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Book
xxvii, 717 p. : ill.
  • Machine generated contents note: Preface xviiPreface to the Second Edition xixR software and functions xxData Sets xxiiOpen Problems in Mixed Models xxiii1 Introduction: Why Mixed Models? 11.1 Mixed effects for clustered data 21.2 ANOVA, variance components, and the mixed model 41.3 Other special cases of the mixed effects model 61.4 A compromise between Bayesian and frequentist approaches 71.5 Penalized likelihood and mixed effects 91.6 Healthy Akaike information criterion 111.7 Penalized smoothing 131.8 Penalized polynomial fitting 161.9 Restraining parameters, or what to eat 181.10 Ill-posed problems, Tikhonov regularization, and mixed effects 201.11 Computerized tomography and linear image reconstruction 231.12 GLMM for PET 261.13 Maple shape leaf analysis 291.14 DNA Western blot analysis 311.15 Where does the wind blow? 331.16 Software and books361.17 Summary points 372 MLE for LME Model 412.1 Example: Weight versus height 422.2 The model and log-likelihood functions 452.3 Balanced random-coefficient model 602.4 LME model with random intercepts 642.5 Criterion for the MLE existence 722.6 Criterion for positive definiteness of matrix D742.7 Preestimation bounds for variance parameters 772.8 Maximization algorithms792.9 Derivatives of the log-likelihood function 812.10 Newton--Raphson algorithm 832.11 Fisher scoring algorithm852.12 EM algorithm 882.13 Starting point 932.14 Algorithms for restricted MLE 962.15 Optimization on nonnegative definite matrices 972.16 lmeFS and lme in R 1082.17 Appendix: Proof of the MLE existence 1122.18 Summary points 1153 Statistical Properties of the LME Model 1193.1 Introduction 1193.2 Identifiability of the LMEmodel 1193.3 Information matrix for variance parameters 1223.4 Profile-likelihood confidence intervals 1333.5 Statistical testing of the presence of random effects 1353.6 Statistical properties of MLE 1393.7 Estimation of random effects 1483.8 Hypothesis and membership testing 1533.9 Ignoring random effects 1573.10 MINQUE for variance parameters 1603.11 Method of moments 1693.12 Variance least squares estimator 1733.13 Projection on D+ space 1783.14 Comparison of the variance parameter estimation 1783.15 Asymptotically efficient estimation for [beta] 1823.16 Summary points 1834 Growth Curve Model and Generalizations 1874.1 Linear growth curve model 1874.2 General linear growth curve model 2034.3 Linear model with linear covariance structure 2214.4 Robust linear mixed effects model 2354.5 Appendix: Derivation of the MM estimator 2434.6 Summary points 2445 Meta-analysis Model 2475.1 Simple meta-analysis model 2485.2 Meta-analysis model with covariates 2755.3 Multivariate meta-analysis model 2805.4 Summary points 2916 Nonlinear Marginal Model 2936.1 Fixed matrix of random effects 2946.2 Varied matrix of random effects 3076.3 Three types of nonlinear marginal models 3186.4 Total generalized estimating equations approach 3236.5 Summary points 3307 Generalized Linear Mixed Models 3337.1 Regression models for binary data 3347.2 Binary model with subject-specific intercept 3577.3 Logistic regression with random intercept 3647.4 Probit model with random intercept 3847.5 Poisson model with random intercept 3887.6 Random intercept model: overview 4037.7 Mixed models with multiple random effects 4047.8 GLMM and simulation methods 4137.9 GEE for clustered marginal GLM 4187.10 Criteria for MLE existence for binary model 4267.11 Summary points 4318 Nonlinear Mixed Effects Model 4358.1 Introduction 4358.2 The model 4368.3 Example: Height of girls and boys 4398.4 Maximum likelihood estimation 4418.5 Two-stage estimator 4448.6 First-order approximation 4508.7 Lindstrom--Bates estimator 4528.8 Likelihood approximations 4578.9 One-parameter exponential model 4608.10 Asymptotic equivalence of the TS and LB estimators 4678.11 Bias-corrected two-stage estimator 4698.12 Distribution misspecification 4718.13 Partially nonlinear marginal mixed model 4748.14 Fixed sample likelihood approach4758.15 Estimation of random effects and hypothesis testing 4788.16 Example (continued) 4798.17 Practical recommendations 4818.18 Appendix: Proof of theorem on equivalence 4828.19 Summary points 4859 Diagnostics and Influence Analysis 4899.1 Introduction 4899.2 Influence analysis for linear regression 4909.3 The idea of infinitesimal influence 4939.4 Linear regression model 4959.5 Nonlinear regression model 5129.6 Logistic regression for binary outcome 5179.7 Influence of correlation structure 5269.8 Influence of measurement error 5279.9 Influence analysis for the