# Applied Multivariate Analysis

Springer Science & Business Media, 21.06.2007 - 695 Seiten
Univariate statistical analysis is concerned with techniques for the analysis of a single random variable. This book is about applied multivariate analysis. It was written to p- vide students and researchers with an introduction to statistical techniques for the ana- sis of continuous quantitative measurements on several random variables simultaneously. While quantitative measurements may be obtained from any population, the material in this text is primarily concerned with techniques useful for the analysis of continuous obser- tions from multivariate normal populations with linear structure. While several multivariate methods are extensions of univariate procedures, a unique feature of multivariate data an- ysis techniques is their ability to control experimental error at an exact nominal level and to provide information on the covariance structure of the data. These features tend to enhance statistical inference, making multivariate data analysis superior to univariate analysis. While in a previous edition of my textbook on multivariate analysis, I tried to precede a multivariate method with a corresponding univariate procedure when applicable, I have not taken this approach here. Instead, it is assumed that the reader has taken basic courses in multiple linear regression, analysis of variance, and experimental design. While students may be familiar with vector spaces and matrices, important results essential to multivariate analysis are reviewed in Chapter 2. I have avoided the use of calculus in this text.

### Was andere dazu sagen -Rezension schreiben

Es wurden keine Rezensionen gefunden.

### Inhalt

 Introduction 1 13 Scope of the Book 3 Vectors and Matrices 7 b Vector Spaces 8 c Vector Subspaces 9 23 Bases Vector Norms and the Algebra of Vector Spaces 12 a Bases 13 c GramSchmidt Orthogonalization Process 15
 62 Random Coefficient Regression Models 352 b Estimating the Parameters 353 c Hypothesis Testing 355 63 Univariate General Linear Mixed Models 357 b Covariance Structures and Model Fit 359 c Model Checking 361 d Balanced Variance Component Experimental Design Models 366 e Multilevel Hierarchical Models 367

