Elsevier S & T

Handbook of Latent Variable and Related Models

Lee, Sik-Yum

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Table of contents
  • Front CoverCover
  • Handbook of Latent Variable and Related ModelsIII
  • Copyright PageIV
  • Handbook Series on Computing and Statistics with ApplicationsV
  • PrefaceVII
  • About the AuthorsIX
  • ContributorsXV
  • Table of ContentsXVII
  • Chapter 1.Covariance Structure Models for Maximal Reliability of Unit-Weighted Composites1
  • 1. Proposed identification condition for factor models3
  • 2. Reliability based on proposed parameterization5
  • 3. Properties of the coefficient6
  • 4. Illustration with exploratory factor analysis7
  • 5. Reliability with general latent variable models8
  • 6. Dimension-free and greatest lower bound reliability11
  • 7. Reliability of weighted composites12
  • 8. Selection of weights for maximal reliability14
  • 9. Conclusions15
  • Acknowledgements16
  • References17
  • Chapter 2. Advances in Analysis of Mean and Covariance Structure when Data are Incomplete21
  • 1. Introduction21
  • 2. Missing data mechanism24
  • 3. Methods for handling missing data26
  • 4. Simulation studies34
  • 5. Sensitivity analysis for missing data mechanism36
  • 6. SEM software for incomplete data41
  • References42
  • Chapter 3. Rotation Algorithms: From Beginning to End45
  • 1. Introduction45
  • 2. Factor analysis46
  • 3. A parameterization for Lambda and Phi48
  • 4. Reference structures49
  • 5. Thurstone's graphical rotation method49
  • 6. Early analytic oblique rotation methods52
  • 7. Pairwise algorithms53
  • 8. Analytic rotation methods: Orthogonal54
  • 9. Direct analytic methods: Oblique59
  • 10. Discussion61
  • References63
  • Chapter 4. Selection of Manifest Variables65
  • 1. Introduction65
  • 2. Manifest variable selection in factor analysis67
  • 3. SEFA and examples with empirical data72
  • 4. Variable selection with a model fit and reliability analysis77
  • 5. Conclusion and final remarks83
  • Acknowledgements84
  • References84
  • Chapter 5. Bayesian Analysis of Mixtures Structural Equation Models with Missing Data87
  • 1. Introduction87
  • 2. Model description89
  • 3. Bayesian analysis of the models90
  • 4. Simulation studies94
  • 5. An illustrative example100
  • 6. Analysis via WinBUGS102
  • 7. Discussion104
  • Acknowledgements104
  • Appendix A. The permutation sampler105
  • Appendix B. Searching for identifiability constraints105
  • Appendix C. Manifest variables in the ICPSR example106
  • References106
  • Chapter 6. Local Influence Analysis for Latent Variable Models with Non-Ignorable Missing Responses109
  • 1. Introduction109
  • 2. Local influence of latent variable models with non-ignorable missing data111
  • 3. Normal mixed effects model114
  • 4. Generalized linear mixed model123
  • 5. Conclusion128
  • Appendix A129
  • Appendix B129
  • Appendix C130
  • References133
  • Chapter 7. Goodness-of-Fit Measures for Latent Variable Models for Binary Data135
  • 1. Introduction135
  • 2. Latent variable models for binary responses136
  • 3. Goodness-of-fit tests for latent variable models for binary data138
  • 4. Limited information statistics141
  • 5. Test based on the log-odds ratio144
  • 6. Simulations146
  • 7. Conclusion158
  • Acknowledgements160
  • References160
  • Chapter 8 Bayesian Structural Equation Modeling163
  • 1. Introduction163
  • 2. Structural equation models165
  • 3. Bayesian approach167
  • 4. Democratization and industrialization application172
  • 5. Discussion and future research181
  • Appendix A. Prior specifications182
  • Appendix B. Results: posterior parameters estimates (see Table B.1)184
  • References186
  • Chapter 9. The Analysis of Structural Equation Model with Ranking Data using Mx189
  • 1. Introduction189
  • 2. Multivariate normal model for analyzing ranking and ordinal categorical data190
  • 3. Implementation by Mx192
  • 4. Applications197
  • 5. Discussion201
  • Acknowledgements202
