Latent variable models and factor analysis : a unified approach.

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....

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Bibliographic Details
Main Author: Bartholomew, David J.
Other Authors: Knott, M. (Martin), Moustaki, Irini
Format: eBook
Language:English
Published: Hoboken, N.J. : Wiley, 2011.
Edition:3rd ed. /
Series:Wiley series in probability and statistics.
Subjects:
Latent variables.
Latent structure analysis.
Factor analysis.
MATHEMATICS > Probability & Statistics > Multivariate Analysis.
Factor analysis
Latent structure analysis
Latent variables
Online Access:Click for online access

MARC

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050 4 |a QA278.6  |b .B37 2011 
072 7 |a MAT  |x 029020  |2 bisacsh 
049 |a HCDD 
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. 
650 0 |a Latent variables. 
650 0 |a Latent structure analysis. 
650 0 |a Factor analysis. 
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.proquest.com/lib/holycrosscollege-ebooks/detail.action?docID=819225  |y Click for online access 
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. 
903 |a EBC-AC 
994 |a 92  |b HCD 

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