LME model 5309.10 Appendix: MLE derivative with respect to σ 2 5369.11 Summary points 53710 Tumor Regrowth Curves 54110.1 Survival curves 54310.2 Double--exponential regrowth curve 54510.3 Exponential growth with fixed regrowth time 55910.4 General regrowth curve 56510.5 Double--exponential transient regrowth curve 56610.6 Gompertz transient regrowth curve 57310.7 Summary points 57611 Statistical Analysis of Shape 57911.1 Introduction 57911.2 Statistical analysis of random triangles 58111.3 Face recognition 58411.4 Scale-irrelevant shape model 58511.5 Gorilla vertebrae analysis 58911.6 Procrustes estimation of the mean shape 59111.7 Fourier descriptor analysis 59811.8 Summary points 60712 Statistical Image Analysis 60912.1 Introduction 60912.2 Testing for uniform lighting 61212.3 Kolmogorov--Smirnov image comparison 61612.4 Multinomial statistical model for images 62012.5 Image entropy 62312.6 Ensemble of unstructured images 62712.7 Image alignment and registration 64012.8 Ensemble of structured images 65212.9 Modeling spatial correlation 65412.10 Summary points 66013 Appendix: Useful Facts and Formulas 66313.1 Basic facts of asymptotic theory 66313.2 Some formulas of matrix algebra 67013.3 Basic facts of optimization theory 674References 683Index 713.
"Mixed modeling is one of the most promising and exciting areas of statistical analysis, enabling the analysis of nontraditional, clustered data that may come in the form of shapes or images. This book provides in-depth mathematical coverage of mixed models' statistical properties and numerical algorithms, as well as applications such as the analysis of tumor regrowth, shape, and image. The new edition includes significant updating, over 300 exercises, stimulating chapter projects and model simulations, inclusion of R subroutines, and a revised text format. The target audience continues to be graduate students and researchers. An author-maintained web site is available with solutions to exercises and a compendium of relevant data sets"-- Provided by publisher.
Book
xiii, 287 p. : ill. ; 24 cm.
  • Preface-- Introduction to analysis of variance-- Introduction to model structures-- Part I. Model Structures: 1. One-factor designs-- 2. Nested designs-- 3. Fully replicated factorial designs-- 4. Randomised block designs-- 5. Split plot designs-- 6. Repeated measures designs-- 7. Unreplicated designs-- Part II. Further Topics: 8. Further topics-- 9. Choosing experimental designs-- 10. Best practice in presentation of the design-- 11. Troubleshooting problems during analysis-- Glossary-- Categories of model-- Bibliography-- Index of all ANOVA models with up to three factors-- Index.
  • (source: Nielsen Book Data)9780521684477 20160528
Analysis of variance (ANOVA) is a core technique for analysing data in the Life Sciences. This reference book bridges the gap between statistical theory and practical data analysis by presenting a comprehensive set of tables for all standard models of analysis of variance and covariance with up to three treatment factors. The book will serve as a tool to help post-graduates and professionals define their hypotheses, design appropriate experiments, translate them into a statistical model, validate the output from statistics packages and verify results. The systematic layout makes it easy for readers to identify which types of model best fit the themes they are investigating, and to evaluate the strengths and weaknesses of alternative experimental designs. In addition, a concise introduction to the principles of analysis of variance and covariance is provided, alongside worked examples illustrating issues and decisions faced by analysts.
(source: Nielsen Book Data)9780521684477 20160528
SAL3 (off-campus storage)
Book
xxv, 480 p. : ill.
  • v. 1. Balanced data
  • v. 2. Unbalanced data.
Book
v : ill. ; 25. cm.
  • v. 1. Balanced data
  • v. 2. Unbalanced data.
ANOVA models involving random effects have found widespread application to experimental design in varied fields such as biology, econometrics, and engineering. Volume I of this two-part work is a comprehensive presentation of methods and techniques for point estimation, interval estimation, and hypotheses tests for linear models involving random effects. Volume I examines models with balanced data (orthogonal models); Volume II studies models with unbalanced data (non-orthogonal models). Accessible to readers with a modest mathematical and statistical background, the work will appeal to a broad audience of graduate students, researchers, and practitioners. It can be used as a graduate text or as a self-study reference.
