{"product_id":"mixed-models-9781118091579","title":"Mixed Models","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePraise for the \u003ci\u003eFirst Edition\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eThis book will serve to greatly complement the growing number of texts dealing with mixed models, and I highly recommend including it in one's personal library.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eJournal of the American Statistical Association\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eMixed modeling is a crucial area of statistics, enabling the analysis of clustered and longitudinal data. \u003ci\u003eMixed Models: Theory and Applications with R, Second Edition\u003c\/i\u003e fills a gap in existing literature between mathematical and applied statistical books by presenting a powerful examination of mixed model theory and application with special attention given to the implementation in R.\u003c\/p\u003e \u003cp\u003eThe new edition provides in-depth mathematical coverage of mixed models' statistical properties and numerical algorithms, as well as nontraditional applications, such as regrowth curves, shapes, and images. The book features the latest topics in statistics including modeling of complex clustered or longitudinal data\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003ePreface to the Second Edition xix\u003c\/p\u003e \u003cp\u003eR software and Functions xx\u003c\/p\u003e \u003cp\u003eData Sets xxii\u003c\/p\u003e \u003cp\u003eOpen Problems in Mixed Models xxiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction: Why Mixed Models? 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Mixed effects for clustered data 2\u003c\/p\u003e \u003cp\u003e1.2 ANOVA, variance components, and the mixed model 4\u003c\/p\u003e \u003cp\u003e1.3 Other special cases of the mixed effects model 6\u003c\/p\u003e \u003cp\u003e1.4 A compromise between Bayesian and frequentist approaches 7\u003c\/p\u003e \u003cp\u003e1.5 Penalized likelihood and mixed effects 9\u003c\/p\u003e \u003cp\u003e1.6 Healthy Akaike information criterion 11\u003c\/p\u003e \u003cp\u003e1.7 Penalized smoothing 13\u003c\/p\u003e \u003cp\u003e1.8 Penalized polynomial fitting 16\u003c\/p\u003e \u003cp\u003e1.9 Restraining parameters, or what to eat 18\u003c\/p\u003e \u003cp\u003e1.10 Ill-posed problems, Tikhonov regularization, and mixed effects 20\u003c\/p\u003e \u003cp\u003e1.11 Computerized tomography and linear image reconstruction 23\u003c\/p\u003e \u003cp\u003e1.12 GLMM for PET 26\u003c\/p\u003e \u003cp\u003e1.13 Maple shape leaf analysis 29\u003c\/p\u003e \u003cp\u003e1.14 DNA Western blot analysis 31\u003c\/p\u003e \u003cp\u003e1.15 Where does the wind blow? 33\u003c\/p\u003e \u003cp\u003e1.16 Software and books 36\u003c\/p\u003e \u003cp\u003e1.17 Summary points 37\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 MLE for LME Model 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Example: Weight versus height 42\u003c\/p\u003e \u003cp\u003e2.2 The model and log-likelihood functions 45\u003c\/p\u003e \u003cp\u003e2.3 Balanced random-coefficient model 60\u003c\/p\u003e \u003cp\u003e2.4 LME model with random intercepts 64\u003c\/p\u003e \u003cp\u003e2.5 Criterion for the MLE existence 72\u003c\/p\u003e \u003cp\u003e2.6 Criterion for positive definiteness of matrix D 74\u003c\/p\u003e \u003cp\u003e2.7 Preestimation bounds for variance parameters 77\u003c\/p\u003e \u003cp\u003e2.8 Maximization algorithms 79\u003c\/p\u003e \u003cp\u003e2.9 Derivatives of the log-likelihood function 81\u003c\/p\u003e \u003cp\u003e2.10 Newton—Raphson algorithm 83\u003c\/p\u003e \u003cp\u003e2.11 Fisher scoring algorithm 85\u003c\/p\u003e \u003cp\u003e2.12 EM algorithm 88\u003c\/p\u003e \u003cp\u003e2.13 Starting point 93\u003c\/p\u003e \u003cp\u003e2.14 Algorithms for restricted MLE 96\u003c\/p\u003e \u003cp\u003e2.15 Optimization on nonnegative definite matrices 97\u003c\/p\u003e \u003cp\u003e2.16 lmeFS and lme in R 108\u003c\/p\u003e \u003cp\u003e2.17 Appendix: Proof of the MLE existence 112\u003c\/p\u003e \u003cp\u003e2.18 Summary points 