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 (ie, 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 60 (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://wwwpsypresscom/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 (ie, 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

Structural Equation Modeling With Mplus: Basic Concepts, Applications, And Programming

Measurement invariance is usually tested using Multigroup Confirmatory Factor Analysis, which examines the change in the goodness-of-fit index (GFI) when cross-group constraints are imposed on a measurement model. Although many studies have examined the properties of GFI as indicators of overall model fit for single-group data, there have been none to date that examine how GFIs change when between-group constraints are added to a measurement model. The lack of a consensus about what constitutes significant GFI differences places limits on measurement invariance testing. We examine 20 GFIs based on the minimum fit function. A simulation under the two-group situation was used to examine changes in the GFIs (ΔGFIs) when invariance constraints were added. Based on the results, we recommend using Δcomparative fit index, ΔGamma hat, and ΔMcDonald's Noncentrality Index to evaluate measurement invariance. These three ΔGFIs are independent of both model complexity and sample size, and are not correlated with the o...

Evaluating Goodness-of-Fit Indexes for Testing Measurement Invariance

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.

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Structural Equation Modelling: Guidelines for Determining Model Fit

This article explores the possibility that romantic love is an attachment process--a biosocial process by which affectional bonds are formed between adult lovers, just as affectional bonds are formed earlier in life between human infants and their parents. Key components of attachment theory, developed by Bowlby, Ainsworth, and others to explain the development of affectional bonds in infancy, were translated into terms appropriate to adult romantic love. The translation centered on the three major styles of attachment in infancy--secure, avoidant, and anxious/ambivalent--and on the notion that continuity of relationship style is due in part to mental models (Bowlby's "inner working models") of self and social life. These models, and hence a person's attachment style, are seen as determined in part by childhood relationships with parents. Two questionnaire studies indicated that relative prevalence of the three attachment styles is roughly the same in adulthood as in infancy, the three kinds of adults differ predictably in the way they experience romantic love, and attachment style is related in theoretically meaningful ways to mental models of self and social relationships and to relationship experiences with parents. Implications for theories of romantic love are discussed, as are measurement problems and other issues related to future tests of the attachment perspective.

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Romantic Love Conceptualized as an Attachment Process

"With its emphasis on practical and conceptual aspects, rather than mathematics or formulas, this accessible book has established itself as the go-to resource on confirmatory factor analysis (CFA). Detailed, worked-through examples drawn from psychology, management, and sociology studies illustrate the procedures, pitfalls, and extensions of CFA methodology. The text shows how to formulate, program, and interpret CFA models using popular latent variable software packages (LISREL, Mplus, EQS, SAS/CALIS); understand the similarities and differences between CFA and exploratory factor analysis (EFA); and report results from a CFA study. It is filled with useful advice and tables that outline the procedures. The companion website offers data and program syntax files for most of the research examples, as well as links to CFA-related resources. New to This Edition *Updated throughout to incorporate important developments in latent variable modeling. *Chapter on Bayesian CFA and multilevel measurement models. *Addresses new topics (with examples): exploratory structural equation modeling, bifactor analysis, measurement invariance evaluation with categorical indicators, and a new method for scaling latent variables. *Utilizes the latest versions of major latent variable software packages"--

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Confirmatory Factor Analysis for Applied Research

Contents: Part I: Introduction. Structural Equation Models: The Basics. Using the EQS Program. Part II: Single-Group Analyses. Application 1: Testing for the Factorial Validity of a Theoretical Construct (First-Order CFA Model). Application 2: Testing for the Factorial Validity of Scores From a Measuring Instrument (First-Order CFA Model). Application 3: Testing for the Factorial Validity of Scores from a Measuring Instrument (Second-Order CFA Model). Application 4: Testing for the Validity of a Causal Structure. Part III: Multiple-Group Analyses. Application 5: Testing for the Factorial Invariance of a Measuring Instrument. Application 6: Testing for the Invariance of a Causal Structure. Application 7: Testing for Latent Mean Differences (First-Order CFA Model). Application 8: Testing for Latent Mean Differences (Second-Order CFA Model). Part IV: Other Important Topics. Application 9: Testing for Construct Validity: The Multitrait-Multimethod Model. Application 10: Testing for Change Over Time: The Latent Growth Curve Model. Application 11: Testing for Within- and Between-Level Variance: The Multilevel Model.

