# Structural equation modeling with Mplus: Basic concepts, applications, and programming

**Barbara M. Byrne**

CiteWeb id: 20120000008

CiteWeb score: 9215

Psychology is a science that advances by leaps and bounds. The impulse of new mathematical models along with the incorporation of computers to research has drawn a new reality with many methodological progresses that only a few people could imagine not too long ago. Such progress has no doubt revolutionized the panorama of research in the behavioral sciences. Structural Equation Models are a clear example of this. Under this label are usually included a series of state-of-the-art multivariate statistical procedures that allow the researcher to test theoryguided hypotheses with clearly confi rmatory ends as well as to establish causal relations among variables. Confi rmatory factor analysis, the study of measurement invariance, or the multitraitmultimethod models are some of the procedures that stem from this methodology. In this sense, it would be diffi cult to fi nd a scientifi c journal that publishes empirical works in psychology that does not address some of these issues, so their current transcendence is undeniable. The manual written by the Full Professor of the University of Ottawa, Barbara M. Byrne, is a link in a series of books that address this topic. Throughout her long academic trajectory, Professor Byrne developed interesting and popular work focused on bringing the researcher and the professional layman—and not so layman—closer to the diverse statistical programs available on the market for data analysis from the perspective of structural equation models (i.e., LISREL, AMOS, EQS) (Byrne, 1998, 2001, 2006). Bearing this in mind, the main goal of this work is to introduce the reader to the basic concepts of this methodology, in a simple and entertaining way, avoiding mathematical technicisms and statistical jargon. For this purpose, we used the statistical program Mplus 6.**0** (Muthen & Muthen, 2007-2010), an extremely suggestive software that incorporates interesting applications. The authoress provides a practical guide that leads the reader through illustrative examples of how to proceed step by step with the Mplus, from the initial specifi cations of the model to the interpretation of the output fi les. On the one hand, we underline that the data used proceed from prior investigations and can be consulted in the Internet, offering the reader the possibility of practicing with them (http://www.psypress.com/sem-with-mplus/ datasets/); on the other hand, updating the information with novel and apt bibliographic references allows the reader to study in more depth the diverse topics that are presented in the manual, if he or she so desires. The book consists of four sections, with a total of 12 chapters. The fi rst section, Chapters 1 and 2, addresses introductory terms related to structural equation models and working with the Mplus program at a user-level. The second unit focuses on data analysis with a single group. In Chapter 3, the factor validity of the self-concept is tested by means of confi rmatory factor analysis. In Chapter 4, the authoress performs a fi rst-order confi rmatory factor analysis, in which she examines the validity of the scores of the Maslach Burnout Inventory (MBI) in a sample of teachers. In Chapter 5, the internal structure of the scores on the Beck Depression Inventory-II is analyzed by means of second-order confi rmatory factor analysis in a sample of Chinese adolescents. In the next chapter, the complete model of structural equations is tested, and the authoress examines the causal relation established between diverse variables (i.e., work climate, self-esteem, social support) and Burnout. The third section of the manual is, in my opinion, the most interesting, not only because of the expansion of the study of measurement invariance in recent years but also because of the expansion it may possibly have in the future. In this section, Professor Byrne goes into multigroup comparisons. Specifi cally, in Chapter 7, she examines the factor equivalence of the MBI in two samples of teachers by means of the analysis of covariance structures. In this chapter, she introduces relevant concepts, such as types of invariance (confi gural, metric, and strict) or the invariance of partial measurement. In Chapter 8, she also analyzes measurement invariance, using for this purpose the analysis of mean and covariance structures. This analysis, in comparison to the analysis of covariance structures, allows contrasting the latent means of two or more groups. With this goal, she verifi es whether there is measurement invariance between the scores on the Self-description Questionnaire-I in Nigerian and Australian adolescents. In Chapter 9, she proposes a complete model of structural equations in which she tests the causal structure through the procedure of cross validation. Lastly, in the fourth section, she reveals three very interesting topics, that are also up-to-date and that, to some degree, go beyond the initial goal of the book, such as the multitrait-multimethod models, latent growth curves, and multilevel models. Summing up, the work “Structural Equation Modeling with Mplus: Basic concepts, applications, and programming” is of enormous interest and utility for all professionals of psychology and related sciences who, without having exhaustive knowledge of the details of structural equation models, wish to test their hypothetical models by means of the Mplus program. No doubt, this is a reference manual, a must-read that is accessible and that has a high degree of methodological rigor. We hope that the readers

- psycnet.apa.org/index.cfm?fa=main.doiLanding&uid=2006-03173-000
- ci.nii.ac.jp/ncid/BB06794586
- www.researchgate.net/profile/Eduardo_Fonseca-Pedrero/publication/236176286_Structural_equation_modeling_with_Mplus_Basic_concepts_applications_and_programming/links/00b49516dce7d01e85000000.pdf?disableCoverPage=true

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