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Book Cover
E-book
Author Bartholomew, David J.

Title Latent variable models and factor analysis : a unified approach
Edition 3rd ed. / David Bartholomew, Martin Knott, Irini Moustaki
Published Hoboken, N.J. : Wiley, 2011

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Description 1 online resource (xiii, 277 pages) : illustrations
Series Wiley series in probability and statistics
Wiley series in probability and statistics.
Contents 880-01 Front matter -- Basic ideas and examples -- The general linear latent variable model -- The normal linear factor model -- Binary data : latent trait models -- Polytomous data : latent trait models -- Latent class models -- Models and methods for manifest variables of mixed type -- Relationships between latent variables -- Related techniques for investigating dependency -- Software appendix -- References -- Author index -- Subject index
880-01/(S Machine generated contents note: 1. Basic ideas and examples -- 1.1. statistical problem -- 1.2. basic idea -- 1.3. Two examples -- 1.3.1. Binary manifest variables and a single binary latent variable -- 1.3.2. model based on normal distributions -- 1.4. broader theoretical view -- 1.5. Illustration of an alternative approach -- 1.6. overview of special cases -- 1.7. Principal components -- 1.8. historical context -- 1.9. Closely related fields in statistics -- 2. general linear latent variable model -- 2.1. Introduction -- 2.2. model -- 2.3. Some properties of the model -- 2.4. special case -- 2.5. sufficiency principle -- 2.6. Principal special cases -- 2.7. Latent variable models with non-linear terms -- 2.8. Fitting the models -- 2.9. Fitting by maximum likelihood -- 2.10. Fitting by Bayesian methods -- 2.11. Rotation -- 2.12. Interpretation -- 2.13. Sampling error of parameter estimates -- 2.14. prior distribution -- 2.15. Posterior analysis -- 2.16. further note on the prior -- 2.17. Psychometric inference -- 3. normal linear factor model -- 3.1. model -- 3.2. Some distributional properties -- 3.3. Constraints on the model -- 3.4. Maximum likelihood estimation -- 3.5. Maximum likelihood estimation by the E-M algorithm -- 3.6. Sampling variation of estimators -- 3.7. Goodness of fit and choice of q -- 3.7.1. Model selection criteria -- 3.8. Fitting without normality assumptions: least squares methods -- 3.9. Other methods of fitting -- 3.10. Approximate methods for estimating Φ -- 3.11. Goodness of fit and choice of q for least squares methods -- 3.12. Further estimation issues -- 3.12.1. Consistency -- 3.12.2. Scale-invariant estimation -- 3.12.3. Heywood cases -- 3.13. Rotation and related matters -- 3.13.1. Orthogonal rotation -- 3.13.2. Oblique rotation -- 3.13.3. Related matters -- 3.14. Posterior analysis: the normal case -- 3.15. Posterior analysis: least squares -- 3.16. Posterior analysis: a reliability approach -- 3.17. Examples -- 4. Binary data: latent trait models -- 4.1. Preliminaries -- 4.2. logit/normal model -- 4.3. probit/normal model -- 4.4. equivalence of the response function and underlying variable approaches -- 4.5. Fitting the logit/normal model: the E-M algorithm -- 4.5.1. Fitting the probit/normal model -- 4.5.2. Other methods for approximating the integral -- 4.6. Sampling properties of the maximum likelihood estimators -- 4.7. Approximate maximum likelihood estimators -- 4.8. Generalised least squares methods -- 4.9. Goodness of fit -- 4.10. Posterior analysis -- 4.11. Fitting the logit/normal and probit/normal models: Markov chain Monte Carlo -- 4.11.1. Gibbs sampling -- 4.11.2. Metropolis-Hastings -- 4.11.3. Choosing prior distributions -- 4.11.4. Convergence diagnostics in MCMC -- 4.12. Divergence of the estimation algorithm -- 4.13. Examples -- 5. Polytomous data: latent trait models -- 5.1. Introduction -- 5.2. response function model based on the sufficiency principle -- 5.3. Parameter interpretation -- 5.4. Rotation -- 5.5. Maximum likelihood estimation of the polytomous logit model -- 5.6. approximation to the likelihood -- 5.6.1. One factor -- 5.6.2. More than one factor -- 5.7. Binary data as a special case -- 5.8. Ordering of categories -- 5.8.1. response function model for ordinal variables -- 