Structural equation modeling with AMOS: basic concepts, applications, and programming

Contents: Preface. Part I: Introduction. Structural Equation Models: The Basics. Using LISREL, PRELIS, and SIMPLIS. Part II: Single-Group Analyses. Application 1: Testing the Factorial Validity of a Theoretical Construct (First-Order CFA Model). Application 2: Testing the Factorial Validity of Scores From a Measuring Instrument (First-Order CFA Model). Application 3: Testing the Factorial Validity of Scores From a Measuring Instrument (Second-Order CFA Model). Application 4: Testing for Construct Validity: The Multitrait-Multimethod Model. Application 5: Testing the Validity of a Causal Structure. Part III: Multiple Group Analyses. Application 6: Testing for the Invariant Factorial Structure of a Theoretical Construct (First-Order CFA Model). Application 7: Testing for Invariant Factorial Structure of Scores From a Measuring Instrument (First-Order CFA Model). Application 8: Testing for Invariant Latent Mean Structures. Application 9: Testing for Invariant Pattern of Causal Structure. Part IV: LISREL, PRELIS, and SIMPLIS Through Windows. Application 10: Testing for Causal Predominance Using a Two-Wave Panel Model.

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Structural Equation Modeling With Lisrel, Prelis, and Simplis: Basic Concepts, Applications, and Programming

Addresses issues related to partial measurement in variance using a tutorial approach based on the LISREL confirmatory factor analytic model. Specifically, we demonstrate procedures for (a) using "sensitivity analyses" to establish stable and substantively well-fitting baseline models, (b) determining partially invariant measurement parameters, and (c) testing for the invariance of factor covariance and mean structures, given partial measurement invariance. We also show, explicitly, the transformation of parameters from an all-^fto an all-y model specification, for purposes of testing mean structures. These procedures are illustrated with multidimensional self-concept data from low (« = 248) and high (n = 582) academically tracked high school adolescents. An important assumption in testing for mean differences is that the measurement (Drasgow & Kanfer, 1985; Labouvie, 1980; Rock, Werts, & Haugher, 1978) and the structure (Bejar, 1980; Labouvie, 1980; Rock etal., 1978) of the underlying construct are equivalent across groups. One methodological strategy used in testing for this equivalence is the analysis of covariance structures using the LISREL confirmatory factor analytic (CFA) model (Joreskog, 1971). Although a number of empirical investigations and didactic expositions have used this methodology in testing assumptions of factorial invariance for multiple and single parameters, the analyses have been somewhat incomplete. In particular, researchers have not considered the possibility of partial measurement invariance. The primary purpose of this article is to demonstrate the application of CFA in testing for, and with, partial measurement invariance. Specifically, we illustrate (a) testing, independently, for the invariance of factor loading (i.e., measurement) parameters, (b) testing for the invariance of factor variance-covariance (i.e., structural) parameters, given partially invariant factor loadings, and (c) testing for the invariance of factor mean structures.1 Invariance testing across groups, however, assumes wellfitting single-group models; the problem here is to know when to stop fitting the model. A secondary aim of this article, then, is to demonstrate "sensitivity analyses" that can be used to establish stable and substantively meaningful baseline models.

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Testing for the equivalence of factor covariance and mean structures: The issue of partial measurement invariance.

Foreword - Peter M Bentler PART ONE: INTRODUCTION Structural Equation Models Using the EQS Program PART TWO: SINGLE-GROUP ANALYSES Application 1 Testing the Factorial Validity of a Theoretical Construct (1st-order CFA Model) Application 2 Testing the Factorial Validity of a Measuring Instrument (1st-order CFA Model) Application 3 Testing the Factorial Validity of a Measuring Instrument (2nd-order CFA Model) Application 4 Testing for Construct Validity Via the Multitrait-Multimethod Model Application 5 Testing the Validity of a Causal Structure PART THREE: MULTIPLE GROUP ANALYSES Application 6 Testing for Invariant Factorial Structure of a Theoretical Construct (1st-order CFA Model) Application 7 Testing for Invariant Factorial Structure of a Measuring Instrument (1st-order CFA Model) Application 8 Testing for Invariant Latent Mean Structures Application 9 Testing for Invariant Causal Structure PART FOUR: WINDOW TREATMENTS: A LOOK AT EQS/WINDOWS (VERSION 4) Introduction to EQS/Windows Application 10 Preliminary Data-Screening Analyses Application 11 Building an EQS Model File - Instantly!

Barbara M. Byrne

Papers

Structural Equation Modeling With Mplus: Basic Concepts, Applications, And Programming

Structural equation modeling with AMOS: basic concepts, applications, and programming

Structural Equation Modeling With Lisrel, Prelis, and Simplis: Basic Concepts, Applications, and Programming

Testing for the equivalence of factor covariance and mean structures: The issue of partial measurement invariance.

Structural Equation Modeling with EQS and EQS/WINDOWS: Basic Concepts, Applications, and Programming