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Latent variable models and factor analysis : a unified approach.
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....
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, N.J. :
Wiley,
2011.
|
| Edición: | 3rd ed. / |
| Colección: | Wiley series in probability and statistics.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Bartholomew, David J. | |
| 245 | 1 | 0 | |a Latent variable models and factor analysis : |b a unified approach. |
| 250 | |a 3rd ed. / |b David Bartholomew, Martin Knott, Irini Moustaki. | ||
| 260 | |a Hoboken, N.J. : |b Wiley, |c 2011. | ||
| 300 | |a 1 online resource (xiii, 277 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 490 | 1 | |a Wiley series in probability and statistics | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | 0 | |6 880-01 |t Front matter -- |t Basic ideas and examples -- |t The general linear latent variable model -- |t The normal linear factor model -- |t Binary data : latent trait models -- |t Polytomous data : latent trait models -- |t Latent class models -- |t Models and methods for manifest variables of mixed type -- |t Relationships between latent variables -- |t Related techniques for investigating dependency -- |t Software appendix -- |t References -- |t Author index -- |t Subject index. |
| 520 | |a 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. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Latent variables. | |
| 650 | 0 | |a Latent structure analysis. | |
| 650 | 0 | |a Factor analysis. | |
| 650 | 2 | |a Factor Analysis, Statistical | |
| 650 | 6 | |a Variables latentes. | |
| 650 | 6 | |a Analyse de structure latente. | |
| 650 | 6 | |a Analyse factorielle. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x Multivariate Analysis. |2 bisacsh | |
| 650 | 7 | |a Factor analysis |2 fast | |
| 650 | 7 | |a Latent structure analysis |2 fast | |
| 650 | 7 | |a Latent variables |2 fast | |
| 700 | 1 | |a Knott, M. |q (Martin) |1 https://id.oclc.org/worldcat/entity/E39PBJtX7RrhPgmDDmX6drBdcP | |
| 700 | 1 | |a Moustaki, Irini. | |
| 758 | |i has work: |a Latent variable models and factor analysis (Text) |1 https://id.oclc.org/worldcat/entity/E39PCH4cbWYW4JKKjdmkW74W9P |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Bartholomew, David J. |t Latent variable models and factor analysis. |b 3rd ed. |d Hoboken, N.J. : Wiley, 2011 |z 9780470971925 |w (DLC) 2011007711 |w (OCoLC)710044915 |
| 830 | 0 | |a Wiley series in probability and statistics. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=819225 |z Texto completo |
| 880 | 0 | 0 | |6 505-01/(S |g Machine generated contents note: |g 1. |t Basic ideas and examples -- |g 1.1. |t statistical problem -- |g 1.2. |t basic idea -- |g 1.3. |t Two examples -- |g 1.3.1. |t Binary manifest variables and a single binary latent variable -- |g 1.3.2. |t model based on normal distributions -- |g 1.4. |t broader theoretical view -- |g 1.5. |t Illustration of an alternative approach -- |g 1.6. |t overview of special cases -- |g 1.7. |t Principal components -- |g 1.8. |t historical context -- |g 1.9. |t Closely related fields in statistics -- |g 2. |t general linear latent variable model -- |g 2.1. |t Introduction -- |g 2.2. |t model -- |g 2.3. |t Some properties of the model -- |g 2.4. |t special case -- |g 2.5. |t sufficiency principle -- |g 2.6. |t Principal special cases -- |g 2.7. |t Latent variable models with non-linear terms -- |g 2.8. |t Fitting the models -- |g 2.9. |t Fitting by maximum likelihood -- |g 2.10. |t Fitting by Bayesian methods -- |g 2.11. |t Rotation -- |g 2.12. |t Interpretation -- |g 2.13. |t Sampling error of parameter estimates -- |g 2.14. |t prior distribution -- |g 2.15. |t Posterior analysis -- |g 2.16. |t further note on the prior -- |g 2.17. |t Psychometric inference -- |g 3. |t normal linear factor model -- |g 3.1. |t model -- |g 3.2. |t Some distributional properties -- |g 3.3. |t Constraints on the model -- |g 3.4. |t Maximum likelihood estimation -- |g 3.5. |t Maximum likelihood estimation by the E-M algorithm -- |g 3.6. |t Sampling variation of estimators -- |g 3.7. |t Goodness of fit and choice of q -- |g 3.7.1. |t Model selection criteria -- |g 3.8. |t Fitting without normality assumptions: least squares methods -- |g 3.9. |t Other methods of fitting -- |g 3.10. |t Approximate methods for estimating Φ -- |g 3.11. |t Goodness of fit and choice of q for least squares methods -- |g 3.12. |t Further estimation issues -- |g 3.12.1. |t Consistency -- |g 3.12.2. |t Scale-invariant estimation -- |g 3.12.3. |t Heywood cases -- |g 3.13. |t Rotation and related matters -- |g 3.13.1. |t Orthogonal rotation -- |g 3.13.2. |t Oblique rotation -- |g 3.13.3. |t Related matters -- |g 3.14. |t Posterior analysis: the normal case -- |g 3.15. |t Posterior analysis: least squares -- |g 3.16. |t Posterior analysis: a reliability approach -- |g 3.17. |t Examples -- |g 4. |t Binary data: latent trait models -- |g 4.1. |t Preliminaries -- |g 4.2. |t logit/normal model -- |g 4.3. |t