This popular text provides an accessible guide to the application, interpretation, and pitfalls of structural equation modeling (SEM). Reviewed are fundamental statistical conceptssuch as correlation, regressions, data preparation and screening, path analysis, and confirmatory factor analysisas well as more advanced methods, including the evaluation of nonlinear effects, measurement models and structural regression models, latent growth models, and multilevel SEM. The companion Web page offers data and program syntax files for many of the research examples, electronic overheads that can be downloaded and printed by instructors or students, and links to SEM-related resources.
About the Author
Rex B. Kline, PhD, is an associate professor of Psychology at Concordia University in Montréal. Since earning a PhD in psychology, his areas of research and writing have included the psychometric evaluation of cognitive abilities, child clinical assessment, structural equation modeling, and usability engineering in computer science. Dr. Kline has published three books and more than 40 articles in research journals and is the coauthor of a teacher-informant rating scale for referred children.
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Principles and Practice of Structural Equation Modeling
By Rex B. Kline
The Guilford PressCopyright © 2005 The Guilford Press
All right reserved.
This book is intended to serve as a guide to the principles, assumptions, strengths, limitations, and application of structural equation modeling (SEM) for researchers and students who do not have extensive quantitative backgrounds. Some familiarity with basic concepts such as correlation is assumed, but higher levels of statistical knowledge are not required before reading this book. Accordingly, the presentation is conceptually rather than mathematically oriented, the use of formulas and symbols is kept to a minimum, and many examples are offered of the application of SEM to a wide variety of research problems in psychology, education, and health sciences, among other areas. This book also has a home page on the Internet. From the home page, readers can freely access support materials for this book, including data and program syntax files for many of the research examples, resources for instructors and students, and links to related Web pages. It is hoped that readers who complete this book will have acquired the skills necessary to begin to use SEM in their own research in a reasoned, disciplined way.
1.1 PLAN OF THE BOOK
The topic of SEM is very broad and every aspect of it cannot be coveredcomprehensively in a single volume. With this reality in mind, the main goals of this book are to introduce the fundamental concepts that underlie most facets of SEM and some more advanced techniques that allow additional kinds of hypotheses to be tested. A learning-by-doing approach is strongly encouraged and is facilitated by two things. First, the data for every example reviewed in this book are summarized in tables, which allows the reader to reproduce any of the analyses discussed here. Many of these data summaries can also be downloaded from this book's Web site. Second, several widely used SEM computer programs are described in Chapter 4, including Amos, EQS, and LISREL, among others, and student versions of some of these programs are freely available over the Internet. (Links to these sites are provided in later chapters.) Readers who at present have no experience using an SEM computer program are not at any disadvantage, however. This is because the presentation in this book of fundamental concepts in SEM is not based on a particular software package. (More about this point later.)
Part I introduces ideas and vocabulary that are essential to understanding the general rationale of SEM. The latter part of the present chapter is about characteristics that all facets of SEM have in common. The main goal of Chapters 2 and 3 is to review basic statistical principles that form the foundation for learning more about SEM. Topics such as bivariate and multivariate correlation and regression, the rationale of statistical significance testing, and other fundamental statistical concepts are covered in Chapter 2. Readers already quite familiar with these topics may be able to skip this chapter. However, all readers should pay close attention to Chapter 3, which deals with the screening and preparation of data for SEM, a topic so important that it is considered before any specific techniques are described in detail. Ways to identify and rectify potential problems, such as severely nonnormal distributions, missing data, and outliers, are covered in this chapter. Chapter 4 builds a conceptual context for SEM relative to other, more conventional kinds of statistical methods such as multiple regression. Assumptions and examples of the types of research questions that can (and cannot) be evaluated with different types of analytical methods are considered. Chapter 4 also describes a total of eight different SEM computer programs. All of these programs can estimate a wide range of structural equation models, and most researchers use one of them to conduct SEM analyses.
