Linear Causal Modeling with Structural Equations

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