probit/normal model -- |g 4.4. |t equivalence of the response function and underlying variable approaches -- |g 4.5. |t Fitting the logit/normal model: the E-M algorithm -- |g 4.5.1. |t Fitting the probit/normal model -- |g 4.5.2. |t Other methods for approximating the integral -- |g 4.6. |t Sampling properties of the maximum likelihood estimators -- |g 4.7. |t Approximate maximum likelihood estimators -- |g 4.8. |t Generalised least squares methods -- |g 4.9. |t Goodness of fit -- |g 4.10. |t Posterior analysis -- |g 4.11. |t Fitting the logit/normal and probit/normal models: Markov chain Monte Carlo -- |g 4.11.1. |t Gibbs sampling -- |g 4.11.2. |t Metropolis-Hastings -- |g 4.11.3. |t Choosing prior distributions -- |g 4.11.4. |t Convergence diagnostics in MCMC -- |g 4.12. |t Divergence of the estimation algorithm -- |g 4.13. |t Examples -- |g 5. |t Polytomous data: latent trait models -- |g 5.1. |t Introduction -- |g 5.2. |t response function model based on the sufficiency principle -- |g 5.3. |t Parameter interpretation -- |g 5.4. |t Rotation -- |g 5.5. |t Maximum likelihood estimation of the polytomous logit model -- |g 5.6. |t approximation to the likelihood -- |g 5.6.1. |t One factor -- |g 5.6.2. |t More than one factor -- |g 5.7. |t Binary data as a special case -- |g 5.8. |t Ordering of categories -- |g 5.8.1. |t response function model for ordinal variables -- |g 5.8.2. |t Maximum likelihood estimation of the model with ordinal variables -- |g 5.8.3. |t partial credit model -- |g 5.8.4. |t underlying variable model -- |g 5.9. |t alternative underlying variable model -- |g 5.10. |t Posterior analysis -- |g 5.11. |t Further observations -- |g 5.12. |t Examples of the analysis of polytomous data using the logit model -- |g 6. |t Latent class models -- |g 6.1. |t Introduction -- |g 6.2. |t latent class model with binary manifest variables -- |g 6.3. |t latent class model for binary data as a latent trait model -- |g 6.4. |t K latent classes within the GLLVM -- |g 6.5. |t Maximum likelihood estimation -- |g 6.6. |t Standard errors -- |g 6.7. |t Posterior analysis of the latent class model with binary manifest variables -- |g 6.8. |t Goodness of fit -- |g 6.9. |t Examples for binary data -- |g 6.10. |t Latent class models with unordered polytomous manifest variables -- |g 6.11. |t Latent class models with ordered polytomous manifest variables -- |g 6.12. |t Maximum likelihood estimation -- |g 6.12.1. |t Allocation of individuals to latent classes -- |g 6.13. |t Examples for unordered polytomous data -- |g 6.14. |t Identifiability -- |g 6.15. |t Starting values -- |g 6.16. |t Latent class models with metrical manifest variables -- |g 6.16.1. |t Maximum likelihood estimation -- |g 6.16.2. |t Other methods -- |g 6.16.3. |t Allocation to categories -- |g 6.17. |t Models with ordered latent classes -- |g 6.18. |t Hybrid models -- |g 6.18.1. |t Hybrid model with binary manifest variables -- |g 6.18.2. |t Maximum likelihood estimation -- |g 7. |t Models and methods for manifest variables of mixed type -- |g 7.1. |t Introduction -- |g 7.2. |t Principal results -- |g 7.3. |t Other members of the exponential family -- |g 7.3.1. |t binomial distribution -- |g 7.3.2. |t Poisson distribution -- |g 7.3.3. |t gamma distribution -- |g 7.4. |t Maximum likelihood estimation -- |g 7.4.1. |t Bernoulli manifest variables -- |g 7.4.2. |t Normal manifest variables -- |g 7.4.3. |t general E-M approach to solving the likelihood equations -- |g 7.4.4. |t Interpretation of latent variables -- |g 7.5. |t Sampling properties and goodness of fit -- |g 7.6. |t Mixed latent class models -- |g 7.7. |t Posterior analysis -- |g 7.8. |t Examples -- |g 7.9. |t Ordered categorical variables and other generalisations -- |g 8. |t Relationships between latent variables -- |g 8.1. |t Scope -- |g 8.2. |t Correlated latent variables -- |g 8.3. |t Procrustes methods -- |g 8.4. |t Sources of prior knowledge -- |g 8.5. |t Linear structural relations models -- |g 8.6. |t LISREL model -- |g 8.6.1. |t structural model -- |g 8.6.2. |t measurement model -- |g 8.6.3. |t model as a whole -- |g 8.7. |t Adequacy of a structural equation model -- |g 8.8. |t Structural relationships in a general setting -- |g 8.9. |t Generalisations of the LISREL model -- |g 8.10. |t Examples of models which are indistinguishable -- |g 8.11. |t Implications for analysis -- |g 9. |t Related techniques for investigating dependency -- |g 9.1. |t Introduction -- |g 9.2. |t Principal components analysis -- |g 9.2.1. |t distributional treatment -- |g 9.2.2. |t sample-based treatment -- |g 9.2.3. |t Unordered categorical data -- |g 9.2.4. |t Ordered categorical data -- |g 9.3. |t alternative to the normal factor model -- |g 9.4. |t Replacing latent variables by linear functions of the manifest variables -- |g 9.5. |t Estimation of correlations and regressions between latent variables -- |g 9.6. |t Q-Methodology -- |g 9.7. |t Concluding reflections of the role of latent variables in statistical modelling. |
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