Part II consists of four chapters devoted to basic SEM techniques. The majority of SEM analyses described in the research literature involve these core techniques. Chapters 5 and 6 are about path analysis. Path analysis is the original SEM technique, and path models concern effects among observed variables. The conceptual foundations of path analysis are introduced in Chapter 5, and Chapter 6 deals with the specifics of analyzing path models and testing hypotheses. Most of the issues considered in these chapters generalize to the analysis of models where hypothetical constructs are represented as latent variables. Their introduction in chapters that deal with path analysis reflects a pedagogical goal of ensuring that readers understand fundamental issues in SEM concerning observed variables before dealing with the added complexities of analyzing latent variables. The next two chapters are about standard kinds of latent variable models in SEM. Chapter 7 deals with the technique of confirmatory factor analysis (CFA) of measurement models. Chapter 8 extends these ideas to structural regression (SR or "hybrid") models that have features of both path models and factor analysis models. It is possible to evaluate a wide variety of hypotheses with these core SEM techniques, as is demonstrated with numerous examples.
Part III is concerned with advanced methods and avoiding common mistakes in SEM. Chapter 9 is concerned with the analysis of models with feedback loops, which reflect the presumption of mutual causal effects among two or more variables measured at the same time. These kinds of models require some special considerations in their analysis compared with more standard models where causal effects are represented as unidirectional (i.e., from presumed cause to effect but not in the reverse direction). Chapter 10 deals with the analysis of means in SEM, including latent growth models, and Chapter 11 is about the analysis of structural equation models across multiple samples. The latter type of analysis is concerned with whether a model has generalizability across more than one population. Chapter 12 is written as a "how-not-to" manual that summarizes ways that researchers can mislead themselves with SEM. Although most of these points are mentioned in earlier chapters in the book in the context of particular SEM techniques, they are all considered together in this chapter. Chapter 13 provides an overview of two additional advanced methods in SEM. These include the estimation of interaction or curvilinear effects of latent variables and the analysis of multilevel structural equation models for hierarchical data sets where some units are clustered under other units, such as students within classrooms. Although these methods cannot be covered in detail in a single chapter, this review is intended to at least make the reader aware of even more possibilities in SEM and provide pertinent references.
As with other statistical techniques, there is no "gold standard" for notation in SEM. Although the symbol set associated with the LISREL program is probably the most widely used in books and journal articles about SEM, it features a profusion of subscripted Greek letters (e.g., ([PHI].sub.11] or [[LAMBDA].sub.31]) and matrix algebra that can be confusing to follow unless the reader has memorized the entire system. Instead, a minimum number of alphabetic characters are used to represent various aspects of SEM such as observed variables versus latent variables. Also, to avoid double notation, a distinction is not usually made between population values and sample statistics. It is assumed that readers are already aware of this difference and know that sample data can only be considered as estimates of population values.
1.3 COMPUTER PROGRAMS FOR SEM
Computer programs are important tools for the conduct of SEM. About 30 years ago, LISREL was essentially the only widely available SEM program. The situation is now very different, however, as there are many other choices of SEM computer programs including Amos, CALIS, EQS, Mplus, Mx Graph, RAMONA, and SEPATH, among others. For this reason, the presentation of concepts in this book is not linked to a particular SEM computer program. Instead, essential principles of SEM that users of any computer tool must understand are emphasized. In other words, the book is more like a guide to writing style and composition than a guide to how to use a particular word processing program. Nevertheless, the aforementioned chapter (4) about features of the SEM computer programs just listed should be helpful to readers who intend to use one of them for their own analyses.
Two further comments about SEM computer programs are warranted. First, it used to be that these types of programs were difficult to use, for two reasons. They required users to generate a lot of rather arcane code for each analysis, which was a time-consuming, tedious, and error-prone process. They also tended to be available only on mainframe computers, which required batch-file-type programming with stark command-line user interfaces. The increasing availability of powerful microprocessors and large amounts of memory and storage on affordable personal computers has dramatically changed both of these situations, however. Specifically, statistical software programs for personal computers with graphical user interfaces are much easier to use than their character-based predecessors. "User friendliness" in contemporary SEM computer programs is a near-revolution compared with older programs.