5.8.2. Maximum likelihood estimation of the model with ordinal variables -- 5.8.3. partial credit model -- 5.8.4. underlying variable model -- 5.9. alternative underlying variable model -- 5.10. Posterior analysis -- 5.11. Further observations -- 5.12. Examples of the analysis of polytomous data using the logit model -- 6. Latent class models -- 6.1. Introduction -- 6.2. latent class model with binary manifest variables -- 6.3. latent class model for binary data as a latent trait model -- 6.4. K latent classes within the GLLVM -- 6.5. Maximum likelihood estimation -- 6.6. Standard errors -- 6.7. Posterior analysis of the latent class model with binary manifest variables -- 6.8. Goodness of fit -- 6.9. Examples for binary data -- 6.10. Latent class models with unordered polytomous manifest variables -- 6.11. Latent class models with ordered polytomous manifest variables -- 6.12. Maximum likelihood estimation -- 6.12.1. Allocation of individuals to latent classes -- 6.13. Examples for unordered polytomous data -- 6.14. Identifiability -- 6.15. Starting values -- 6.16. Latent class models with metrical manifest variables -- 6.16.1. Maximum likelihood estimation -- 6.16.2. Other methods -- 6.16.3. Allocation to categories -- 6.17. Models with ordered latent classes -- 6.18. Hybrid models -- 6.18.1. Hybrid model with binary manifest variables -- 6.18.2. Maximum likelihood estimation -- 7. Models and methods for manifest variables of mixed type -- 7.1. Introduction -- 7.2. Principal results -- 7.3. Other members of the exponential family -- 7.3.1. binomial distribution -- 7.3.2. Poisson distribution -- 7.3.3. gamma distribution -- 7.4. Maximum likelihood estimation -- 7.4.1. Bernoulli manifest variables -- 7.4.2. Normal manifest variables -- 7.4.3. general E-M approach to solving the likelihood equations -- 7.4.4. Interpretation of latent variables -- 7.5. Sampling properties and goodness of fit -- 7.6. Mixed latent class models -- 7.7. Posterior analysis -- 7.8. Examples -- 7.9. Ordered categorical variables and other generalisations -- 8. Relationships between latent variables -- 8.1. Scope -- 8.2. Correlated latent variables -- 8.3. Procrustes methods -- 8.4. Sources of prior knowledge -- 8.5. Linear structural relations models -- 8.6. LISREL model -- 8.6.1. structural model -- 8.6.2. measurement model -- 8.6.3. model as a whole -- 8.7. Adequacy of a structural equation model -- 8.8. Structural relationships in a general setting -- 8.9. Generalisations of the LISREL model -- 8.10. Examples of models which are indistinguishable -- 8.11. Implications for analysis -- 9. Related techniques for investigating dependency -- 9.1. Introduction -- 9.2. Principal components analysis -- 9.2.1. distributional treatment -- 9.2.2. sample-based treatment -- 9.2.3. Unordered categorical data -- 9.2.4. Ordered categorical data -- 9.3. alternative to the normal factor model -- 9.4. Replacing latent variables by linear functions of the manifest variables -- 9.5. Estimation of correlations and regressions between latent variables -- 9.6. Q-Methodology -- 9.7. Concluding reflections of the role of latent variables in statistical modelling
Summary Latent Variable Models and Factor Analysis provides a comprehensive and unified approach to factor analysis and latent variable modeling from a statistical perspective. This book presents a general framework to enable the derivation of the commonly used models, along with updated numerical examples. Nature and interpretation of a latent variable is also introduced along with related techniques for investigating dependency. This book:Provides a unified approach showing how such apparently diverse methods as Latent Class Analysis and Factor Analysis are actually members of the same family. Presen
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Latent variables.
Latent structure analysis.
Factor analysis.
Factor Analysis, Statistical
MATHEMATICS -- Probability & Statistics -- Multivariate Analysis.
Factor analysis
Latent structure analysis
Latent variables
Form Electronic book
Author Knott, M. (Martin)
Moustaki, Irini.
LC no. 2011007711
ISBN 9781119970583
111997058X
9781119970590
1119970598
0470971924
9780470971925
9786613177698
6613177695
1283177692
9781283177696