  • Appendix A. Mx input script for p=4, auto data set, basic Thurstonian model202
  • Appendix B. Mx input script, auto data set, factor analysis model204
  • Appendix C. Mx input script, auto data set, model of reduced form parameters205
  • References206
  • Chapter 10. Multilevel Structural Equation Modeling209
  • 1. Introduction209
  • 2. Response types210
  • 3. Multilevel measurement models212
  • 4. Multilevel structural equation models217
  • 5. Estimation219
  • 6. Application: Student ability and teacher excellence220
  • References226
  • Chapter 11. Statistical Inference of Moment Structures229
  • 1. Introduction229
  • 2. Moment structures models229
  • 3. Minimum discrepancy function estimation approach234
  • 4. Consistency of MDF estimators237
  • 5. Asymptotic analysis of the MDF estimation procedure239
  • 6. Asymptotic robustness of the MDF statistical inference252
  • Acknowledgements258
  • References258
  • Chapter 12. Meta-Analysis and Latent Variable Models for Binary Data261
  • 1. Introduction261
  • 2. Meta-analysis for binary data263
  • 3. Publication bias and sensitivity analysis267
  • 4. An illustrated example271
  • 5. Discussion and further development275
  • References277
  • Chapter 13. Analysis of Multisample Structural Equation Models with Applications to Quality of Life279
  • 1. Introduction279
  • 2. A multisample SEM with missing ordered categorical variables281
  • 3. ML analysis283
  • 4. Illustrative example: analysis of multisample synthetic QOL data288
  • 5. Discussion297
  • Acknowledgements298
  • Appendix A298
  • Appendix B300
  • References300
  • Chapter 14. The Set of Feasible Solutions for Reliability and Factor Analysis303
  • 1. Introduction304
  • 2. The Ledermann bound306
  • 3. Reliability theory and a convex set of possible solutions for (2)307
  • 4. Minimizing the sum and the sum of squares of unexplained common variances310
  • 5. The feasible set from two perspectives312
  • 6. Reliability measures derived from a single factor solution313
  • 7. Reliability derived from multiple factor analysis315
  • 8. Discussion318
  • References319
  • Chapter 15. Nonlinear Structural Equation Modeling as a Statistical Method321
  • 1. Introduction321
  • 2. General nonlinear structural equation model322
  • 3. Pseudo-likelihood estimation for the general nonlinear structural equation model327
  • 4. Example332
  • 5. Discussion338
  • References341
  • Chapter 16. Matrix Methods and their Applications to Factor Analysis345
  • 1. Introduction345
  • 2. Fundamentals of matrix methods346
  • 3. Applications of matrix methods to factor analysis350
  • Acknowledgements365
  • References365
  • Chapter 17. Robust Procedures in Structural Equation Modeling367
  • 1. Introduction367
  • 2. Normal theory ML and related procedures370
  • 3. Generalized Least Squares (GLS) procedures374
  • 4. Real robust procedures377
  • 5. Misspecified models385
  • 6. Illustration388
  • References393
  • Chapter 18. Stochastic Approximation Algorithms for Estimation of Spatial Mixed Models399
  • 1. Introduction399
  • 2. Spatial mixed models401
  • 3. Estimation procedure403
  • 4. Applications411
  • Acknowledgements418
  • References418
  • Author Index423
  • Subject Index431
Book details
  • Vendor Elsevier S & T
  • SKU 9780444520449
  • ISBN-13 9780080471266
  • Author Lee, Sik-Yum
  • Category Mathematics
  • Subject Multivariate Analysis

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Description eBook delivery & access Reviews
This Handbook covers latent variable models, which are a flexible class of models for modeling multivariate data to explore relationships among observed and latent variables.

- Covers a wide class of important models
- Models and statistical methods described provide tools for analyzing a wide spectrum of complicated data
- Includes illustrative examples with real data sets from business, education, medicine, public health and sociology.
- Demonstrates the use of a wide variety of statistical, computational, and mathematical techniques.