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Journal ArticleDOI: 10.1080/10705511.2020.1855076

Multilevel analysis of mediation, moderation, and nonlinear effects in small samples, using expected a posteriori estimates of factor scores

02 Mar 2021-Structural Equation Modeling (Routledge)-Vol. 28, Iss: 4, pp 529-546
Abstract: In the analysis of hierarchical data, multilevel structural equation modeling (multilevel SEM) has become the standard in the social sciences. To estimate these models, maximum likelihood (ML) appr...

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7 results found


Open accessJournal ArticleDOI: 10.3390/PSYCH3020012
01 Apr 2021-Psychosomatics
Abstract: Background: Researchers frequently use the responses of individuals in clusters to measure cluster-level constructs. Examples are the use of student evaluations to measure teaching quality, or the use of employee ratings of organizational climate. In earlier research, Stapleton and Johnson (2019) provided advice for measuring cluster-level constructs based on a simulation study with inadvertently confounded design factors. We extended their simulation study using both Mplus and lavaan to reveal how their conclusions were dependent on their study conditions. Methods: We generated data sets from the so-called configural model and the simultaneous shared-and-configural model, both with and without nonzero residual variances at the cluster level. We fitted models to these data sets using different maximum likelihood estimation algorithms. Results: Stapleton and Johnson’s results were highly contingent on their confounded design factors. Convergence rates could be very different across algorithms, depending on whether between-level residual variances were zero in the population or in the fitted model. We discovered a worrying convergence issue with the default settings in Mplus, resulting in seemingly converged solutions that are actually not. Rejection rates of the normal-theory test statistic were as expected, while rejection rates of the scaled test statistic were seriously inflated in several conditions. Conclusions: The defaults in Mplus carry specific risks that are easily checked but not well advertised. Our results also shine a different light on earlier advice on the use of measurement models for shared factors.

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Topics: Test statistic (53%), Population (51%)

3 Citations


Open accessJournal ArticleDOI: 10.1080/00461520.2021.1991799
Lisa Bardach1, Robert M. Klassen2Institutions (2)
Abstract: Recent years have witnessed a burgeoning interest in the study of teacher motivation. Although links between teacher motivation and teacher well-being, commitment to the profession, and other teach...

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3 Citations


Open accessJournal ArticleDOI: 10.3389/FPSYG.2021.612570
Steffen Zitzmann1, Lukas Loreth2Institutions (2)
Abstract: Our outline points out three aspects of a new post-modern methodology in psychology: liberal, pluralistic, and more tolerant: liberal because it rejects rules that are too strict in favor of more freedom in the choice of method, pluralistic because it conveys an “almost anything goes” attitude toward methods, and more tolerant because mutual tolerance among researchers is vital for a pluralism of methods. Psychological phenomena are complex and can best be understood by using different methods. However, to get things working, tolerance must actively be lived. Of course, much depends on our own willingness as researchers but also on the system’s arrangements. Psychology could be more colorful, and we could all have more fun if we were to be more committed to such a methodology.

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2 Citations


Open accessJournal ArticleDOI: 10.3390/PSYCH3030025
30 Jul 2021-Psychosomatics
Abstract: Bayesian modeling using Markov chain Monte Carlo (MCMC) estimation requires researchers to decide not only whether estimation has converged but also whether the Bayesian estimates are well-approximated by summary statistics from the chain. On the contrary, software such as the Bayes module in Mplus, which helps researchers check whether convergence has been achieved by comparing the potential scale reduction (PSR) with a prespecified maximum PSR, the size of the MCMC error or, equivalently, the effective sample size (ESS), is not monitored. Zitzmann and Hecht (2019) proposed a method that can be used to check whether a minimum ESS has been reached in Mplus. In this article, we evaluated this method with a computer simulation. Specifically, we fit a multilevel structural equation model to a large number of simulated data sets and compared different prespecified minimum ESS values with the actual (empirical) ESS values. The empirical values were approximately equal to or larger than the prespecified minimum ones, thus indicating the validity of the method.

