Introduction
The Rise of Structural Equation Modeling
An Example of Structural Equation Modeling
Mathematical Foundations for Structural Equation Modeling
Introduction
Scalar Algebra
Vectors
Matrix Algebra
Determinants
Treatment of Variables as Vectors
Maxima and Minima of Functions
Causation
Historical Background
Perception of Causation
Causality
Conditions for Causal Inference
Nonlinear Causation
Science as Knowledge of Objects Demands Testing of Causal Hypotheses
Summary and Conclusion
Graph Theory for Causal Modeling
Directed Acyclic Graphs
Structural Equation Models
Basics of Structural Equation Models
Path Diagrams
From Path Diagrams to Structural Equations
Formulas for Variances and Covariances in Structural Equation Models
Matrix Equations
Identification
Incompletely Specified Models
Identification
Estimation of Parameters
Discrepancy Functions
Derivatives of Elements of Matrices
Parameter Estimation Algorithms
Designing SEM Studies
Preliminary Considerations
Multiple Indicators
The Four-Step Procedure
Testing Invariance across Groups of Subjects
Modeling Mean Structures
Confirmatory Factor Analysis
Introduction
Early Attempts at Confirmatory Factor Analysis
An Example of Confirmatory Factor Analysis
Faceted Classification Designs
Multirater-Multioccasion Studies
Multitrait-Multimethod Covariance Matrices
Equivalent Models
Introduction
Definition of Equivalent Models
Replacement Rule
Equivalent Models That Do Not Fit Every Covariance Matrix
A Conjecture about Avoiding Equivalent Models by Specifying Nonzero Parameters
Instrumental Variables
Introduction
Instrumental Variables and Mediated Causation
Conclusion
Multilevel Models
Introduction
Multilevel Factor Analysis on Two Levels
Multilevel Path Analysis
Longitudinal Models
Introduction
Simplex Models
Latent Curve Models
Reality or Just Saving Appearances?
Nonrecursive Models
Introduction
Flow Graph Analysis
Mason’s Direct Rule
Covariances and Correlations with Nonrecursive-Related Variables
Identification
Estimation
Applications
Model Evaluation
Introduction
Errors of Fit
Chi-Square Test of Fit
Properties of Chi-Square and Noncentral Chi-Square
Goodness-of-Fit Indices, CFI, and Others
The Meaning of Degrees of Freedom
"Badness-of-Fit" Indices, RMSEA, and ER
Parsimony
Information Theoretic Measures of Model Discrepancy
AIC Does Not Correct for Parsimony
Is the Noncentral Chi-Square Distribution Appropriate?
BIC
Cross-Validation Index
Confusion of "Likelihoods" in the AIC
Other Information Theoretic Indices, ICOMP
LM, WALD, and LR Tests
Modifying Models Post hoc
Recent Developments
Criticisms of Indices of Approximation
Conclusion
Polychoric Correlation and Polyserial Correlation
Introduction
Polychoric Correlation
Polyserial Correlation
Evaluation
References
Index
Biography
Stanley A. Mulaik is Professor Emeritus in the School of Psychology at the Georgia Institute of Technology.
"…an accessible yet rigorous treatment of the subject and is likely to be appealing to a wide statistical audience. … I enjoyed reading this book and suspect others will too. I would recommend this book for students and researchers [who] are familiar with standard applied statistics and causal inference but are looking for an introduction to structural equation modeling."
—Eric Laber, Journal of the American Statistical Association, September 2013"The book is written by one of the most prominent researchers in the field of structural equation models (SEM). … It is primarily a useful textbook for graduate students but could also be very useful for researchers in quantitative methods. … the book presents the standard methods of SEM in a form that makes them interesting to students and researchers with interests in the philosophical treatment of causality using SEM. … a very useful textbook for graduate students. It stands out for its rigorous treatment of SEM as a whole and for a particularly useful philosophical treatment of causality. … Stanley Mulaik’s book is one of the most useful ones with which to start a journey in this field."
—Spiridon Penev, Australian & New Zealand Journal of Statistics, 2011"The book benefits very substantially from the author’s mixed background in multivariate analysis, psychometrics, and philosophy of science—a background which is ideally suited to the eclectic issues raised by considerations of causality. I am sure the volume will prove to be a very useful contribution to the literature, an excellent text for someone intending to research in this area, and a useful reference source for those already doing so."
—David J. Hand, International Statistical Review (2011), 79