(source: Nielsen Book Data)9780817632304 20160528
Analysis of variance (ANOVA) models have become widely used tools and play a fundamental role in much of the application of statistics today. In particular, ANOVA models involving random effects have found widespread application to experimental design in a variety of fields requiring measurements of variance, including agriculture, biology, animal breeding, applied genetics, econometrics, quality control, medicine, engineering, and social sciences.This two-volume work is a comprehensive presentation of different methods and techniques for point estimation, interval estimation, and tests of hypotheses for linear models involving random effects. Both Bayesian and repeated sampling procedures are considered. Volume 1 examines models with balanced data (orthogonal models); Volume 2 studies models with unbalanced data (nonorthogonal models).Accessible to readers with only a modest mathematical and statistical background, the work will appeal to a broad audience of students, researchers, and practitioners in the mathematical, life, social, and engineering sciences. It may be used as a textbook in upper-level undergraduate and graduate courses, or as a reference for readers interested in the use of random effects models for data analysis.
(source: Nielsen Book Data)9780817632298 20160528
Vol. 1 SpringerLink
SAL3 (off-campus storage)
Book
xviii, 704 p. : ill. ; 25 cm.
  • Preface.1. Introduction: Why Mixed Models?2. MLE for LME Model.3. Statistical Properties of the LME Model.4. Growth Curve Model and Generalizations.5. Meta-analysis Model.6. Nonlinear Marginal Model.7. Generalized Linear Mixed Models.8. Nonlinear Mixed Effects Model.9. Diagnostics and Influence Analysis.10. Tumor Regrowth Curves.11. Statistical Analysis of Shape.12. Statistical Image Analysis.13. Appendix: Useful Facts and Formulas.References.Index.
  • (source: Nielsen Book Data)9780471601616 20160528
This timely and state--of--the--art topic is covered comprehensively in this book. Providing a complete and in--depth mathematical coverage of the topic -- linear, generalized linear, and nonlinear mixed models, along with diagnostics -- the book has dual appeal as both a graduate--level text and a reference. Special attention is given to algorithms and their implementations and several appendices make the text self--contained.
(source: Nielsen Book Data)9780471601616 20160528
dx.doi.org Wiley Online Library
Science Library (Li and Ma)
Book
1 online resource (487 pages)
  • Introduction * Estimation * Testing Hypotheses * One-Way ANOVA * Multiple Comparison Techniques * Regression Analysis * Multifactor Analysis of Variance * Experimental Design Models * Analysis of Covariance * Estimation and Testing in General Gauss-Markov Models * Split Plot Models * Mixed Models and Variance Components * Checking Assumptions, Residuals, and Influential Observations * Variable Selection and Collinearity.
  • (source: Nielsen Book Data)9780387953618 20180521
This textbook provides a wide-ranging introduction to the use and theory of linear models for analyzing data. The authors emphasis is on providing a unified treatment of linear models, including analysis of variance models and regression models, based on projections, orthogonality, and other vector space ideas. Every chapter comes with numerous exercises and examples that make it ideal for a graduate- level course. All of the standard topics are covered in depth. In addition, the book covers topics that are not usually treated at this level, but which are important in their own right. The author, Ronald Christensen, is a Professor of Statistics at the University of New Mexico.
(source: Nielsen Book Data)9780387953618 20180521
Book
xii, 180 p. : ill. ; 24 cm.
  • Introduction The Need for Analysis of Variance (ANOVA) Means, Variances, Sums of Squares and Degrees of Freedom Independent Group ANOVAs One-Factor Independent Groups ANOVA Multiple Comparisons: Independent Groups t-Tests Two-Factor Independent Groups ANOVA Repeated Measures ANOVAs One-Factor Repeated Measures ANOVA Multiple Comparisons: Dependent Measures t-Tests Two-Factor Mixed Measures ANOVA Two-Factor Repeated Measures ANOVA Overview and Final Thoughts Some Tips for Tests on ANOVA Every Day Benefits of a Feel for Statistics and for Evaluating Data.
  • (source: Nielsen Book Data)9780803970755 20160618
Organized so that the reader moves from the simplest type of design to more complex ones, the authors introduce five different kinds of ANOVA techniques and explain which design/analysis is appropriate to answer specific questions.