As an example of the issues just mentioned, consider a feature of the most recent versions of Amos, EQS, LISREL, and Mx Graph for personal computers. Users of any of these packages can still choose to write code in the applications' matrix algebra- or equations-based syntax. As an alternative, however, they can use a graphical editor to draw the model on the screen with boxes, circles, arrows, and so on. The programs then translate the figure into lines of code, which are then used to generate the output. Thus, the user need not know very much about how to write program code in order to conduct a very sophisticated type of statistical analysis. And this means that the importance of highly technical programming skills for the conduct of SEM is likely to diminish even further. For researchers who have a good understanding of the fundamental concepts of SEM, this development can only be a boon-anything that reduces the drudgery and gets one to the results quicker is a benefit.
The second comment is to point out that "push-button modeling" has potential drawbacks. For example, no- or low-effort programming could encourage the use of SEM in an uninformed or careless way. It is thus more important than ever to be familiar with the conceptual bases of SEM. Computer programs, however easy to use, should be only the tools of your knowledge and not its master. Steiger (2001) makes the related point that the emphasis on the ease of use of computer tools can give beginners the false impression that SEM itself is easy. That is, to beginners it may appear that all one has to do is draw the model on the screen and let the computer take care of everything else. However, the reality is that things often can and do go wrong in SEM. Specifically, beginners often quickly discover that analyses fail because of technical problems, including a computer system crash or a terminated program run with many error messages or uninterpretable output (Steiger, 2001). This type of thing happens because actual research problems can be very technical, and the availability of user-friendly SEM computer programs does not change this fact. Accordingly, one of the goals of this book is to point out the kinds of things that can go wrong in SEM and, I hope, provide readers with the conceptual knowledge to deal with problems in the analysis (i.e., to understand what went wrong and why). For the same reason, not all examples of SEM analyses described in later chapters are problem-free. Ways to deal with these problems are suggested in such cases, however.
1.4 STATISTICAL JOURNEYS
Learning to use and understand a new set of statistical procedures is like making a long journey through a strange land. Such a journey requires a substantial commitment of time, patience, and a willingness to tolerate the frustration of some initial uncertainty and inevitable trial and error. But this is one journey that you do not have to make alone. Think of this book as a travel atlas or even as someone to talk to about language and customs, what to see and what to avoid, and what is coming over the horizon. I hope that the combination of a conceptually based approach, numerous examples, and the occasional bit of useful advice presented in this book will help to make this journey a little easier, maybe even enjoyable.
Kühnel (2001) reminds us that learning about SEM has the byproduct that students must deal with many fundamental issues of methods and general statistical concepts. One of these issues is measurement: It is impossible to analyze a structural equation model with latent variables that represent hypothetical constructs without thinking about how those constructs are to be measured. Measurement theory is too often neglected nowadays in undergraduate and graduate degree programs in psychology (Frederich, Buday, & Kerr, 2000) and related areas, but SEM requires strong knowledge in this area. The technique of SEM is a priori, which means that the researcher must specify a model in order to conduct the analysis. The model's specification must have some basis, whether it be theory, results of previous studies, or an educated guess that reflects the researcher's domain knowledge and experience. The emphasis SEM places on testing a whole model may be a kind of antidote to overreliance on statistical tests of individual hypotheses. Data analysis methods in the behavioral sciences need reform (Kline, 2004), and increased use of model-fitting techniques, including SEM, should be part of that. SEM techniques require that researchers consider alternative models that may explain the same data equally well. Use of SEM (and related techniques) should also foster a better awareness of the difference between a statistical model of reality and reality itself.
Let us begin our journey with an overview of properties common to almost all SEM techniques.
