: 461–470, 2007.     

Issues in applied structural equation modeling research

When using the popular structural equation modeling (SEM) methodology, the issues of sample size, method of parameter estimation, assessment of model fit, and capitalization on chance are of great importance in the process of evaluating the results of an empirical study. We focus first on implications of the large‐sample theory underlying applications of the methodology. The utility for applied contexts of the asymptotically distribution‐free parameter estimation and model testing method is discussed next. We then argue for wider use of a recently developed, non conventional model‐fit assessment strategy in SEM. We conclude by discussing the issue of capitalization on chance, primarily in situations in which exploratory and confirmatory analyses are conducted on the same data set.     

Effects of sample size,estimation methods,and model specification on structural equation modeling fit indexes

A Monte Carlo simulation study was conducted to investigate the effects on structural equation modeling (SEM) fit indexes of sample size, estimation method, and model specification. Based on a balanced experimental design, samples were generated from a prespecified population covariance matrix and fitted to structural equation models with different degrees of model misspecification. Ten SEM fit indexes were studied. Two primary conclusions were suggested: (a) some fit indexes appear to be noncomparable in terms of the information they provide about model fit for misspecified models and (b) estimation method strongly influenced almost all the fit indexes examined, especially for misspecified models. These 2 issues do not seem to have drawn enough attention from SEM practitioners. Future research should study not only different models vis‐à‐vis model complexity, but a wider range of model specification conditions, including correctly specified models and models specified incorrectly to varying degrees.     

A review of using partial least square structural equation modeling in e-learning research

Partial least squares structural equation modeling (PLS-SEM) has become a key multivariate statistical modeling technique that educational researchers frequently use. This paper reviews the uses of PLS-SEM in 16 major e-learning journals, and provides guidelines for improving the use of PLS-SEM as well as recommendations for future applications in e-learning research. A total of 53 articles using PLS-SEM published in January 2009–August 2019 are reviewed. We assess these published applications in terms of the following key criteria: reasons for using PLS-SEM, model characteristics, sample characteristics, model evaluations and reporting. Our results reveal that small sample size and nonnormal data are the first two major reasons for using PLS-SEM. Moreover, we have identified how to extend the applications of PLS-SEM in the e-learning research field.     

On the growth of structural equation modeling in psychological journals

This study investigates the distribution of technical and substantive structural equation modeling articles (SEM) that were published in psychological journals from 1987 to 1994. An inspection of more than 1050 abstracts on PsycLit 1987–1995 (PsycINFO, 1973–1995) revealed a number of clear trends: (a) an increase by year of articles concerned with SEM, (b) an increase in the number of journals that publish structural equation modeling articles, (c) a relatively stable output of technical articles across years, and (d) an increase of substantive articles across years. Furthermore, when the substantive articles are classified as either causal models or confirmatory factor analyses, a similar “growth” trend across years occurs for both categories. We further inspected the growth trend by considering the ratio of SEM articles to the total number of psychology articles and by comparing these results to distributions of analysis of variance, multivariate analysis of variance, regression, and factor analyses articles for the period of 1973 to 1994.     

Simultaneous study of individual and group patterns of latent longitudinal change using structural equation modeling

This article utilizes structural equation modeling for purposes of simultaneous study of individual and group latent change patterns on several longitudinally assessed variables. The approach is based on a special case of the comprehensive latent curve analysis by Meredith and Tisak (1990). Substantively interesting aspects of individual and group growth curves, as well as the interrelations among their patterns, are parameterized at the latent ability level. The method is illustrated on data from a two‐group study by Baltes, Dittmann‐Kohli, and Kliegl (1986).     

Using structural equation modeling to fit models incorporating principal components

The aim of this article is to consider models incorporating principal components from the perspective of structural equation modeling. These models include the principal component analysis of patterned matrices, multiple analysis of variance based on principal components, and multigroup principal component analysis. We demonstrate that these models can be fit readily using the programs LISREL 8 and Mx. The models and certain extensions are discussed, and several illustrations are given.     

