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Linear Causal 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. Les mer
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Innbundet
Legg i
Vår pris: 1350,-

(Innbundet) Fri frakt!
Leveringstid: Sendes innen 21 dager

Om boka

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.

Fakta

Innholdsfortegnelse

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

Om forfatteren

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