Structural equation modeling with AMOS

418 Pages·2010·5.09 MB·English

Structural Equation
Modeling with AMOS
Basic Concepts, Applications, and Programming
SECOND EDITION
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Multivariate Applications Series
Sponsored by the Society of Multivariate Experimental Psychology,
the goal of this series is to apply complex statistical methods to signifi-
cant social or behavioral issues, in such a way so as to be accessible to
a nontechnical-oriented readership (e.g., nonmethodological researchers,
teachers, students, government personnel, practitioners, and other profes-
sionals). Applications from a variety of disciplines such as psychology,
public health, sociology, education, and business are welcome. Books can
be single- or multiple-authored or edited volumes that (a) demonstrate
the application of a variety of multivariate methods to a single, major
area of research; (b) describe a multivariate procedure or framework that
could be applied to a number of research areas; or (c) present a variety of
perspectives on a controversial subject of interest to applied multivariate
researchers.
There are currently 15 books in the series:
• What if There Were No Significance Tests? coedited by Lisa L. Harlow,
Stanley A. Mulaik, and James H. Steiger (1997)
• Structural Equation Modeling With LISREL, PRELIS, and SIMPLIS:
Basic Concepts, Applications, and Programming, written by Barbara M.
Byrne (1998)
• Multivariate Applications in Substance Use Research: New Methods
for New Questions, coedited by Jennifer S. Rose, Laurie Chassin,
Clark C. Presson, and Steven J. Sherman (2000)
• Item Response Theory for Psychologists, coauthored by Susan E.
Embretson and Steven P. Reise (2000)
• Structural Equation Modeling With AMOS: Basic Concepts, Applications,
and Programming, written by Barbara M. Byrne (2001)
• Conducting Meta-Analysis Using SAS, written by Winfred Arthur,
Jr., Winston Bennett, Jr., and Allen I. Huffcutt (2001)
• Modeling Intraindividual Variability With Repeated Measures Data:
Methods and Applications, coedited by D. S. Moskowitz and Scott
L. Hershberger (2002)
• Multilevel Modeling: Methodological Advances, Issues, and Applications,
coedited by Steven P. Reise and Naihua Duan (2003)
• The Essence of Multivariate Thinking: Basic Themes and Methods, written
by Lisa Harlow (2005)
• Contemporary Psychometrics: A Festschrift for Roderick P. McDonald,
coedited by Albert Maydeu-Olivares and John J. McArdle (2005)
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• Structural Equation Modeling With EQS: Basic Concepts, Applications,
and Programming, 2nd edition, written by Barbara M. Byrne (2006)
• Introduction to Statistical Mediation Analysis, written by David
P. MacKinnon (2008)
• Applied Data Analytic Techniques for Turning Points Research, edited by
Patricia Cohen (2008)
• Cognitive Assessment: An Introduction to the Rule Space Method, written
by Kikumi K. Tatsuoka (2009)
• Structural Equation Modeling With AMOS: Basic Concepts, Applications,
and Programming, 2nd edition, written by Barbara M. Byrne (2010)
Anyone wishing to submit a book proposal should send the follow-
ing: (a) the author and title; (b) a timeline, including completion date; (c) a
brief overview of the book’s focus, including table of contents and, ideally,
a sample chapter (or chapters); (d) a brief description of competing publi-
cations; and (e) targeted audiences.
For more information, please contact the series editor, Lisa
Harlow, at Department of Psychology, University of Rhode Island,
10 Chafee Road, Suite 8, Kingston, RI 02881-0808; phone (401)
874-4242; fax [phone]; or e-mail [email protected]. Information
may also be obtained from members of the advisory board: Leona
Aiken (Arizona State University), Gwyneth Boodoo (Educational Testing
Services), Barbara M. Byrne (University of Ottawa), Patrick Curran
(University of North Carolina), Scott E. Maxwell (University of Notre
Dame), David Rindskopf (City University of New York), Liora Schmelkin
(Hofstra University), and Stephen West (Arizona State University).
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Structural Equation
Modeling with AMOS
Basic Concepts, Applications, and Programming
SECOND EDITION
Barbara M. Byrne
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Routledge Routledge
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Library of Congress Cataloging-in-Publication Data
Byrne, Barbara M.
Structural equation modeling with AMOS: basic concepts, applications, and
programming / Barbara M. Byrne. -- 2nd ed.
p. cm. -- (Multivariate applications series)
Includes bibliographical references and index.