Using structural equation modeling techniques to evaluate HIV risk models

Structural equation modeling (SEM) techniques were used to compare 5 methods of assessing HIV/AIDS sexual risk in a large prediction model. These were: (a) multiple measures; (b) a single latent factor; (c) modifying the computation of the dependent variables used in Methods 1 and 2 to weight sexual encounters by specific partner risk; (d) use of risk composites, obtained by multiplying number of sexual partners by number of occasions of unprotected sex; and (e) use of risk indexes that assign a number based on responses to general questions about risk behaviors. Data from 452 at‐risk women from a New England community were analyzed in 5 versions of an HIV/AIDS sexual risk prediction model. Models were compared in terms of SEM empirical fit indexes (x² [df], average absolute standardized residuals, and Comparative Fit Index); significant paths, explained variance, theoretical fit, and simplicity. Results indicate that: (a) multiple measures and latent factor models are preferable to all others by each of the standards of comparison, (b) in the composite dependent variable models, including information about the partners' number of partners provided little additional explained variance beyond knowing the number of occasions of unprotected sex, and (c) dependent measures that did not remain close to Centers for Disease Control criteria may not be adequately predicting HIV/AIDS sexual risk. Several recommendations are presented for selecting an appropriate conceptualization of HIV/AIDS sexual risk.     

A review of the mx computer program for structural equation modeling

Mx. Michael C. Neale, Virginia Institute for Psych and Behavioral Genetics, Box 980126, Richmond, VA 23298. Freeware, ftp: neale@gems.vcu.edu; http: \\www.griffin.vcu.edu\mx. Mx is available for IBM, Mac, UNIX, and VMS platforms.     

Cultural,social, and economic capital constructs in international assessments: an evaluation using exploratory structural equation modeling

The article employs exploratory structural equation modeling (ESEM) to evaluate constructs of economic, cultural, and social capital in international large-scale assessment (LSA) data from the Progress in International Reading Literacy Study (PIRLS) 2006 and the Programme for International Student Assessment (PISA) 2009. ESEM integrates the theory-generating approach of exploratory factor analysis (EFA) and theory-testing approach of confirmatory factor analysis (CFA). It relaxes the zero-loading restriction in CFA, allowing items to load on different factors simultaneously, and it provides measurement invariance tests across countries not available in EFA. A main criticism of international LSA studies is the extended use of indicators poorly grounded in theory, like socioeconomic status, that prevent the study of mechanisms underlying associations with student outcomes. This article contributes to addressing this criticism by providing statistical criteria to evaluate the fit of well-defined sociological constructs with the empirical data.     

Using the friedman method of ranks for model comparison in structural equation modeling

Empirical researchers maximize their contribution to theory development when they compare alternative theory‐inspired models under the same conditions. Yet model comparison tools in structural equation modeling—χ² difference tests, information criterion measures, and screening heuristics—have significant limitations. This article explores the use of the Friedman method of ranks as an inferential procedure for evaluating competing models. This approach has attractive properties, including limited reliance on sample size, limited distributional assumptions, an explicit multiple comparison procedure, and applicability to the comparison of nonnested models. However, this use of the Friedman method raises important issues regarding the lack of independence of observations and the power of the test.     

The equal correlation baseline model for comparative fit assessment in structural equation modeling

In this article I describe and evaluate an alternative baseline model for comparative fit assessment of structural equation models and compare it to the standard “null” baseline model. The new “equal correlation” baseline model constrains all variables to have equal, rather than zero, correlations, whereas all variances are free. The new baseline model reflects the reality of atheoretical background correlation in nonex‐perimental data sets, and it improves the ability of comparative fit indices to distinguish between better and worse target models. It also helps to preserve the statistical link between these indices and the noncentral χ² distribution. Also, computing the same comparative fit indices using different baseline models will provide more information about model fit than computing multiple comparative fit indices using the same baseline. I also point out some limitations of the proposed baseline model.     

