{"product_id":"latent-variable-models-and-factor-analysis-9780470971925","title":"Latent Variable Models and Factor Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eLatent 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“Latent Variable Models and Factor Analysis provides a comprehensive and unified approach to factor analysis and latent variable modeling from a statistical perspective.”  (\u003ci\u003eMathematical Reviews\u003c\/i\u003e, 2012)\u003c\/p\u003e \"Statistical techniques to study the nature and interpretation of a latent variable should be highly useful for researchers and practitioners across several fields. The third edition of this book is comprehensive and provides a solid foundation for understanding these techniques, and is strongly recommended.\" (Book Pleasures, 2012)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cb\u003ePreface xi\u003c\/b\u003e   \u003cp\u003e\u003cb\u003eAcknowledgements xv\u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Basic Ideas and Examples 1\u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e1.1 The statistical problem 1 \u003c\/p\u003e \u003cp\u003e1.2 The basic idea 3\u003c\/p\u003e \u003cp\u003e1.3 Two Examples 4\u003c\/p\u003e \u003cp\u003e1.4 A broader theoretical view 6 \u003c\/p\u003e \u003cp\u003e1.5 Illustration of an alternative approach 8\u003c\/p\u003e \u003cp\u003e1.6 An overview of special cases 10\u003c\/p\u003e \u003cp\u003e1.7 Principal components 11\u003c\/p\u003e \u003cp\u003e1.8 The historical context 12\u003c\/p\u003e \u003cp\u003e1.9 Closely related fields in Statistics 17 \u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 The General Linear Latent Variable Model 19\u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e2.1 Introduction 19\u003c\/p\u003e \u003cp\u003e2.2 The model 19 \u003c\/p\u003e \u003cp\u003e2.3 Some properties of the model 20 \u003c\/p\u003e \u003cp\u003e2.4 A special case 21\u003c\/p\u003e \u003cp\u003e2.5 The sufficiency principle 22 \u003c\/p\u003e \u003cp\u003e2.6 Principal special cases 24\u003c\/p\u003e \u003cp\u003e2.7 Latent variable models with non-linear terms 25 \u003c\/p\u003e \u003cp\u003e2.8 Fitting the models 27 \u003c\/p\u003e \u003cp\u003e2.9 Fitting by maximum likelihood 29 \u003c\/p\u003e \u003cp\u003e2.10 Fitting by Bayesian methods 30\u003c\/p\u003e \u003cp\u003e2.11 Rotation 33\u003c\/p\u003e \u003cp\u003e2.12 Interpretation 35 \u003c\/p\u003e \u003cp\u003e2.13 Sampling error of parameter estimates 38 \u003c\/p\u003e \u003cp\u003e2.14 The prior distribution 39 \u003c\/p\u003e \u003cp\u003e2.15 Posterior analysis 41\u003c\/p\u003e \u003cp\u003e2.16 A further note on the prior 43 \u003c\/p\u003e \u003cp\u003e2.17 Psychometric Inference 44\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 The Normal Linear Factor Model 47\u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e3.1 The model 47\u003c\/p\u003e \u003cp\u003e3.2 Some distributional properties 48 \u003c\/p\u003e \u003cp\u003e3.3 Constraints on the model 50\u003c\/p\u003e \u003cp\u003e3.4 Maximum likelihood estimation 50 \u003c\/p\u003e \u003cp\u003e3.5 Maximum likelihood estimation by the E-M algorithm 53 \u003c\/p\u003e \u003cp\u003e3.6 Sampling variation of estimators 55\u003c\/p\u003e \u003cp\u003e3.7 Goodness of fit and choice of \u003ci\u003eq\u003c\/i\u003e 58 \u003c\/p\u003e \u003cp\u003e3.8 Fitting without normality assumptions: Least squares methods 59 \u003c\/p\u003e \u003cp\u003e3.9 Other methods of