Structural Equations with Latent Variables

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). 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 and contains an integrated comparison of the available strategies for analyzing ordinal data. This is a case study work with illuminating examples taken from across the wide spectrum of ordinal categorical applications. 1984 (0 471-89055-3) 287 pp. Regression Diagnostics Identifying Influential Data and Sources of Collinearity David A. Belsley, Edwin Kuh and Roy E. Welsch This book provides the practicing statistician and econometrician with new tools for assessing the quality and reliability of regression estimates. Diagnostic techniques are developed that aid in the systematic location of data points that are either unusual or inordinately influential; measure the presence and intensity of collinear relations among the regression data and help to identify the variables involved in each; and pinpoint the estimated coefficients that are potentially most adversely affected. The primary emphasis of these contributions is on diagnostics, but suggestions for remedial action are given and illustrated. 1980 (0 471-05856-4) 292 pp. Applied Regression Analysis Second Edition Norman Draper and Harry Smith Featuring a significant expansion of material reflecting recent advances, here is a complete and up-to-date introduction to the fundamentals of regression analysis, focusing on understanding the latest concepts and applications of these methods. The authors thoroughly explore the fitting and checking of both linear and nonlinear regression models, using small or large data sets and pocket or high-speed computing equipment. Features added to this Second Edition include the practical implications of linear regression; the Durbin-Watson test for serial correlation; families of transformations; inverse, ridge, latent root and robust regression; and nonlinear growth models. Includes many new exercises and worked examples. 1981 (0 471-02995-5) 709 pp. The EPUB format of this title may not be compatible for use on all handheld devices.

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 and contains an integrated comparison of the available strategies for analyzing ordinal data. This is a case study work with illuminating examples taken from across the wide spectrum of ordinal categorical applications. 1984 (0 471-89055-3) 287 pp. Regression Diagnostics Identifying Influential Data and Sources of Collinearity David A. Belsley, Edwin Kuh and Roy E. Welsch This book provides the practicing statistician and econometrician with new tools for assessing the quality and reliability of regression estimates. Diagnostic techniques are developed that aid in the systematic location of data points that are either unusual or inordinately influential; measure the presence and intensity of collinear relations among the regression data and help to identify the variables involved in each; and pinpoint the estimated coefficients that are potentially most adversely affected. The primary emphasis of these contributions is on diagnostics, but suggestions for remedial action are given and illustrated. 1980 (0 471-05856-4) 292 pp. Applied Regression Analysis Second Edition Norman Draper and Harry Smith Featuring a significant expansion of material reflecting recent advances, here is a complete and up-to-date introduction to the fundamentals of regression analysis, focusing on understanding the latest concepts and applications of these methods. The authors thoroughly explore the fitting and checking of both linear and nonlinear regression models, using small or large data sets and pocket or high-speed computing equipment. Features added to this Second Edition include the practical implications of linear regression; the Durbin-Watson test for serial correlation; families of transformations; inverse, ridge, latent root and robust regression; and nonlinear growth models. Includes many new exercises and worked examples. 1981 (0 471-02995-5) 709 pp.

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. Cause Indicators; Summary; Appendix 6a Lisrel Program for the Multitrait-multimethod Example; Chapter 7: Confirmatory Factor Analysis; Exploratory and Confirmatory Factor Analysis; Model Specification; Implied Covariance Matrix; Identification; Three-indicator Rules; Two-indicator Rules; Summary Of Rules; An Insufficient Condition Of Identification; Empirical Tests Of Identification; Recommendations For Checking Identification; Political Democracy Example; Estimation; Nonconvergence; Model Evaluation; Overall Model Fit Measures; Residuals; A Chi-square (x2) Test A comprehensive introduction to the general structure equation systems--commonly known as the LISREL model--used for quantitative research in the social sciences. Unified approach presents path analysis, recursive and nonrecursive models, classical econometrics, and confirmatory factor analysis as special cases of a general model. Also discusses application of these techniques to empirical examples, including some LISREL and EQS programs.