Teacher self-efficacy,instructional quality,and student motivational beliefs: An analysis using multilevel structural equation modeling

Teacher self-efficacy (TSE) is one of the most salient motivational characteristics that is assumed to affect teachers’ instructional quality and student motivational beliefs. However, discussions of these associations have primarily been often primarily conceptual and/or based on empirical research that has suffered from methodological shortcomings. Therefore, the aim of this study was to examine the relationships between TSE, instructional quality (i.e., classroom management, cognitive activation, and supportive climate) and student motivational beliefs (i.e., self-efficacy and intrinsic motivation) by using responses from both teachers and students and implementing a sophisticated doubly latent multilevel structural equation modeling approach. A total of 94 high school teachers and their 2087 students participated in the study. The results demonstrated that, at the class level, TSE was positively related to the three dimensions of instructional quality but not to student motivational beliefs. As expected, instructional quality was positively related to student motivational beliefs.     

Morphological awareness and bilingual word learning: a longitudinal structural equation modeling study

This longitudinal study examined the contribution of morphological awareness to bilingual word learning of Malay–English bilingual children in Singapore where English is the medium of instruction. Participants took morphological awareness and lexical inference tasks in both English and Malay twice with an interval of about half a year, the first time at the end of Grade 3 (Time 1) and the second time at the end of the first semester of Grade 4 (Time 2). Structural equation modeling (SEM) analyses revealed that within both languages, morphological awareness significantly predicted lexical inference at Time 1 as well as Time 2, and the contribution also became strengthened over time. Cross-linguistic SEM analyses showed that concurrently at both Time 1 and Time 2, English morphological awareness only had a significant indirect effect on Malay lexical inference. The exact indirect relationships, however, varied between Time 1 and Time 2. In addition, an indirect effect of Time 1 English morphological awareness on Time 2 Malay lexical inference also surfaced. These findings suggest concurrent as well as longitudinal cross-linguistic transfer of morphological awareness from English to Malay.     

Theoretical and technical contributions to structural equation modeling: An updated annotated bibliography

Theoretical and technical research in structural equation modeling (SEM) focuses on the procedures per se rather than on substantive applications of the procedures. An earlier bibliography annotated nearly 300 technical publications about latent variable models. Since that bibliography was published in 1991, there has been a distinct surge in theoretical‐technical publications, organized around model evaluation, multifaceted extensions to levels, groups, and occasions, ordinal level data, statistical power, categorical data, and new computer programs (Mx, MECOSA, RAMONA, SEPath). This article updates the earlier bibliography to acknowledge the growth of more specialized refinements of SEM and to guide developers, researchers, and instructors. As an indicator of the surge in this literature, over 320 new publications are annotated in this version within a 9‐part categorization system. The groupings were selected to be reasonably exhaustive and not too extensive, resulting in this set: (a) Model Specification and Identification, (b) Model Estimation (including asymptotics), (c) Model Testing, Evaluation, and Modification, d) Monte Carlo/Simulation, (e) Reviews and Critiques/Debates, (0 Introductory and Pedagogical, (g) Philosophical, (h) Special Purpose Models (e.g., multitrait‐multimethod, multilevel, behavior genetics, developmental/change), and (i) Computer Programs and Programming.     

Investigating the theoretical structure of the DAS‐II core battery at school age using Bayesian structural equation modeling

Bayesian structural equation modeling (BSEM) was used to investigate the latent structure of the Differential Ability Scales—Second Edition core battery using the standardization sample normative data for ages 7–17. Results revealed plausibility of a three‐factor model, consistent with publisher theory, expressed as either a higher‐order (HO) or a bifactor (BF) model. The results also revealed an alternative structure with the best model fit, a two‐factor BF model with Matrices (MA) and Sequential and Quantitative Reasoning (SQ) loading on g only with no respective group factor loading. This was only the second study to use BSEM to investigate the structure of a commercial ability test and the first to use a large normative sample and the specification of both approximate zero cross‐loadings and correlated residual terms. It is believed that the results produced from the current study will advance the field's understanding of not only the factor structure of the DAS‐II core battery but also the potential utility of BSEM in psychometric investigations of intelligence test structures.     

Examining technology acceptance of pre-service mathematics teachers in Turkey: A structural equation modeling approach

Education and Information Technologies - Among teacher beliefs, technology acceptance has a crucial role in effective technology integration into teaching. There is a need to examine the factors...