(source: Nielsen Book Data)9780803970755 20160618
Law Library (Crown)
Book
1 online resource (xii, 180 p.) : ill.
  • Introduction The Need for Analysis of Variance (ANOVA) Means, Variances, Sums of Squares and Degrees of Freedom Independent Group ANOVAs One-Factor Independent Groups ANOVA Multiple Comparisons: Independent Groups t-Tests Two-Factor Independent Groups ANOVA Repeated Measures ANOVAs One-Factor Repeated Measures ANOVA Multiple Comparisons: Dependent Measures t-Tests Two-Factor Mixed Measures ANOVA Two-Factor Repeated Measures ANOVA Overview and Final Thoughts Some Tips for Tests on ANOVA Every Day Benefits of a Feel for Statistics and for Evaluating Data.
  • (source: Nielsen Book Data)9780803970755 20160618
Organized so that the reader moves from the simplest type of design to more complex ones, the authors introduce five different kinds of ANOVA techniques and explain which design/analysis is appropriate to answer specific questions.
(source: Nielsen Book Data)9780803970755 20160618
Book
xix, 204 p. : ill. ; 23 cm.
  • The Study of Variation. One-Way Classification. Two-Way Cross-Classification. Randomized Blocks. BIBDs and Latin Squares. Nested Classifications. Maximum Likelihood Estimation. The MINQUE and MIVQUE. Non-Negative Estimation of Variance Components. Confidence Intervals. Genetic and Environmental Effects.
  • (source: Nielsen Book Data)9780412728600 20160528
Variance Components Estimation deals with the evaluation of the variation between observable data or classes of data. This is an up-to-date, comprehensive work that is both theoretical and applied. Topics include ML and REML methods of estimation; Steepest-Acent, Newton-Raphson, scoring, and EM algorithms; MINQUE and MIVQUE, confidence intervals for variance components and their ratios; Bayesian approaches and hierarchical models; mixed models for longitudinal data; repeated measures and multivariate observations; as well as non-linear and generalized linear models with random effects.
(source: Nielsen Book Data)9780412728600 20160528
SAL3 (off-campus storage)
Book
565 p.
Covers topics in the analysis of variance, such as: the nature of interaction and its interpretation, in terms of theory and response scale transformations; non-orthogonal designs; generalized forms of analysis of covariance; and discussion of functional measurement.
(source: Nielsen Book Data)9780275947200 20160528
SAL3 (off-campus storage)
Book
xiv, 161 p. : ill. ; 28 cm.
SAL3 (off-campus storage)

13. Variance components [1992]

Book
xxiii, 501 p. ; 25 cm.
  • History and comment-- the 1-way classification-- balanced data-- analysis of variance estimation for unbalanced data-- maximum likelihood (ML) and restricted maximum likelihood (REML)-- prediction of random variables-- computing ML and REML estimates-- hierarchical models and Bayesian estimation-- binary and discrete data-- other procedures-- the dispersion-mean model.
  • (source: Nielsen Book Data)9780471621621 20160527
This text presents a broad coverage of variance components. It deals with the estimation of variance components and the prediction of realized but unobservable values of random variables in analysis of variance models and in binary and discrete data. The authors begin with an introduction to the subject, which details more complicated types of data appearing in subsequent chapters. All the major methods of estimating components are discussed at length, including ANOVA, ML, REML, and Bayes. Topics covered include history, analysis of variance estimation, maximum likelihood (ML) estimation, prediction in mixed models, Bayes estimation and hierarchical models, categorical data, covariance components and minimum norm estimation, dispersion-mean model, kurtosis and fourth moments.
(source: Nielsen Book Data)9780471621621 20160527
dx.doi.org Wiley Online Library
Marine Biology Library (Miller), Science Library (Li and Ma)
Book
430 p.
  • Concepts and Examples in Analysis of Variance (J. Tukey, et al.)-- Purposes of Analyzing Data that Come in a Form Inviting Us to Apply Tools from the Analysis of Variance (F. Mosteller & J. Tukey)-- Preliminary Examination of Data (F. Mosteller & D. Hoaglin)-- Types of Factors and Their Structural Layouts (J. Singer)-- Value-Splitting: Taking the Data Apart (C. Schmid)-- Value-Splitting Involving More Factors (K. Halvorsen)-- Mean Squares, F Tests, and Estimates of Variance (F. Mosteller, et al.)-- Graphical Display as an Aid to Analysis (J. Emerson)-- Components of Variance (C. Brown & F. Mosteller)-- Which Denominator?-- (T. Blackwell, et al.)-- Assessing Changes (J. Tukey, et al.)-- Qualitative and Quantitative Confidence (J. Tukey & D. Hoaglin)-- Introduction to Transformation (J. Emerson)-- Appendix-- Index.
