Description |
1 online resource (xiii, 277 pages) : illustrations |
Series |
Wiley series in probability and statistics |
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Wiley series in probability and statistics.
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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 |
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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.
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Latent structure analysis.
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Factor analysis.
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Factor Analysis, Statistical
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MATHEMATICS -- Probability & Statistics -- Multivariate Analysis.
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Factor analysis
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Latent structure analysis
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Latent variables
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Form |
Electronic book
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Author |
Knott, M. (Martin)
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Moustaki, Irini.
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LC no. |
2011007711 |
ISBN |
9781119970583 |
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111997058X |
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9781119970590 |
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1119970598 |
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0470971924 |
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9780470971925 |
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9786613177698 |
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6613177695 |
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1283177692 |
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9781283177696 |
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