Linear Casual Modeling With Structural Equations

Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal relations directly by perceiving quantities in magnitudes and motions of causes that are conserved in the effects of causal exchanges.

The author surveys the basic concepts of graph theory useful in the formulation of structural models. Focusing on SEM, he shows how to write a set of structural equations corresponding to the path diagram, describes two ways of computing variances and covariances of variables in a structural equation model, and introduces matrix equations for the general structural equation model. The text then discusses the problem of identifying a model, parameter estimation, issues involved in designing structural equation models, the application of confirmatory factor analysis, equivalent models, the use of instrumental variables to resolve issues of causal direction and mediated causation, longitudinal modeling, and nonrecursive models with loops. It also evaluates models on several dimensions and examines the polychoric and polyserial correlation coefficients and their derivation.

Covering the fundamentals of algebra and the history of causality, this book provides a solid understanding of causation, linear causal modeling, and SEM. It takes readers through the process of identifying, estimating, analyzing, and evaluating a range of models.

Stanley A. Mulaik is Professor Emeritus in the School of Psychology at the Georgia Institute of Technology.

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