{"product_id":"linear-model-theory-9780471214885","title":"Linear Model Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eA precise and accessible presentation of linear model theory, illustrated with data examples\u003c\/b\u003e  \u003cp\u003eStatisticians often use linear models for data analysis and for developing new statistical methods. Most books on the subject have historically discussed univariate, multivariate, and mixed linear models separately, whereas \u003ci\u003eLinear Model Theory: Univariate, Multivariate, and Mixed Models\u003c\/i\u003e presents a unified treatment in order to make clear the distinctions among the three classes of models.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eLinear Model Theory: Univariate, Multivariate, and Mixed Models\u003c\/i\u003e begins with six chapters devoted to providing brief and clear mathematical statements of models, procedures, and notation. Data examples motivate and illustrate the models. Chapters 7-10 address distribution theory of multivariate Gaussian variables and quadratic forms. Chapters 11-19 detail methods for estimation, hypothesis testing, and confidence intervals. The final chapters, 20-23, concentrate on choosing a sam\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This text successfully offers a unified context for the theory of univariate, multivariate, and mixed modeling settings and may be useful supplemental text for individuals interested in multivariate modeling.\" (\u003ci\u003eJournal of the American Statistician\u003c\/i\u003e, December 2008)  \u003c\/p\u003e\u003cp\u003e\"I believe that this text provides an important contribution to the long-memory time series literature.  I feel that it largely achieves its aims and could be useful for those instructors wishing to teach a semester-long special topics course … .I strongly recommend this book to anyone interested in long-memory time series.  Both researchers and beginners alike will find this text extremely useful.\" (\u003ci\u003eJournal of the American Statistician,\u003c\/i\u003e December 2008)\u003c\/p\u003e \u003cp\u003e\"The book will certainly be useful for Ph.D. students and researchers in biostatistics who want to learn a little bit of theory of linear models.\" (\u003ci\u003eMathematical Reviews\u003c\/i\u003e, 2007)\u003c\/p\u003e \u003cp\u003e\"...stands out from the others...will certainly have its enthusiastic supporters.\" (\u003ci\u003eBiometrics\u003c\/i\u003e, March 2007)\u003c\/p\u003e \u003cp\u003e\"…an excellent book for graduate students and professional researchers.\" (\u003ci\u003eMAA Reviews\u003c\/i\u003e, February 2007)\u003c\/p\u003e \u003cp\u003e\"The focus of this book is on linear models with correlated observations and Gaussian errors.\" (\u003ci\u003eZentralblatt MATH,\u003c\/i\u003e April 2007)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.  \u003cp\u003e PART I: MODELS AND EXAMPLES.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e1. Matrix Algebra for Linear Models.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 1.1 Notation.  \u003c\/p\u003e\u003cp\u003e 1.2 Some Operators and Special Types of Matrices.  \u003c\/p\u003e\u003cp\u003e 1.3 Five Kinds of Multiplication.  \u003c\/p\u003e\u003cp\u003e 1.4 The Direct Sum.  \u003c\/p\u003e\u003cp\u003e 1.5 Rules of Operations.  \u003c\/p\u003e\u003cp\u003e 1.6 Other Special Types of matrices.  \u003c\/p\u003e\u003cp\u003e 1.7 Quadratic and Bilinear Forms.  \u003c\/p\u003e\u003cp\u003e 1.8 Vector Spaces and Rank.  \u003c\/p\u003e\u003cp\u003e 1.9 Finding Rank.  \u003c\/p\u003e\u003cp\u003e 1.10 Determinants.  \u003c\/p\u003e\u003cp\u003e 1.11 The Inverse and Generalized Inverse.  \u003c\/p\u003e\u003cp\u003e 1.12 Eigenanalysis (Spectral Decomposition).  \u003c\/p\u003e\u003cp\u003e 1.13 Some Factors of Symmetric Matrices.  \u003c\/p\u003e\u003cp\u003e 1.14 Singular Value Decomposition.  \u003c\/p\u003e\u003cp\u003e 1.15 Projections and Other Functions of a Design matrix.  \u003c\/p\u003e\u003cp\u003e 1.16 Special Properties of Patterned Matrices.  \u003c\/p\u003e\u003cp\u003e 1.17 Functional Optimization and Matrix Derivatives.  \u003c\/p\u003e\u003cp\u003e 1.18 Statistical Notation Involving Matrices.  \u003c\/p\u003e\u003cp\u003e 1.19 Statistical Formulas.  \u003c\/p\u003e\u003cp\u003e 1.20 Principal Components.  \u003c\/p\u003e\u003cp\u003e 1.21 Special Covariance Patterns.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e2. The General Linear Univariate Model.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 2.1 Introduction.  \u003c\/p\u003e\u003cp\u003e 2.2 Model Concepts.  \u003c\/p\u003e\u003cp\u003e 2.3 The General Linear Univariate Linear Model.  \u003c\/p\u003e\u003cp\u003e 2.4 The Univariate General Linear Hypothesis.  \u003c\/p\u003e\u003cp\u003e 2.5 Tests about Variances.  \u003c\/p\u003e\u003cp\u003e 2.6 The Role of the Intercept.  \u003c\/p\u003e\u003cp\u003e 2.7 Population Correlation and Strength of Relationship.  \u003c\/p\u003e\u003cp\u003e 2.8 Statistical Estimates.  \u003c\/p\u003e\u003cp\u003e 2.9 Testing the General Linear Hypothesis.  \u003c\/p\u003e\u003cp\u003e 2.10 Confidence Regions for θ.  \u003c\/p\u003e\u003cp\u003e 2.11 Sufficient Statistics for the Univariate Model.  \u003c\/p\u003e\u003cp\u003e Exercises.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e3. The General Linear Multivariate Model.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 3.1 Motivation.  \u003c\/p\u003e\u003cp\u003e 3.2 Definition of the Multivariate Model.  \u003c\/p\u003e\u003cp\u003e 3.3 The Multivariate General Linear Hypothesis.  \u003c\/p\u003e\u003cp\u003e 3.4 Tests About Covariance Matrices.  \u003c\/p\u003e\u003cp\u003e 3.5 Population Correlation.  \u003c\/p\u003e\u003cp\u003e 3.6 Statistical Estimates.  \u003c\/p\u003e\u003cp\u003e 3.7 Overview of Testing Multivariate Hypotheses.  \u003c\/p\u003e\u003cp\u003e 3.8 Computing MULTIREP Tests.  \u003c\/p\u003e\u003cp\u003e 3.9 Computing UNIREP tests.  \u003c\/p\u003e\u003cp\u003e 3.10 Confidence Regions for Θ.  \u003c\/p\u003e\u003cp\u003e 3.11 Sufficient Statistics for the Multivariate Model.  \u003c\/p\u003e\u003cp\u003e 3.12 Allowing Missing Data in the Multivariate Model.  \u003c\/p\u003e\u003cp\u003e Exercises.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e4. Generalizations of the Multivariate Linear Model.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 4.1 Motivation.  \u003c\/p\u003e\u003cp\u003e 4.2 The Generalized General Linear Univariate Model: Exact and Approximate Weighted Least Squares.  \u003c\/p\u003e\u003cp\u003e 4.3 Doubly Multivariate Models.  \u003c\/p\u003e\u003cp\u003e 4.4 Seemingly Unrelated Regression.  \u003c\/p\u003e\u003cp\u003e 4.5 Growth Curve Models (GMANOVA).  \u003c\/p\u003e\u003cp\u003e 4.6 The Relationship of the GCM to the Multivariate Model.  \u003c\/p\u003e\u003cp\u003e 4.7 Mixed, Hierarchical, and Related Models.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e5. The Linear Mixed Model.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 5.1 Motivation.  \u003c\/p\u003e\u003cp\u003e 5.2 Definition of the Mixed Model.  \u003c\/p\u003e\u003cp\u003e 5.3 Distribution-Free and Noniterative Estimates.  \u003c\/p\u003e\u003cp\u003e 5.4 Gaussian Likelihood and Iterative Estimates.  \u003c\/p\u003e\u003cp\u003e 5.5 Tests about β (Means, Fixed Effects).  \u003c\/p\u003e\u003cp\u003e 5.6 Tests of Covariance Parameters, τ (random Effects).  \u003c\/p\u003e\u003cp\u003e Exercises.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e6. Choosing the Form of a Linear Model for Analysis.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 6.1 The Importance of Understanding Dependence.  \u003c\/p\u003e\u003cp\u003e 6.2 How Many Variables per Independent Sampling Unit?  \u003c\/p\u003e\u003cp\u003e 6.3 What Types of Variables Play a Role?  \u003c\/p\u003e\u003cp\u003e 6.4 What Repeated Sampling Scheme Was Used?  \u003c\/p\u003e\u003cp\u003e 6.5 Analysis Strategies for Multivariate Data.  \u003c\/p\u003e\u003cp\u003e 6.6 cautions and Recommendations.  \u003c\/p\u003e\u003cp\u003e 6.7 Review of Linear Model Notation.  \u003c\/p\u003e\u003cp\u003e PART II: MULTIVARIATE DISTRIBUTION THEORY.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e7. General Theory of Multivariate Distributions.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 7.1 Motivation.  \u003c\/p\u003e\u003cp\u003e 7.2 Notation and Concepts.  \u003c\/p\u003e\u003cp\u003e 7.3 Families of Distributions.  \u003c\/p\u003e\u003cp\u003e 7.4 Cumulative Distribution Function.  \u003c\/p\u003e\u003cp\u003e 7.5 Probability Density Function.  \u003c\/p\u003e\u003cp\u003e 7.6 Formulas for Probabilities and Moments.  \u003c\/p\u003e\u003cp\u003e 7.7 Characteristic Function.  \u003c\/p\u003e\u003cp\u003e 7.8 Moment Generating Function.  \u003c\/p\u003e\u003cp\u003e 7.9 Cumulant generating Function.  \u003c\/p\u003e\u003cp\u003e 7.10 Transforming Random Variables.  \u003c\/p\u003e\u003cp\u003e 7.11 Marginal Distributions.  \u003c\/p\u003e\u003cp\u003e 7.12 Independence of Random Vectors.  \u003c\/p\u003e\u003cp\u003e 7.13 Conditional Distributions.  \u003c\/p\u003e\u003cp\u003e 7.14 (Joint) Moments of Multivariate Distributions.  \u003c\/p\u003e\u003cp\u003e 7.15 Conditional Moments of Distributions.  \u003c\/p\u003e\u003cp\u003e 7.16 Special Considerations for Random Matrices.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e8. Scalar, vector, and Matrix Gaussian Distributions.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 8.1 Motivation.  \u003c\/p\u003e\u003cp\u003e 8.2 The Scalar Gaussian Distribution.  \u003c\/p\u003e\u003cp\u003e 8.3 The Vector (“Multivariate”) Gaussian Distribution.  \u003c\/p\u003e\u003cp\u003e 8.4 Marginal Distributions.  \u003c\/p\u003e\u003cp\u003e 8.5 Independence.  \u003c\/p\u003e\u003cp\u003e 8.6 Conditional Distributions.  \u003c\/p\u003e\u003cp\u003e 8.7 Asymptotic Properties.  \u003c\/p\u003e\u003cp\u003e 8.8 The matrix Gaussian Distribution.  \u003c\/p\u003e\u003cp\u003e 8.9 Assessing, Multivariate Gaussian Distribution.  \u003c\/p\u003e\u003cp\u003e 8.10 Tests for Gaussian Distribution.  \u003c\/p\u003e\u003cp\u003e Exercises.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e9. Univariate Quadratic Forms.