fitting 61\u003c\/p\u003e \u003cp\u003e3.10 Approximate methods for estimating 62 \u003c\/p\u003e \u003cp\u003e3.11 Goodness-of-fit and choice of q for least squares methods 63\u003c\/p\u003e \u003cp\u003e3.12 Further estimation issues 64\u003c\/p\u003e \u003cp\u003e3.13 Rotation and related matters 69 \u003c\/p\u003e \u003cp\u003e3.14 Posterior analysis: The normal case 67 \u003c\/p\u003e \u003cp\u003e3.15 Posterior analysis: least squares 72\u003c\/p\u003e \u003cp\u003e3.16 Posterior analysis: a reliability approach 74 \u003c\/p\u003e \u003cp\u003e3.17 Examples 74\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Binary Data: Latent Trait Models 83\u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e4.1 Preliminaries 83\u003c\/p\u003e \u003cp\u003e4.2 The logit\/normal model 84 \u003c\/p\u003e \u003cp\u003e4.3 The probit\/normal model 86 \u003c\/p\u003e \u003cp\u003e4.4 The equivalence of the response function and underlying variable approaches 88 \u003c\/p\u003e \u003cp\u003e4.5 Fitting the logit\/normal model: the E-M algorithm 90\u003c\/p\u003e \u003cp\u003e4.6 Sampling properties of the maximum likelihood estimators 94 \u003c\/p\u003e \u003cp\u003e4.7 Approximate maximum likelihood estimators 95 \u003c\/p\u003e \u003cp\u003e4.8 Generalised least squares methods 96 \u003c\/p\u003e \u003cp\u003e4.9 Goodness of fit 97\u003c\/p\u003e \u003cp\u003e4.10 Posterior analysis 100 \u003c\/p\u003e \u003cp\u003e4.11 Fitting the logit\/normal and probit\/normal models: Markov Chain Monte Carlo 102 \u003c\/p\u003e \u003cp\u003e4.12 Divergence of the estimation algorithm 109\u003c\/p\u003e \u003cp\u003e4.13 Examples 109\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Polytomous Data: Latent Trait Models 119\u003c\/b\u003e  \u003c\/p\u003e \u003cp\u003e5.1 Introduction 119\u003c\/p\u003e \u003cp\u003e5.2 A response function model based on the sufficiency principle 120 \u003c\/p\u003e \u003cp\u003e5.3 Parameter interpretation 124\u003c\/p\u003e \u003cp\u003e5.4 Rotation 124\u003c\/p\u003e \u003cp\u003e5.5 Maximum likelihood estimation of the polytomous logit model 125 \u003c\/p\u003e \u003cp\u003e5.6 An approximation to the likelihood 126 \u003c\/p\u003e \u003cp\u003e5.7 Binary data as a special case 134 \u003c\/p\u003e \u003cp\u003e5.8 Ordering of categories 136\u003c\/p\u003e \u003cp\u003e5.9 An alternative underlying variable model 144 \u003c\/p\u003e \u003cp\u003e5.10 Posterior analysis 147\u003c\/p\u003e \u003cp\u003e5.11 Further observations 148\u003c\/p\u003e \u003cp\u003e5.12 Examples of the analysis of polytomous data using the logit model 149\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Latent Class Models 157\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 157\u003c\/p\u003e \u003cp\u003e6.2 The latent class model with binary manifest variables 158 \u003c\/p\u003e \u003cp\u003e6.3 The latent class model for binary data as a latent trait model 159 \u003c\/p\u003e \u003cp\u003e6.4 Latent Classes within the GLLVM 161\u003c\/p\u003e \u003cp\u003e6.5 Maximum likelihood estimation 162\u003c\/p\u003e \u003cp\u003e6.6 Standard errors 164\u003c\/p\u003e \u003cp\u003e6.7 Posterior analysis of the latent class model with binary manifest variables 166 \u003c\/p\u003e \u003cp\u003e6.8 Goodness of Fit 167\u003c\/p\u003e \u003cp\u003e6.9 Examples for binary Data 167 \u003c\/p\u003e \u003cp\u003e6.10 Latent class models with unordered polytomous manifest variables 170 \u003c\/p\u003e \u003cp\u003e6.11 Latent class