{"product_id":"structural-equation-modeling-a-bayesian-approach-hardback-9780470024232","title":"Structural Equation Modeling; A Bayesian Approach (Hardback) 9780470024232","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eStructural Equation Modeling\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eA Bayesian Approach\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eSik-Yum Lee (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470024232, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 26 January 2007\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e464 pages\u003cbr\u003e23.5 x 16 x 3 cm, 0.771 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"This book is a welcome addition to any library and should be a valuable resource for research and teaching.\" (\u003ci\u003eTechnometrics\u003c\/i\u003e, August 2008)\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cb\u003e***Winner of the 2008 Ziegel Prize for outstanding new book of the year***\u003c\/b\u003e  \u003cp\u003eStructural equation modeling (SEM) is a powerful multivariate method allowing the evaluation of a series of simultaneous hypotheses about the impacts of latent and manifest variables on other variables, taking measurement errors into account. As SEMs have grown in popularity in recent years, new models and statistical methods have been developed for more accurate analysis of more complex data. A Bayesian approach to SEMs allows the use of prior information resulting in improved parameter estimates, latent variable estimates, and statistics for model comparison, as well as offering more reliable results for smaller samples.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eStructural Equation Modeling\u003c\/i\u003e introduces the Bayesian approach to SEMs, including the selection of prior distributions and data augmentation, and offers an overview of the subject’s recent advances.\u003c\/p\u003e \u003cul\u003e \u003cli\u003eDemonstrates how to utilize powerful statistical computing tools, including the Gibbs sampler, the Metropolis-Hasting algorithm, bridge sampling and path sampling to obtain the Bayesian results.\u003c\/li\u003e \u003cli\u003eDiscusses the Bayes factor and Deviance Information Criterion (DIC) for model comparison.\u003c\/li\u003e \u003cli\u003eIncludes coverage of complex models, including SEMs with ordered categorical variables, and dichotomous variables, nonlinear SEMs, two-level SEMs, multisample SEMs, mixtures of SEMs, SEMs with missing data, SEMs with variables from an exponential family of distributions, and some of their combinations.\u003c\/li\u003e \u003cli\u003eIllustrates the methodology through simulation studies and examples with real data from business management, education, psychology, public health and sociology.\u003c\/li\u003e \u003cli\u003eDemonstrates the application of the freely available software WinBUGS via a supplementary website featuring computer code and data sets.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eStructural Equation Modeling: A Bayesian Approach\u003c\/i\u003e is a multi-disciplinary text ideal for researchers and students in many areas, including: statistics, biostatistics, business, education, medicine, psychology, public health and social science.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eAbout the Author xi\u003c\/p\u003e \u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Standard Structural Equation Models 1\u003c\/p\u003e \u003cp\u003e1.2 Covariance Structure Analysis 2\u003c\/p\u003e \u003cp\u003e1.3 Why a New Book? 3\u003c\/p\u003e \u003cp\u003e1.4 Objectives of the Book 4\u003c\/p\u003e \u003cp\u003e1.5 Data Sets and Notations 6\u003c\/p\u003e \u003cp\u003eAppendix 1.1 7\u003c\/p\u003e \u003cp\u003eReferences 10\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Some Basic Structural Equation Models 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 13\u003c\/p\u003e \u003cp\u003e2.2 Exploratory Factor Analysis 15\u003c\/p\u003e \u003cp\u003e2.3 Confirmatory and Higher-order Factor Analysis Models 18\u003c\/p\u003e \u003cp\u003e2.4 The LISREL Model 22\u003c\/p\u003e \u003cp\u003e2.5 The Bentler–Weeks Model 26\u003c\/p\u003e \u003cp\u003e2.6 Discussion 27\u003c\/p\u003e \u003cp\u003eReferences 28\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Covariance Structure Analysis 31\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 31\u003c\/p\u003e \u003cp\u003e3.2 Definitions, Notations and Preliminary Results 33\u003c\/p\u003e \u003cp\u003e3.3 GLS Analysis of Covariance Structure 36\u003c\/p\u003e \u003cp\u003e3.4 ml Analysis of Covariance Structure 41\u003c\/p\u003e \u003cp\u003e3.5 Asymptotically Distribution-free Methods 44\u003c\/p\u003e \u003cp\u003e3.6 Some Iterative Procedures 47\u003c\/p\u003e \u003cp\u003eAppendix 3.1: Matrix Calculus 53\u003c\/p\u003e \u003cp\u003eAppendix 3.2: Some Basic Results in Probability Theory 57\u003c\/p\u003e \u003cp\u003eAppendix 3.3: Proofs of Some Results 59\u003c\/p\u003e \u003cp\u003eReferences 65\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Bayesian Estimation of Structural Equation Models 67\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 67\u003c\/p\u003e \u003cp\u003e4.2 Basic Principles and Concepts of Bayesian Analysis of SEMs 70\u003c\/p\u003e \u003cp\u003e4.3 Bayesian Estimation of the CFA Model 81\u003c\/p\u003e \u003cp\u003e4.4 Bayesian Estimation of Standard SEMs 95\u003c\/p\u003e \u003cp\u003e4.5 Bayesian Estimation via WinBUGS 98\u003c\/p\u003e \u003cp\u003eAppendix 4.1: The Metropolis–Hastings Algorithm 104\u003c\/p\u003e \u003cp\u003eAppendix 4.2: EPSR Value 105\u003c\/p\u003e \u003cp\u003eAppendix 4.3: Derivations of Conditional Distributions 106\u003c\/p\u003e \u003cp\u003eReferences 108\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Model Comparison and Model Checking 111\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 111\u003c\/p\u003e \u003cp\u003e5.2 Bayes Factor 113\u003c\/p\u003e \u003cp\u003e5.3 Path Sampling 115\u003c\/p\u003e \u003cp\u003e5.4 An Application: Bayesian Analysis of SEMs with Fixed Covariates 120\u003c\/p\u003e \u003cp\u003e5.5 Other Methods 127\u003c\/p\u003e \u003cp\u003e5.6 Discussion 130\u003c\/p\u003e \u003cp\u003eAppendix 5.1: Another Proof of Equation (5.10) 131\u003c\/p\u003e \u003cp\u003eAppendix 5.2: Conditional Distributions for Simulating (θ, ΩlY, t) 133\u003c\/p\u003e \u003cp\u003eAppendix 5.3: PP p-values for Model Assessment 136\u003c\/p\u003e \u003cp\u003eReferences 136\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Structural Equation Models with Continuous and Ordered Categorical Variables 139\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 139\u003c\/p\u003e \u003cp\u003e6.2 The Basic Model 142\u003c\/p\u003e \u003cp\u003e6.3 Bayesian Estimation and Goodness-of-fit 144\u003c\/p\u003e \u003cp\u003e6.4 Bayesian Model Comparison 155\u003c\/p\u003e \u003cp\u003e6.5 Application 1: Bayesian Selection of the Number of Factors in EFA 159\u003c\/p\u003e \u003cp\u003e6.6 Application 2: Bayesian Analysis of Quality of Life Data 164\u003c\/p\u003e \u003cp\u003eReferences 172\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Structural Equation Models with Dichotomous Variables 175\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 175\u003c\/p\u003e \u003cp\u003e7.2 Bayesian Analysis 177\u003c\/p\u003e \u003cp\u003e7.3 Analysis of a Multivariate Probit Confirmatory Factor Analysis Model 186\u003c\/p\u003e \u003cp\u003e7.4 Discussion 190\u003c\/p\u003e \u003cp\u003eAppendix 7.1: Questions Associated with the Manifest Variables 191\u003c\/p\u003e \u003cp\u003eReferences 192\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Nonlinear Structural Equation Models 195\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 195\u003c\/p\u003e \u003cp\u003e8.2 Bayesian Analysis of a Nonlinear SEM 197\u003c\/p\u003e \u003cp\u003e8.3 Bayesian Estimation of Nonlinear SEMs with Mixed Continuous and Ordered Categorical Variables 215\u003c\/p\u003e \u003cp\u003e8.4 Bayesian Estimation of SEMs with Nonlinear Covariates and Latent Variables 220\u003c\/p\u003e \u003cp\u003e8.5 Bayesian Model Comparison 230\u003c\/p\u003e \u003cp\u003eReferences 239\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Two-level Nonlinear Structural Equation Models 243\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 243\u003c\/p\u003e \u003cp\u003e9.2 A Two-level Nonlinear SEM with Mixed Type Variables 244\u003c\/p\u003e \u003cp\u003e9.3 Bayesian Estimation 247\u003c\/p\u003e \u003cp\u003e9.4 Goodness-of-fit and Model Comparison 255\u003c\/p\u003e \u003cp\u003e9.5 An Application: Filipina CSWs Study 259\u003c\/p\u003e \u003cp\u003e9.6 Two-level Nonlinear SEMs with Cross-level Effects 267\u003c\/p\u003e \u003cp\u003e9.7 Analysis of Two-level Nonlinear SEMs using WinBUGS 275\u003c\/p\u003e \u003cp\u003eAppendix 9.1: Conditional Distributions: Two-level Nonlinear Sem 279\u003c\/p\u003e \u003cp\u003eAppendix 9.2: MH Algorithm: Two-level Nonlinear SEM 283\u003c\/p\u003e \u003cp\u003eAppendix 9.3: PP p-value for Two-level NSEM with Mixed Continuous and Ordered-categorical Variables 285\u003c\/p\u003e \u003cp\u003eAppendix 9.4: Questions Associated with the Manifest Variables 286\u003c\/p\u003e \u003cp\u003eAppendix 9.5: Conditional Distributions: SEMs with Cross-level Effects 286\u003c\/p\u003e \u003cp\u003eAppendix 9.6: The MH algorithm: SEMs with Cross-level Effects 289\u003c\/p\u003e \u003cp\u003eReferences 290\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Multisample Analysis of Structural Equation Models 293\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 293\u003c\/p\u003e \u003cp\u003e10.2 The Multisample Nonlinear Structural Equation Model 294\u003c\/p\u003e \u003cp\u003e10.3 Bayesian Analysis of Multisample Nonlinear SEMs 297\u003c\/p\u003e \u003cp\u003e10.4 Numerical Illustrations 302\u003c\/p\u003e \u003cp\u003eAppendix 10.1: Conditional Distributions: Multisample SEMs 313\u003c\/p\u003e \u003cp\u003eReferences 316\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Finite Mixtures in Structural Equation Models 319\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 319\u003c\/p\u003e \u003cp\u003e11.2 Finite Mixtures in SEMs 321\u003c\/p\u003e \u003cp\u003e11.3 Bayesian Estimation and Classification 323\u003c\/p\u003e \u003cp\u003e11.4 Examples and Simulation Study 330\u003c\/p\u003e \u003cp\u003e11.5 Bayesian Model Comparison of Mixture SEMs 344\u003c\/p\u003e \u003cp\u003eAppendix 11.1: The Permutation Sampler 351\u003c\/p\u003e \u003cp\u003eAppendix 11.2: Searching for Identifiability Constraints 352\u003c\/p\u003e \u003cp\u003eReferences 352\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Structural Equation Models with Missing Data 355\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 355\u003c\/p\u003e \u003cp\u003e12.2 A General Framework for SEMs with Missing Data that are Mar 357\u003c\/p\u003e \u003cp\u003e12.3 Nonlinear SEM with Missing Continuous and Ordered Categorical Data 359\u003c\/p\u003e \u003cp\u003e12.4 Mixture of SEMs with Missing Data 370\u003c\/p\u003e \u003cp\u003e12.5 Nonlinear SEMs with Nonignorable Missing Data 375\u003c\/p\u003e \u003cp\u003e12.6 Analysis of SEMs with Missing Data via WinBUGS 386\u003c\/p\u003e \u003cp\u003eAppendix 12.1: Implementation of the MH Algorithm 389\u003c\/p\u003e \u003cp\u003eReferences 390\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Structural Equation Models with Exponential Family of Distributions 393\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 393\u003c\/p\u003e \u003cp\u003e13.2 The SEM Framework with Exponential Family of Distributions 394\u003c\/p\u003e \u003cp\u003e13.3 A Bayesian Approach 398\u003c\/p\u003e \u003cp\u003e13.4 A Simulation Study 402\u003c\/p\u003e \u003cp\u003e13.5 A Real Example: A Compliance Study of Patients 404\u003c\/p\u003e \u003cp\u003e13.6 Bayesian Analysis of an Artificial Example using WinBUGS 411\u003c\/p\u003e \u003cp\u003e13.7 Discussion 416\u003c\/p\u003e \u003cp\u003eAppendix 13.1: Implementation of the MH Algorithms 417\u003c\/p\u003e \u003cp\u003eAppendix 13.2 419\u003c\/p\u003e \u003cp\u003eReferences 419\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Conclusion 421\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences 425\u003c\/p\u003e \u003cp\u003eIndex 427\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52256240599320,"sku":"9780470024232","price":89.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780470024232.jpg?v=1781274508","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/structural-equation-modeling-a-bayesian-approach-hardback-9780470024232","provider":"Freshly Printed Books","version":"1.0","type":"link"}