Excerpted from Principles and Practice of Structural Equation Modeling by Rex B. Kline Copyright © 2005 by The Guilford Press. Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Table of Contents
I. Fundamental Concepts
1.1. Plan of the Book
1.3. Computer Programs for SEM
1.4. Statistical Journeys
1.5. Family Values
1.6. Extend Latent Variable Families
1.7. Family History
1.8. Internet Resources
2. Basic Statistical Concepts: I. Correlation and Regression
2.1. Standardized and Unstandardized Variables
2.2. Bivariate Correlation and Regression
2.3. Partial Correlation
2.4. Multiple Correlation and Regression
2.5. Statistical Tests
2.8. Recommended Readings
3. Basic Statistical Concepts: II. Data Preparation and Screening
3.1. Data Preparation
3.2. Data Screening
3.3. Score Reliability and Validity
3.5. Recommended Readings
4. Core SEM Techniques and Software
4.1. Steps of SEM
4.2. Path Analysis: A Structural Model of Illness Factors
4.3. Confirmatory Factor Analysis: A Measurement Model of Arousal
4.4. A Structural Regression Model of Family Risk and Child Adjustment
4.6. SEM Computer Programs
4.8. Recommended Readings
II. Core SEM Techniques
5. Introduction to Path Analysis
5.1. Correlation and Causation
5.2. Specification of Path Models
5.3. Types of Path Models
5.4. Principles of Identification
5.5. Sample Size
5.6. Overview of Estimation Options
5.7. Maximum Likelihood Estimation
5.8. Other Issues
5.10. Recommended Readings
Appendix 5.a. Recommendations for Start Values
Appendix 5.b. Effect Size Interpretation of Standardized Path Coefficients
6. Details of Path Analysis
6.1. Detailed Analysis of a Recursive Model of Illness Factors
6.2. Assessing Model Fit
6.3. Testing Hierarchical Models
6.4. Comparing Nonhierarchical Models
6.5. Equivalent Models
6.6. Power Analysis
6.7. Other Estimation Options
6.9. Recommended Readings
Appendix 6.a. Statistical Tests for Indirect Effects in Recursive Path Models
Appendix 6.b. Amos Basic Syntax
Appendix 6.c. Estimation of Recursive Path Models with Multiple Regression
7. Measurement Models and Confirmatory Factor Analysis
7.1. Specification of CFA Models
7.2. Identification of CFA Models
7.3. Naming and Reification Fallacies
7.4. Estimation of CFA Models
7.5. Testing CFA Models
7.6. Equivalent CFA Models
7.7. Analyzing Indicators with Non-Normal Distributions
7.8. Special Types of CFA Models
7.9. Other Issues
7.11. Recommended Readings
Appendix 7.a. Recommendations for Start Values
Appendix 7.b. CALIS Syntax
8. Models with Structural and Measurement Components
8.1. Characteristics of SR Models
8.2. Analysis of SR Models
8.3. Estimation of SR Models
8.4. A Detailed Example
8.5. Other Issues
8.7. Recommended Readings
Appendix 8.a. SEPATH Syntax
III. Advanced Techniques, Avoiding Mistakes
9. Nonrecursive Structural Models
9.1. Specification of Nonrecursive Models
9.2. Identification of Nonrecursive Models
9.3. Estimation of Nonrecursive Models
9.6. Recommended Readings
Appendix 9.a. EQS Syntax
10. Mean Structures and Latent Growth Models
10.1. Introduction to Mean Structures
10.2. Identification of Mean Structures
10.3. Estimation of Mean Structures
10.4. Structured Means in Measurement Models
10.5. Latent Growth Models
10.8. Recommended Readings
Appendix 10.a. Mplus Syntax
11. Multiple-Sample SEM
11.1. Rationale of Multiple-Sample SEM
11.2. Multiple-Sample Path Analysis
11.3. Multiple-Sample CFA
11.5. MIMIC Models as an Alternative to Multiple-Sample Analysis
11.7. Recommended Readings
Appendix 11.a. LISREL SIMPLIS Syntax
12. How to Fool Yourself with SEM
12.1. Tripping at the Starting Line: Specification
12.2. Improper Care and Feeding: Data
12.3. Checking Critical Judgment at the Door: Analysis and Respecification
12.4. The Garden Path: Interpretation
12.6. Recommended Readings
13. Other Horizons
13.1. Interaction and Curvilinear Effects
13.2. Multilevel Structural Equation Models
13.4. Recommended Readings
Graduate students, instructors, and researchers in psychology, education, management, sociology, nursing, public health, criminal justice, and social work. Also of interest to SEM users in the fields of communication research and counseling. Serves as a text for graduate-level courses in structural equation modeling, advanced quantitative methods, or advanced research methodology.
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