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 9.1 Motivation.  \u003c\/p\u003e\u003cp\u003e 9.2 Chi-Square Distributions.  \u003c\/p\u003e\u003cp\u003e 9.3 General Properties of Quadratic Forms.  \u003c\/p\u003e\u003cp\u003e 9.4 Properties of Quadratic Forms in Gaussian Vectors.  \u003c\/p\u003e\u003cp\u003e 9.5 Independence among Linear and Quadratic Forms.  \u003c\/p\u003e\u003cp\u003e 9.6 The ANOVA Theorem.  \u003c\/p\u003e\u003cp\u003e 9.7 Ratios Involving Quadratic Forms.  \u003c\/p\u003e\u003cp\u003e Exercises.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e10. Multivariate Quadratic Forms.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 10.1 The Wishart Distribution.  \u003c\/p\u003e\u003cp\u003e 10.2 The Characteristic Function of the Wishart.  \u003c\/p\u003e\u003cp\u003e 10.3 Properties of the Wishart.  \u003c\/p\u003e\u003cp\u003e 10.4 The Inverse Wishart.  \u003c\/p\u003e\u003cp\u003e 10.5 Related Distributions.  \u003c\/p\u003e\u003cp\u003e Exercises.  \u003c\/p\u003e\u003cp\u003e PART III: ESTIMATION IN LINEAR MODELS.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e11. Estimation for Univariate and Weighted Linear Models.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 11.1 Motivation.  \u003c\/p\u003e\u003cp\u003e 11.2 Statement of the Problem.  \u003c\/p\u003e\u003cp\u003e 11.3 (Unrestricted) Linear Equivalent Linear Models.  \u003c\/p\u003e\u003cp\u003e 11.4 Estimability and Criteria for Checking It.  \u003c\/p\u003e\u003cp\u003e 11.5 Coding Schemes and the Essence matrix.  \u003c\/p\u003e\u003cp\u003e 11.6 Unrestricted Maximum Likelihood Estimation of β.  \u003c\/p\u003e\u003cp\u003e 11.7 Unrestricted BLUE Estimation of β.  \u003c\/p\u003e\u003cp\u003e 11.8 Unrestricted Least Squares Estimation of β.  \u003c\/p\u003e\u003cp\u003e 11.9 Unrestricted Maximum Likelihood Estimation of θ.  \u003c\/p\u003e\u003cp\u003e 11.10 Unrestricted BLUE of θ.  \u003c\/p\u003e\u003cp\u003e 11.11 Related Distributions.  \u003c\/p\u003e\u003cp\u003e 11.12 Formulations of Explicit Restrictions of β and θ.  \u003c\/p\u003e\u003cp\u003e 11.13 Restricted Estimation Via Equivalent Models.  \u003c\/p\u003e\u003cp\u003e 11.14 Fitting Piecewise Polynomial Models Via Splines.  \u003c\/p\u003e\u003cp\u003e 11.15 Estimation for the GGLM: Weighted Least Squares.  \u003c\/p\u003e\u003cp\u003e Exercises.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e12. Estimation for Multivariate Linear Models.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 12.1 Alternate Formulations of the Model.  \u003c\/p\u003e\u003cp\u003e 12.2 Estimability in the Multivariate GLM.  \u003c\/p\u003e\u003cp\u003e 12.3 Unrestricted Likelihood Estimation.  \u003c\/p\u003e\u003cp\u003e 12.4 Estimation of Secondary Parameters.  \u003c\/p\u003e\u003cp\u003e 12.5 Estimation with Multivariate Restrictions.  \u003c\/p\u003e\u003cp\u003e 12.6 Unrestricted Estimation With Compound Symmetry: the “Univariate” Approach to Repeated Measures.  \u003c\/p\u003e\u003cp\u003e Exercises.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e13. Estimation for Generalizations of Multivariate Models.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 13.1 Motivation.  \u003c\/p\u003e\u003cp\u003e 13.2 Criteria and Algorithms.  \u003c\/p\u003e\u003cp\u003e 13.3 Weighted Estimation of β and Σ.  \u003c\/p\u003e\u003cp\u003e 13.4 Transformations among Growth Curve Designs.  \u003c\/p\u003e\u003cp\u003e 13.5 Within-Individual Design matrices.  \u003c\/p\u003e\u003cp\u003e 13.6 Estimation Methods.  \u003c\/p\u003e\u003cp\u003e 13.7 Relationships to the Univariate and Mixed Models.  \u003c\/p\u003e\u003cp\u003e Exercises.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e14. Estimation for Linear Mixed Models.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 14.1 Motivation.  \u003c\/p\u003e\u003cp\u003e 14.2 Statement of the General Linear Mixed Models.  \u003c\/p\u003e\u003cp\u003e 14.3 Estimation and Estimability.  \u003c\/p\u003e\u003cp\u003e 14.4 Some Special Types of Models.  \u003c\/p\u003e\u003cp\u003e 14.5 ML Estimation.  \u003c\/p\u003e\u003cp\u003e 14.6 REML Estimation.  \u003c\/p\u003e\u003cp\u003e 14.7 Small-Sample Properties of Estimators.  \u003c\/p\u003e\u003cp\u003e 14.8 Large-Sample Properties of Variance Estimators.  \u003c\/p\u003e\u003cp\u003e 14.9 Conditional Estimation of \u003cb\u003e\u003ci\u003ed\u003c\/i\u003e\u003c\/b\u003e\u003csub\u003ei\u003c\/sub\u003e and BLUP Prediction.  \u003c\/p\u003e\u003cp\u003e Exercises.  \u003c\/p\u003e\u003cp\u003e PART IV: TESTS IN GAUSSIAN LINEAR MODELS.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e15. Tests for Univariate Linear Models.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 15.1 Motivation.  \u003c\/p\u003e\u003cp\u003e 15.2 Testability of Univariate Hypotheses.  \u003c\/p\u003e\u003cp\u003e 15.3 Tests of a Priori Hypotheses.  \u003c\/p\u003e\u003cp\u003e 15.4 Related Distributions.  \u003c\/p\u003e\u003cp\u003e 15.5 Transformations and Invariance Properties.  \u003c\/p\u003e\u003cp\u003e 15.6 Confidence Regions for θ.  \u003c\/p\u003e\u003cp\u003e Exercises.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e16. Tests for Multivariate Linear Models.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 16.1 Motivation.  \u003c\/p\u003e\u003cp\u003e 16.2 Testability of Multivariate Hypotheses.  \u003c\/p\u003e\u003cp\u003e 16.3 Tests of a Priori Hypotheses.  \u003c\/p\u003e\u003cp\u003e 16.4 Linear Invariance.  \u003c\/p\u003e\u003cp\u003e 16.5 Four Multivariate Test Statistics.  \u003c\/p\u003e\u003cp\u003e 16.6 Which Multivariate Test Is Best?  \u003c\/p\u003e\u003cp\u003e 16.7 Univariate Approach to Repeated Measures: UNIREP.  \u003c\/p\u003e\u003cp\u003e 16.8 More on Invariance Properties.  \u003c\/p\u003e\u003cp\u003e 16.9 Tests of Hypotheses about Σ.  \u003c\/p\u003e\u003cp\u003e 16.10 Confidence Regions for Θ.  \u003c\/p\u003e\u003cp\u003e Exercises.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e17. Tests for Generalizations of Multivariate Linear Models.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 17.1 Motivation.  \u003c\/p\u003e\u003cp\u003e 17.2 Doubly Multivariate Models.  \u003c\/p\u003e\u003cp\u003e 17.3 Missing Responses in Multivariate Linear Models.  \u003c\/p\u003e\u003cp\u003e 17.4 Exact and Approximate Weighted Least Squares.  \u003c\/p\u003e\u003cp\u003e 17.5 Seemingly Unrelated Regressions.  \u003c\/p\u003e\u003cp\u003e 17.6 Growth Curve Models (GMANOVA).  \u003c\/p\u003e\u003cp\u003e 17.7 Testing Hypotheses in the GCM.  \u003c\/p\u003e\u003cp\u003e 17.8 Confidence Bands for Growth Curves.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e18. Tests for Linear Mixed Models.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 18.1 Overview.  \u003c\/p\u003e\u003cp\u003e 18.2 Estimability of θ = \u003ci\u003eC\u003c\/i\u003eβ.  \u003c\/p\u003e\u003cp\u003e 18.3 Likelihood Ratio Tests of \u003ci\u003eC\u003c\/i\u003eβ.  \u003c\/p\u003e\u003cp\u003e 18.4 Likelihood Ratio Tests Involving τ.  \u003c\/p\u003e\u003cp\u003e 18.5 Test Size of Wald-Type Tests of β Using REML.  \u003c\/p\u003e\u003cp\u003e 18.6 Using Wald-Type Tests of β with REML.  \u003c\/p\u003e\u003cp\u003e 18.7 Using Wald-Type Tests of {β,τ} with REML.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e19. A Review of Multivariate and Univariate Linear Models.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 19.1 Matrix Gaussian and Wishart Properties.  \u003c\/p\u003e\u003cp\u003e 19.2 Design Matrix Properties.  \u003c\/p\u003e\u003cp\u003e 19.3 Model Components.  \u003c\/p\u003e\u003cp\u003e 19.4 Primary Parameter and Related Estimators.  \u003c\/p\u003e\u003cp\u003e 19.5 Secondary Parameter Estimators.  \u003c\/p\u003e\u003cp\u003e 19.6 Added-Last and Added-in-Order Tests.  \u003c\/p\u003e\u003cp\u003e PART V: CHOOSING A SIMPLE SIZE IN GAUSSIAN LINEAR MODELS.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e20. Sample Size for Univariate Linear Model.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 20.1 Sample Size Consulting: Before You begin.  \u003c\/p\u003e\u003cp\u003e 20.2 The Machinery of a Power Analysis.  \u003c\/p\u003e\u003cp\u003e 20.3 Independent \u003ci\u003et\u003c\/i\u003e Example.  \u003c\/p\u003e\u003cp\u003e 20.4 Paired \u003ci\u003et\u003c\/i\u003e Example.  \u003c\/p\u003e\u003cp\u003e 20.5 The Impact of σ\u003csup\u003e2\u003c\/sup\u003e or β in Power analysis.  \u003c\/p\u003e\u003cp\u003e 20.6 Random Predictors.  \u003c\/p\u003e\u003cp\u003e 20.7 Internal Pilot Design.  \u003c\/p\u003e\u003cp\u003e 20.8 Other Criteria for Choosing a Sample Size.  \u003c\/p\u003e\u003cp\u003e Exercises.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e21. Sample Size for Multivariate Linear Model.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 21.1 The Machinery of a Power Analysis.  \u003c\/p\u003e\u003cp\u003e 21.2 Paired \u003ci\u003et\u003c\/i\u003e Example.  \u003c\/p\u003e\u003cp\u003e 21.3 Time by Treatment Example.  \u003c\/p\u003e\u003cp\u003e 21.4 Comparing between and within Designs.  \u003c\/p\u003e\u003cp\u003e 21.5 Some Invariance Properties.  \u003c\/p\u003e\u003cp\u003e 21.6 Random Predictors.  \u003c\/p\u003e\u003cp\u003e 21.7 Internal Pilot Designs.  \u003c\/p\u003e\u003cp\u003e Exercises.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e22. Sample Size for Generalizations of Multivariate Models.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 22.1 Motivation.  \u003c\/p\u003e\u003cp\u003e 22.2 Sample Size Methods for Growth Curve Models.  \u003c\/p\u003e\u003cp\u003e \u003cb\u003e23. Sample Size for Linear Mixed Models.\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003e 23.1 Motivation.  \u003c\/p\u003e\u003cp\u003e 23.2 Methods.  \u003c\/p\u003e\u003cp\u003e 23.3 Internal Pilot Designs.  \u003c\/p\u003e\u003cp\u003e Appendix: Computing Resources.  \u003c\/p\u003e\u003cp\u003e References.  \u003c\/p\u003e\u003cp\u003e Index.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":53515423023447,"sku":"9780471214885","price":117.85,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/linear-model-theory-9780471214885","provider":"Book Curl","version":"1.0","type":"link"}