115\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Statistical Properties of the LME Model 119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 119\u003c\/p\u003e \u003cp\u003e3.2 Identifiability of the LME model 119\u003c\/p\u003e \u003cp\u003e3.3 Information matrix for variance parameters 122\u003c\/p\u003e \u003cp\u003e3.4 Profile-likelihood confidence intervals 133\u003c\/p\u003e \u003cp\u003e3.5 Statistical testing of the presence of random effects 135\u003c\/p\u003e \u003cp\u003e3.6 Statistical properties of MLE 139\u003c\/p\u003e \u003cp\u003e3.7 Estimation of random effects 148\u003c\/p\u003e \u003cp\u003e3.8 Hypothesis and membership testing 153\u003c\/p\u003e \u003cp\u003e3.9 Ignoring random effects 157\u003c\/p\u003e \u003cp\u003e3.10 MINQUE for variance parameters 160\u003c\/p\u003e \u003cp\u003e3.11 Method of moments 169\u003c\/p\u003e \u003cp\u003e3.12 Variance least squares estimator 173\u003c\/p\u003e \u003cp\u003e3.13 Projection on D\u003csub\u003e+\u003c\/sub\u003e space 178\u003c\/p\u003e \u003cp\u003e3.14 Comparison of the variance parameter estimation 178\u003c\/p\u003e \u003cp\u003e3.15 Asymptotically efficient estimation for \u003ci\u003eβ\u003c\/i\u003e 182\u003c\/p\u003e \u003cp\u003e3.16 Summary points 183\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Growth Curve Model and Generalizations 187\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Linear growth curve model 187\u003c\/p\u003e \u003cp\u003e4.2 General linear growth curve model 203\u003c\/p\u003e \u003cp\u003e4.3 Linear model with linear covariance structure 221\u003c\/p\u003e \u003cp\u003e4.4 Robust linear mixed effects model 235\u003c\/p\u003e \u003cp\u003e4.5 Appendix: Derivation of the MM estimator 243\u003c\/p\u003e \u003cp\u003e4.6 Summary points 244\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Meta-analysis Model 247\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Simple meta-analysis model 248\u003c\/p\u003e \u003cp\u003e5.2 Meta-analysis model with covariates 275\u003c\/p\u003e \u003cp\u003e5.3 Multivariate meta-analysis model 280\u003c\/p\u003e \u003cp\u003e5.4 Summary points 291\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Nonlinear Marginal Model 293\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Fixed matrix of random effects 294\u003c\/p\u003e \u003cp\u003e6.2 Varied matrix of random effects 307\u003c\/p\u003e \u003cp\u003e6.3 Three types of nonlinear marginal models 318\u003c\/p\u003e \u003cp\u003e6.4 Total generalized estimating equations approach 323\u003c\/p\u003e \u003cp\u003e6.5 Summary points 330\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Generalized Linear Mixed Models 333\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Regression models for binary data 334\u003c\/p\u003e \u003cp\u003e7.2 Binary model with subject-specific intercept 357\u003c\/p\u003e \u003cp\u003e7.3 Logistic regression with random intercept 364\u003c\/p\u003e \u003cp\u003e7.4 Probit model with random intercept 384\u003c\/p\u003e \u003cp\u003e7.5 Poisson model with random intercept 388\u003c\/p\u003e \u003cp\u003e7.6 Random intercept model: overview 403\u003c\/p\u003e \u003cp\u003e7.7 Mixed models with multiple random effects 404\u003c\/p\u003e \u003cp\u003e7.8 GLMM and simulation methods 413\u003c\/p\u003e \u003cp\u003e7.9 GEE for clustered marginal GLM 418\u003c\/p\u003e \u003cp\u003e7.10 Criteria for MLE existence for binary model 426\u003c\/p\u003e \u003cp\u003e7.11 Summary points 431\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Nonlinear Mixed Effects Model 435\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 435\u003c\/p\u003e \u003cp\u003e8.2 The model 436\u003c\/p\u003e \u003cp\u003e8.3 Example: Height of girls and boys 439\u003c\/p\u003e \u003cp\u003e8.4 Maximum likelihood estimation 441\u003c\/p\u003e \u003cp\u003e8.5 Two-stage estimator 444\u003c\/p\u003e \u003cp\u003e8.6 First-order approximation 450\u003c\/p\u003e \u003cp\u003e8.7 Lindstrom—Bates estimator 452\u003c\/p\u003e \u003cp\u003e8.8 Likelihood approximations 457\u003c\/p\u003e \u003cp\u003e8.9 One-parameter exponential model 460\u003c\/p\u003e \u003cp\u003e8.10 