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Topics: Markov chain Monte Carlo (60%), Bayesian inference (53%), Bayes' theorem (52%) ... read more

1 Citations


Open accessJournal ArticleDOI: 10.1007/S10648-021-09635-4
Steffen Zitzmann1, Wolfgang Wagner1, Martin Hecht1, Christoph Helm2  +3 moreInstitutions (2)
Abstract: A central question in educational research is how classroom climate variables, such as teaching quality, goal structures, or interpersonal teacher behavior, are related to critical student outcomes, such as students’ achievement and motivation. Student ratings are frequently used to measure classroom climate. When using student ratings to assess classroom climate, researchers first ask students to rate classroom climate characteristics and then aggregate the ratings on the class level. Multilevel latent variable modeling is then used to determine whether class-mean ratings of classroom climate are predictive of student outcomes and to correct for unreliability so that the relations can be estimated without bias. In this article, we adopt an optimal design perspective on this specific strategy. Specifically, after briefly recapping a prominent model in climate research, we show and explain (a) how statistical power can be maximized by choosing optimal numbers of classes and students per class given a fixed budget for conducting a study and (b) how the budget required to achieve a prespecified level of power can be minimized. Moreover, we present an example from research on teaching quality to illustrate the procedures and to provide guidance to researchers who are interested in studying the role of classroom climate. Also, we present a Shiny App that can be used to help find optimal designs for classroom climate studies. The app can be accessed at https://psychtools.shinyapps.io/optimalDesignsClassroomClimate

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59 results found


Open accessBook
James A. Calvin1Institutions (1)
03 Mar 1992-
Abstract: Introduction The Logic of Hierarchical Linear Models Principles of Estimation and Hypothesis Testing for Hierarchical Linear Models An Illustration Applications in Organizational Research Applications in the Study of Individual Change Applications in Meta-Analysis and Other Cases Where Level-1 Variances are Known Three-Level Models Assessing the Adequacy of Hierarchical Models Technical Appendix

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Topics: Marginal model (65%), Statistical hypothesis testing (55%), Multilevel model (54%) ... read more

22,551 Citations


Open accessJournal ArticleDOI: 10.3758/BRM.40.3.879
Abstract: Hypotheses involving mediation are common in the behavioral sciences. Mediation exists when a predictor affects a dependent variable indirectly through at least one intervening variable, or mediator. Methods to assess mediation involving multiple simultaneous mediators have received little attention in the methodological literature despite a clear need. We provide an overview of simple and multiple mediation and explore three approaches that can be used to investigate indirect processes, as well as methods for contrasting two or more mediators within a single model. We present an illustrative example, assessing and contrasting potential mediators of the relationship between the helpfulness of socialization agents and job satisfaction. We also provide SAS and SPSS macros, as well as Mplus and LISREL syntax, to facilitate the use of these methods in applications.

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22,179 Citations


Open accessJournal ArticleDOI: 10.18637/JSS.V048.I02
Abstract: Structural equation modeling (SEM) is a vast field and widely used by many applied researchers in the social and behavioral sciences. Over the years, many software packages for structural equation modeling have been developed, both free and commercial. However, perhaps the best state-of-the-art software packages in this field are still closed-source and/or commercial. The R package lavaan has been developed to provide applied researchers, teachers, and statisticians, a free, fully open-source, but commercial-quality package for latent variable modeling. This paper explains the aims behind the development of the package, gives an overview of its most important features, and provides some examples to illustrate how lavaan works in practice.

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Topics: LISREL (55%), Structural equation modeling (50%)

9,469 Citations


Open accessJournal ArticleDOI: 10.1037/1082-989X.7.4.422
Patrick E. Shrout1, Niall Bolger1Institutions (1)
Abstract: Mediation is said to occur when a causal effect of some variable X on an outcome Y is explained by some intervening variable M. The authors recommend that with small to moderate samples, bootstrap methods (B. Efron & R. Tibshirani, 1993) be used to assess mediation. Bootstrap tests are powerful because they detect that the sampling distribution of the mediated effect is skewed away from 0. They argue that R. M. Baron and D. A. Kenny's (1986) recommendation of first testing the X --> Y association for statistical significance should not be a requirement when there is a priori belief that the effect size is small or suppression is a possibility. Empirical examples and computer setups for bootstrap analyses are provided.

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Topics: Mediation (statistics) (53%)

8,000 Citations


MonographDOI: 10.1017/CBO9780511811241
A. Colin Cameron1, Pravin K. Trivedi2Institutions (2)
09 May 2005-
Abstract: This book provides the most comprehensive treatment to date of microeconometrics, the analysis of individual-level data on the economic behavior of individuals or firms using regression methods for cross section and panel data. The book is oriented to the practitioner. A basic understanding of the linear regression model with matrix algebra is assumed. The text can be used for a microeconometrics course, typically a second-year economics PhD course; for data-oriented applied microeconometrics field courses; and as a reference work for graduate students and applied researchers who wish to fill in gaps in their toolkit. Distinguishing features of the book include emphasis on nonlinear models and robust inference, simulation-based estimation, and problems of complex survey data. The book makes frequent use of numerical examples based on generated data to illustrate the key models and methods. More substantially, it systematically integrates into the text empirical illustrations based on seven large and exceptionally rich data sets.

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7,692 Citations


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YearCitations
20217