ISBN 978-0-8058-6372-7 (hardcover : alk. paper) -- ISBN 978-0-8058-6373-4
(pbk. : alk. paper)
1. Structural equation modeling. 2. AMOS. I. Title.
QA278.B96 2009
519.5’35--dc22 2009025275
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the Psychology Press Web site at
http://www.psypress.com
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Contents
Preface ................................................................................................................xv
Acknowledgments ..........................................................................................xix
Section I: Introduction
Chapter 1 Structural equation models: The basics .................................3
Basic concepts .....................................................................................................4
Latent versus observed variables ................................................................4
Exogenous versus endogenous latent variables........................................5
The factor analytic model .............................................................................5
The full latent variable model .....................................................................6
General purpose and process of statistical modeling ..............................7
The general structural equation model ..........................................................9
Symbol notation .............................................................................................9
The path diagram ..........................................................................................9
Structural equations ...................................................................................11
Nonvisible components of a model ..........................................................12
Basic composition ........................................................................................12
The formulation of covariance and mean structures .............................14
Endnotes ............................................................................................................15
Chapter 2 Using the AMOS program ......................................................17
Working with AMOS Graphics: Example 1..................................................18
Initiating AMOS Graphics .........................................................................18
AMOS modeling tools ................................................................................18
The hypothesized model ............................................................................22
Drawing the path diagram ........................................................................23
Understanding the basic components of model 1 ..................................31
The concept of model identification .........................................................33
Working with AMOS Graphics: Example 2..................................................35
The hypothesized model ............................................................................35
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viii Contents
Drawing the path diagram ........................................................................38
Working with AMOS Graphics: Example 3..................................................41
The hypothesized model ............................................................................42
Drawing the path diagram ........................................................................45
Endnotes ............................................................................................................49
Section II: Applications in single-group analyses
Chapter 3 Testing for the factorial validity of a
theoretical construct (First-order CFA model) ....................53
The hypothesized model.................................................................................53
Hypothesis 1: Self-concept is a four-factor structure ..................................54
Modeling with AMOS Graphics ....................................................................56
Model specification .....................................................................................56
Data specification ........................................................................................60
Calculation of estimates .............................................................................62
AMOS text output: Hypothesized four-factor model ............................64
Model summary ..........................................................................................65
Model variables and parameters ...............................................................65
Model evaluation .........................................................................................66
Parameter estimates ....................................................................................67
Feasibility of parameter estimates ..................................................67
Appropriateness of standard errors ................................................67
Statistical significance of parameter estimates ..............................68
Model as a whole .........................................................................................68
The model-fitting process .................................................................70
The issue of statistical significance .................................................71
The estimation process .....................................................................73
Goodness-of-fit statistics ...................................................................73
Model misspecification ...............................................................................84
Residuals .............................................................................................85
Modification indices ..........................................................................86
Post hoc analyses ..............................................................................................89
Hypothesis 2: Self-concept is a two-factor structure ..................................91
Selected AMOS text output: Hypothesized two-factor model .............93
Hypothesis 3: Self-concept is a one-factor structure ...................................93
Endnotes ............................................................................................................95
Chapter 4 Testing for the factorial validity of scores
from a measuring instrument
(First-order CFA model) ...........................................................97
The measuring instrument under study ......................................................98
The hypothesized model.................................................................................98
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Contents ix
Modeling with AMOS Graphics ....................................................................98
Selected AMOS output: The hypothesized model ...............................102
Model summary ..............................................................................102
Assessment of normality ................................................................102
Assessment of multivariate outliers ..............................................105
Model evaluation .......................................................................................106
Goodness-of-fit summary ..............................................................106
Modification indices ........................................................................108
Post hoc analyses .............................................................................................111
Model 2 .............................................................................................................111
Selected AMOS output: Model 2 ..............................................................114
Model 3 .............................................................................................................114
Selected AMOS output: Model 3 ..............................................................114
Model 4 .............................................................................................................118
Selected AMOS output: Model 4 ..............................................................118
Comparison with robust analyses based on the
Satorra-Bentler scaled statistic .................................................................125
Endnotes ..........................................................................................................127
Chapter 5 Testing for the factorial validity of scores from a
measuring instrument (Second-order CFA model) ..........129
The hypothesized model...............................................................................130
Modeling with AMOS Graphics ..................................................................130
Selected AMOS output: Preliminary model .........................................134
Selected AMOS output: The hypothesized model ...............................137
Model evaluation .......................................................................................140
Goodness-of-fit summary ..............................................................140
Model maximum likelihood (ML) estimates ................................141
Estimation of continuous versus categorical variables .............................143
Categorical variables analyzed as continuous variables .....................148
The issues ...................................................................................................148
Categorical variables analyzed as categorical variables ......................149
The theory .........................................................................................149
The assumptions ..............................................................................150
General analytic strategies .............................................................150
The AMOS approach to analysis of categorical variables ........................151
What is Bayesian estimation? ..................................................................151
Application of Bayesian estimation ........................................................152
Chapter 6 Testing for the validity of a causal structure ....................161
The hypothesized model................................................................................161
Modeling with AMOS Graphics ...................................................................162
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