Asymptotic equivalence of the TS and LB estimators 467\u003c\/p\u003e \u003cp\u003e8.11 Bias-corrected two-stage estimator 469\u003c\/p\u003e \u003cp\u003e8.12 Distribution misspecification 471\u003c\/p\u003e \u003cp\u003e8.13 Partially nonlinear marginal mixed model 474\u003c\/p\u003e \u003cp\u003e8.14 Fixed sample likelihood approach 475\u003c\/p\u003e \u003cp\u003e8.15 Estimation of random effects and hypothesis testing 478\u003c\/p\u003e \u003cp\u003e8.16 Example (continued) 479\u003c\/p\u003e \u003cp\u003e8.17 Practical recommendations 481\u003c\/p\u003e \u003cp\u003e8.18 Appendix: Proof of theorem on equivalence 482\u003c\/p\u003e \u003cp\u003e8.19 Summary points 485\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Diagnostics and Influence Analysis 489\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 489\u003c\/p\u003e \u003cp\u003e9.2 Influence analysis for linear regression 490\u003c\/p\u003e \u003cp\u003e9.3 The idea of infinitesimal influence 493\u003c\/p\u003e \u003cp\u003e9.4 Linear regression model 495\u003c\/p\u003e \u003cp\u003e9.5 Nonlinear regression model 512\u003c\/p\u003e \u003cp\u003e9.6 Logistic regression for binary outcome 517\u003c\/p\u003e \u003cp\u003e9.7 Influence of correlation structure 526\u003c\/p\u003e \u003cp\u003e9.8 Influence of measurement error 527\u003c\/p\u003e \u003cp\u003e9.9 Influence analysis for the LME model 530\u003c\/p\u003e \u003cp\u003e9.10 Appendix: MLE derivative with respect to σ2 536\u003c\/p\u003e \u003cp\u003e9.11 Summary points 537\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Tumor Regrowth Curves 541\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Survival curves 543\u003c\/p\u003e \u003cp\u003e10.2 Double—exponential regrowth curve 545\u003c\/p\u003e \u003cp\u003e10.3 Exponential growth with fixed regrowth time 559\u003c\/p\u003e \u003cp\u003e10.4 General regrowth curve 565\u003c\/p\u003e \u003cp\u003e10.5 Double—exponential transient regrowth curve 566\u003c\/p\u003e \u003cp\u003e10.6 Gompertz transient regrowth curve 573\u003c\/p\u003e \u003cp\u003e10.7 Summary points 576\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Statistical Analysis of Shape 579\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 579\u003c\/p\u003e \u003cp\u003e11.2 Statistical analysis of random triangles 581\u003c\/p\u003e \u003cp\u003e11.3 Face recognition 584\u003c\/p\u003e \u003cp\u003e11.4 Scale-irrelevant shape model 585\u003c\/p\u003e \u003cp\u003e11.5 Gorilla vertebrae analysis 589\u003c\/p\u003e \u003cp\u003e11.6 Procrustes estimation of the mean shape 591\u003c\/p\u003e \u003cp\u003e11.7 Fourier descriptor analysis 598\u003c\/p\u003e \u003cp\u003e11.8 Summary points 607\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Statistical Image Analysis 609\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 609\u003c\/p\u003e \u003cp\u003e12.2 Testing for uniform lighting 612\u003c\/p\u003e \u003cp\u003e12.3 Kolmogorov—Smirnov image comparison 616\u003c\/p\u003e \u003cp\u003e12.4 Multinomial statistical model for images 620\u003c\/p\u003e \u003cp\u003e12.5 Image entropy 623\u003c\/p\u003e \u003cp\u003e12.6 Ensemble of unstructured images 627\u003c\/p\u003e \u003cp\u003e12.7 Image alignment and registration 640\u003c\/p\u003e \u003cp\u003e12.8 Ensemble of structured images 652\u003c\/p\u003e \u003cp\u003e12.9 Modeling spatial correlation 654\u003c\/p\u003e \u003cp\u003e12.10 Summary points 660\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Appendix: Useful Facts and Formulas 663\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Basic facts of asymptotic theory 663\u003c\/p\u003e \u003cp\u003e13.2 Some formulas of matrix algebra 670\u003c\/p\u003e \u003cp\u003e13.3 Basic facts of optimization theory 674\u003c\/p\u003e \u003cp\u003eReferences 683\u003c\/p\u003e \u003cp\u003eIndex 713\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406828642647,"sku":"9781118091579","price":106.16,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118091579.jpg?v=1730497255","url":"https:\/\/bookcurl.com\/products\/mixed-models-9781118091579","provider":"Book Curl","version":"1.0","type":"link"}