Linear Causal Modeling with Structural Equations (Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences v. 5)
By: Stanley A. Mulaik (author)Hardback
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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
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