Structural Equations with Latent Variables ( Wiley Series in Probability and Statistics )

Publication series :Wiley Series in Probability and Statistics

Author: Kenneth A. Bollen  

Publisher: John Wiley & Sons Inc‎

Publication year: 2014

E-ISBN: 9781118619162

P-ISBN(Hardback):  9780471011712

Subject: C32 Statistical method, calculating method

Language: ENG

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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 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.

Chapter

Measurement Model

Covariance

Covariance Algebra

Sample Covariances

Path Analysis

Path Diagrams

Decomposition of Covariances and Correlations

Total, Direct, And Indirect Effects

Summary

Chapter 3: Causality And Causal Models

Nature of Causality

Isolation

Association

Direction of Causation

Limitations of “causal” Modeling

Model-data Versus Model-reality Consistency

Experimental and Nonexperimental Research

Criticisms of Structural Equation Models

Summary

Chapter 4: Structural Equation Models With Observed Variables

Model Specification

Implied Covariance Matrix

Identification

T-rule

Null B Rule

Recursive Rule

Rank And Order Conditions

Summary of Identification Rules

Estimation

Maximum Likelihood (ml)

Unweighted Least Squares (uls)

Generalized Least Squares (gls)

Other Estimators

Empirical Examples

Further Topics

Standardized And Unstandardized Coefficients

Alternative Assumptions for x

Interaction Terms

Intercepts

Analysis of Variance (anova) And Related Techniques

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

Starting Values

Steps in the Sequence

Stopping Criteria

Appendix 4d Illustrations of Lisrel and Eqs Programs

Lisrel Program

Eqs Program

Chapter 5: The Consequences of Measurement Error

Univariate Consequences

Bivariate and Simple Regression Consequences

Consequences in Multiple Regression

Correlated Errors of Measurement

Consequences in Multiequation Systems

Union Sentiment Example

Unknown Reliabilities

Objective and Subjective Socioeconomic Status (ses)

Summary

Appendix 5a Illustrations of Lisrel and Eqs Programs

Lisrel Program

Eqs Program

Chapter 6: Measurement Models:the Relation Between Latent And Observed Variables

Measurement Models

Validity

Content Validity

Criterion Validity

Construct Validity

Convergent and Discriminant Validity

Alternatives to Classical Validity Measures

Summary

Reliability

Empirical Means of Assessing Reliability

Alternatives to Classical Reliability Measures

Summary

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

Incremental Fit Indices

Additional Measures of Overall Model Fit

Empirical and Simulation Examples

Summary of Overall Fit Measures

Component Fit Measures

Parameter Estimates

Asymptotic Standard Errors

Asymptotic Correlation Matrix of Parameter Estimates

R2Xi for Observed Variables

Does The Sympathy and Anger Model Fit?

Comparison of Models

Likelihood Ratio (lr) Test

Lagrangian Multiplier (lm) Test

Wald (w) Test

Summary of Lr, Lm, and W Tests

Respecifictlon of Model

Theory and Substantive-based Revisions

Exploratory Lr, Lm, And W Tests

Other Empirical Procedures

Summary of Respecification Procedures

Extensions

Factor Score Estimation

Latent Variable Means And Equation Intercepts

Cause Indicators

Higher-order Factor Analyses

Summary

Appendix 7a Examples Of Program Listings

Example 1: Estimating Means And Intercepts

Example 2: Estimating A Higher-order Factor Analysis

Chapter 8: The General Model, Part I: Latent Variable And Measurement Models Combined

Model Specification

Implied Covariance Matrix

Identification

T-rule

Two-step Rule

Mimic Rule

Summary of Identification Rules

Industrialization and Political Democracy Example

Estimation and Model Evaluation

Power of Significance Test

Standardized and Unstandardized Coefficients

Means and Equation Constants

Comparing Groups

Invariance of Intercepts and Means

Missing Values

Alternative Estimators Of Covariance Matrix

Explicit Estimation

Systematic Missing Values

Total, Direct, and Indirect Effects

Specific Effects

Summary

Appendix 8a Asymptotic Variances of Effects

Appendix 8b Listing of the Lisrel Vi Program for Missing Value Example

Chapter 9: The General Model, Part II: Extensions

Alternative Notations / Representations

Equality and Inequality Constraints

Quadratic and Interaction Terms

Instrumental-variable (iv) Estimators

Distributional Assumptions

Consequences

Detection

Correction

Weighted Least Squares Estimators

Specializations of Fwls

Elliptical Estimator

Summary of Fwls

Categorical Observed Variables

Assumptions Violated and Consequences

Robustness Studies

Summary of Robustness to Categorization

Corrective Procedures

Summary

Appendix 9a Lisrel Program for Model in Figure 9.1(c)

Appendix A: Matrix Algebra Review

Scalars, Vectors, and Matrices

Matrix Operations

Appendix B: Asymptotic Distribution Theory

Convergence in Probability

Convergence in Distributions

References

Index

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