  • (source: Nielsen Book Data)9780471527350 20160528
This text approaches the analysis of variance (ANOVA) from an exploratory point of view while retaining customary least squares fitting methods. The authors go beyond the standard steps of the ANOVA table to emphasize both the individual observations and the separate parts that the analysis produces. The technical level is not advanced and therefore serves as an introduction to ANOVA. The material is self-contained and illustrated with occasional references to more advanced/specialized readings.
(source: Nielsen Book Data)9780471527350 20160528
dx.doi.org Wiley Online Library
SAL3 (off-campus storage)
Book
x, 101 p. : ill. ; 28 cm.
Green Library, Earth Sciences Library (Branner)
Book
vi, 152 p. : ill. ; 28 cm.
Green Library, Earth Sciences Library (Branner)
Book
x, 310 p. : ill. ; 25 cm.
SAL3 (off-campus storage)
Book
x, 144 p. : ill. ; 24 cm.
SAL3 (off-campus storage)
Book
p. 687-699 ; 23 cm.
SAL3 (off-campus storage)
Book
xvii, 1002 p. : ill. ; 25 cm.
  • Estimation of Variance Components (C.R. Rao, J. Kleffe). Multivariate Analysis of Variance of Repeated Measurements (N.H. Timm). Growth Curve Analysis (S. Geisser). Bayesian Inference in MANOVA (S.J. Press). Graphical Methods for Internal Comparisons in ANOVA and MANOVA (R. Gnanadesikan). Monotonicity and Unbiasedness Properties of ANOVA and MANOVA Tests (S.D. Gupta). Robustness of ANOVA and MANOVA Test Procedures (P.K. Ito). Analysis of Variance and Problems under Time Series Models (D.R. Brillinger). Tests of Univariate and Multivariate Normality (K.V. Mardia). Transformations to Normality (G. Kaskey et al.). ANOVA and MANOVA: Models for Categorical Data (V.P. Bhapkar). Inference and the Structural Model for ANOVA and MANOVA (D.A.S. Fraser). Inference Based on Conditionally Specified ANOVA Models Incorporating Preliminary Testing (T.A. Bancroft, C.-P. Han). Quadratic Forms in Normal Variables (C.G. Khatri). Generalized Inverse of Matrices and Applications to Linear Models (S.K. Mitra). Likelihood Ratio Tests for Mean Vectors and Covariance Matrices (P.R. Krishnaiah, J.C. Lee). Assessing Dimensionality in Multivariate Regression (A.J. Izenman). Parameter Estimation in Nonlinear Regression Models (H. Bunke). Early History of Multiple Comparison Tests (H.L. Harter). Representations of Simultaneous Pairwise Comparisons (A.R. Sampson). Simultaneous Test Procedures for Mean Vectors and Covariance Matrices (P.R. Krishnaiah, G.S. Mudholkar, P. Subbaiah). Nonparametric Simultaneous Inference for Some MANOVA Models (P.K. Sen). Comparison of Some Computer Programs for Univariate and Multivariate Analysis of Variance (R.D. Bock, D. Brandt). Computations of Some Multivariate Distributions (P.R. Krishnaiah). Inference on the Structure of Interaction in a Two-Way Classification Model (P.R. Krishnaiah, M.G. Yochmowitz). Index.
  • (source: Nielsen Book Data)9780444853356 20160528
This first volume in the series is devoted to the area of analysis of variance (ANOVA), which was developed by R.A. Fischer and others, and has emerged as a very important branch of statistics. An attempt has been made to cover most of the useful techniques in univariate and multivariate ANOVA in this volume. The chapters are written by prominent workers in the field for persons who are not specialists on the topic. Thus, the volume will appeal to the whole statistics community, as well as to scientists in other disciplines who are interested in statistical methodology. The volume is dedicated to the memory of the late Henry Scheffe.
(source: Nielsen Book Data)9780444853356 20160528
SAL3 (off-campus storage)

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