models with ordered polytomous manifest variables 171\u003c\/p\u003e \u003cp\u003e6.12 Maximum likelihood estimation 172\u003c\/p\u003e \u003cp\u003e6.13 Examples for unordered polytomous data 174 \u003c\/p\u003e \u003cp\u003e6.14 Identifiability 178\u003c\/p\u003e \u003cp\u003e6.15 Starting values 180\u003c\/p\u003e \u003cp\u003e6.16 Latent class models with metrical manifest variables 180\u003c\/p\u003e \u003cp\u003e6.17 Models with ordered latent classes 181\u003c\/p\u003e \u003cp\u003e6.18 Hybrid models 182\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Models and Methods for Manifest Variables of Mixed Type 191\u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e7.1 Introduction 191\u003c\/p\u003e \u003cp\u003e7.2 Principal results 192 \u003c\/p\u003e \u003cp\u003e7.3 Other members of the exponential family 193 \u003c\/p\u003e \u003cp\u003e7.4 Maximum likelihood estimation 195\u003c\/p\u003e \u003cp\u003e7.5 Sampling properties and Goodness of Fit 201 \u003c\/p\u003e \u003cp\u003e7.6 Mixed latent class models 202\u003c\/p\u003e \u003cp\u003e7.7 Posterior analysis 203\u003c\/p\u003e \u003cp\u003e7.8 Examples 204\u003c\/p\u003e \u003cp\u003e7.9 Ordered categorical variables and other generalisations 208 \u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Relationships Between Latent Variables 213\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Scope 213\u003c\/p\u003e \u003cp\u003e8.2 Correlated latent variables 213\u003c\/p\u003e \u003cp\u003e8.3 Procrustes methods 215\u003c\/p\u003e \u003cp\u003e8.4 Sources of prior knowledge 215 \u003c\/p\u003e \u003cp\u003e8.5 Linear structural relations models 216 \u003c\/p\u003e \u003cp\u003e8.6 The LISREL model 218\u003c\/p\u003e \u003cp\u003e8.7 Adequacy of a structural equation model 221 \u003c\/p\u003e \u003cp\u003e8.8 Structural relationships in a general setting 222\u003c\/p\u003e \u003cp\u003e8.9 Generalisations of the LISREL model 223\u003c\/p\u003e \u003cp\u003e8.10 Examples of models which are indistinguishable 224 \u003c\/p\u003e \u003cp\u003e8.11 Implications for analysis 227\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Related Techniques for Investigating Dependency 229\u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e9.1 Introduction 229\u003c\/p\u003e \u003cp\u003e9.2 Principal Components Analysis, (PCA) 229 \u003c\/p\u003e \u003cp\u003e9.3 An alternative to the normal factor model 236 \u003c\/p\u003e \u003cp\u003e9.4 Replacing latent variables by linear functions of the manifest variables 238 \u003c\/p\u003e \u003cp\u003e9.5 Estimation of correlations and regressions between latent variables 240\u003c\/p\u003e \u003cp\u003e9.6 Q-Methodology 242\u003c\/p\u003e \u003cp\u003e9.7 Concluding reflections of the role of latent variables in statistical modelling 244 \u003c\/p\u003e \u003cp\u003eReferences 247\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSoftware appendix 247\u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003eReferences 249\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAuthor Index 265\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSubject Index 271\u003c\/b\u003e\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402468467031,"sku":"9780470971925","price":60.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470971925.jpg?v=1730480497","url":"https:\/\/bookcurl.com\/products\/latent-variable-models-and-factor-analysis-9780470971925","provider":"Book Curl","version":"1.0","type":"link"}