Structural Equations with Latent Variables

Description

Analysis of Ordinal Categorical Data Alan Agresti Statistical Science Now has its first coordinated manual of methods for analyzing ordered categorical data. This book discusses specialized models that, unlike standard methods underlying nominal categorical data, efficiently use the information on ordering. It begins with an introduction to basic descriptive and inferential methods for categorical data, and then gives thorough coverage of the most current developments, such as loglinear and logit models for ordinal data. Special emphasis is placed on interpretation and application of methods a.;Title Page; Dedication; Copyright; Preface; CHAPTER ONE: Introduction; HISTORICAL BACKGROUND; CHAPTER TWO: Model Notation, Covariances, and Path Analysis; MODEL NOTATION; COVARIANCE; PATH ANALYSIS; SUMMARY; CHAPTER THREE: Causality and Causal Models; NATURE OF CAUSALITY; ISOLATION; ASSOCIATION; DIRECTION OF CAUSATION; LIMITATIONS OF "CAUSAL" MODELING; SUMMARY; CHAPTER FOUR: Structural Equation Models with Observed Variables; MODEL SPECIFICATION; IMPLIED COVARIANCE MATRIX; IDENTIFICATION; ESTIMATION; FURTHER TOPICS; SUMMARY; APPENDIX 4A DERIVATION OF FML (y and x MULTINORMAL). Title Page Dedication Copyright Preface CHAPTER ONE: Introduction HISTORICAL BACKGROUND CHAPTER TWO: Model Notation, Covariances, and Path Analysis MODEL NOTATION COVARIANCE PATH ANALYSIS SUMMARY CHAPTER THREE: Causality and Causal Models NATURE OF CAUSALITY ISOLATION ASSOCIATION DIRECTION OF CAUSATION LIMITATIONS OF "CAUSAL" MODELING SUMMARY CHAPTER FOUR: Structural Equation Models with Observed Variables MODEL SPECIFICATION IMPLIED COVARIANCE MATRIX IDENTIFICATION ESTIMATION FURTHER TOPICS SUMMARY APPENDIX 4A DERIVATION OF FML (y and x MULTINORMAL). APPENDIX 4B DERIVATION OF FML (S WISHART DISTRIBUTION)APPENDIX 4C NUMERICAL SOLUTIONS TO MINIMIZE FITTING FUNCTIONS APPENDIX 4D ILLUSTRATIONS OF LISREL AND EQS PROGRAMS CHAPTER FIVE: The Consequences of Measurement Error UNIVARIATE CONSEQUENCES BIVARIATE AND SIMPLE REGRESSION CONSEQUENCES CONSEQUENCES IN MULTIPLE REGRESSION CORRELATED ERRORS OF MEASUREMENT CONSEQUENCES IN MULTIEQUATION SYSTEMS SUMMARY APPENDIX 5A ILLUSTRATIONS OF LISREL AND EQS PROGRAMS CHAPTER SIX: Measurement Models: The Relation between Latent and Observed Variables MEASUREMENT MODELS VALIDITY RELIABILITY. CAUSE INDICATORSSUMMARY APPENDIX 6A LISREL PROGRAM FOR THE MULTITRAIT-MULTIMETHOD EXAMPLE CHAPTER SEVEN: Confirmatory Factor Analysis EXPLORATORY AND CONFIRMATORY FACTOR ANALYSIS MODEL SPECIFICATION IMPLIED COVARIANCE MATRIX IDENTIFICATION ESTIMATION MODEL EVALUATION COMPARISON OF MODELS RESPECIFICATION OF MODEL EXTENSIONS SUMMARY APPENDIX 7A EXAMPLES OF PROGRAM LISTINGS CHAPTER EIGHT: The General Model, Part I: Latent Variable and Measurement Models Combined MODEL SPECIFICATION IMPLIED COVARIANCE MATRIX IDENTIFICATION ESTIMATION AND MODEL EVALUATION. STANDARDIZED AND UNSTANDARDIZED COEFFICIENTSMEANS AND EQUATION CONSTANTS COMPARING GROUPS MISSING VALUES TOTAL, DIRECT, AND INDIRECT EFFECTS SUMMARY APPENDIX 8A ASYMPTOTIC VARIANCES OF EFFECTS APPENDIX 8B LISTING OF THE LISREL VI PROGRAM FOR MISSING VALUE EXAMPLE CHAPTER NINE: The General Model, Part II: Extensions ALTERNATIVE NOTATIONS/REPRESENTATIONS EQUALITY AND INEQUALITY CONSTRAINTS QUADRATIC AND INTERACTION TERMS INSTRUMENTAL-VARIABLE (IV) ESTIMATORS DISTRIBUTIONAL ASSUMPTIONS CATEGORICAL OBSERVED VARIABLES SUMMARY APPENDIX 9A LISREL PROGRAM FOR MODEL IN FIGURE 9.1(c). APPENDIX A: Matrix Algebra ReviewSCALARS, VECTORS, AND MATRICES MATRIX OPERATIONS APPENDIX B: Asymptotic Distribution Theory CONVERGENCE IN PROBABILITY CONVERGENCE IN DISTRIBUTIONS References Index.