 d Orthogonal Spaces 17 e Vector Inequalities Vector Norms and Statistical Distance 21 24 Basic Matrix Operations 25 a Equality Addition and Multiplication of Matrices 26 b Matrix Transposition 28 c Some Special Matrices 29 d Trace and the Euclidean Matrix Norm 30 e Kronecker and Hadamard Products 32 f Direct Sums 35 25 Rank Inverse and Determinant 41 b Generalized Inverses 47 c Determinants 50 26 Systems of Equations Transformations and Quadratic Forms 55 b Linear Transformations 61 c Projection Transformations 63 d Eigenvalues and Eigenvectors 67 e Matrix Norms 71 f Quadratic Forms and Extrema 72 g Generalized Projectors 73 27 Limits and Asymptotics 76 Multivariate Distributions and the Linear Model 79 33 The Multivariate Normal MVN Distribution 84 a Properties of the Multivariate Normal Distribution 86 b Estimating ft and S 88 c The Matrix Normal Distribution 90 34 The ChiSquare and Wishart Distributions 93 b The Wishart Distribution 96 35 Other Multivariate Distributions 99 c The Beta Distribution 101 d Multivariate t F and χ2 Distributions 104 36 The General Linear Model 106 a Regression ANOVA and ANCOVA Models 107 b Multivariate Regression MANOVA and MANCOVA Models 110 c The Seemingly Unrelated Regression SUR Model 114 d The General MANOVA Model GMANOVA 115 37 Evaluating Normality 118 38 Tests of Covariance Matrices 133 c Testing for a Specific Covariance Matrix 137 d Testing for Compound Symmetry 138 e Tests of Sphericity 139 f Tests of Independence 143 g Tests for Linear Structure 145 39 Tests of Location 149 b TwoSample Case 156 c TwoSample Case Nonnormality 160 e Proﬁle Analysis Two Groups 165 f Profile Analysis₁ ₂ 175 310 Univariate Proﬁle Analysis 181 a Univariate OneGroup Proﬁle Analysis 182 Multivariate Regression Models 185 42 Multivariate Regression 186 b Multivariate Regression Estimation and Testing Hypotheses 187 c Multivariate Influence Measures 193 d Measures of Association Variable Selection and LackofFit Tests 197 e Simultaneous Confidence Sets for a New Observation ynew and the Elements ofB 204 Mean Squared Error of Prediction in Multivariate Regression 206 43 Multivariate Regression Example 212 44 OneWay MANOVA and MANCOVA 218 b OneWay MANCOVA 225 c Simultaneous Test Procedures STPfor OneWay MANOVA MANCOVA 230 45 OneWay MANOVAMANCOVA Examples 234 b MANCOVA Example 452 239 46 MANOVAMANCOVA with Unequal i or Nonnormal Data 245 47 OneWay MANOVA with Unequal i Example 246 b Additive TwoWay MAN OVA 252 c TwoWay MANCOVA 256 49 TwoWay MANOVAMANCOVA Example 257 b TwoWay MANCOVA Example 492 261 410 Nonorthogonal TwoWay MANOVA Designs 264 a Nonorthogonal TwoWay MANOVA Designs with andWithout Empty Cells and Interaction 265 b Additive TwoWay MANOVA Designs With Empty Cells 268 412 Higher Ordered Fixed Effect Nested and Other Designs 273 413 Complex Design Examples 276 b Latin Square Design Example 4132 279 414 Repeated Measurement Designs 282 b Extended Linear Hypotheses 286 415 Repeated Measurements and Extended Linear Hypotheses Example 294 b Extended Linear Hypotheses Example 4152 298 416 Robustness and Power Analysis for MR Models 301 417 Power CalculationsPowersas 304 418 Testing for Mean Differences with Unequal Covariance Matrices 307 Seemingly Unrelated Regression Models 310 52 The SUR Model 312 b Prediction 314 53 Seeming Unrelated Regression Example 316 54 The CGMANOVA Model 318 55 CGMANOVA Example 319 56 The GMANOVA Model 320 b Estimation and Hypothesis Testing 321 c Test of Fit 324 e GMANOVA vs SUR 326 57 GMANOVA Example 327 a One Group Design Example 571 328 b Two Group Design Example 572 330 58 Tests of Nonadditivity 333 59 Testing for Nonadditivity Example 335 511 Sum of Proﬁle Designs 338 512 The Multivariate SUR MSUR Model 339 513 Sum of Proﬁle Example 341 514 Testing Model Speciﬁcation in SUR Models 344 515 Miscellanea 348 Multivariate Random and Mixed Models 351
 f Prediction 368 64 Mixed Model Examples 369 a Random Coefﬁcient Regression Example 641 371 b Generalized Randomized Block Design Example 642 376 c Repeated Measurements Example 643 380 d HLM Model Example 644 381 65 Mixed Multivariate Models 385 a Model Speciﬁcation 386 b Hypothesis Testing 388 c Evaluating Expected Mean Square 391 d Estimating the Mean 392 66 Balanced Mixed Multivariate Models Examples 394 a Twoway Mixed MANOVA 395 67 Double Multivariate Model DMM 400 68 Double Multivariate Model Examples 403 a Double Multivariate MAN OVA Example 681 404 b SplitPlot Design Example 682 407 69 Multivariate Hierarchical Linear Models 415 610 Tests of Means with Unequal Covariance Matrices 417 Discriminant and Classiﬁcation Analysis 418 72 Two Group Discrimination and Classiﬁcation 420 a Fishers Linear Discriminant Function 421 b Testing Discriminant Function Coefﬁcients 422 c Classiﬁcation Rules 424 d Evaluating Classiﬁcation Rules 427 73 Two Group Discriminant Analysis Example 429 b Brain Size Example 732 432 74 Multiple Group Discrimination and Classiﬁcation 434 b Testing Discriminant Functions for Signiﬁcance 435 c Variable Selection 437 d Classiﬁcation Rules 438 e Logistic Discrimination and Other Topics 439 75 Multiple Group Discriminant Analysis Example 440 Principal Component Canonical Correlation and Exploratory Factor Analysis 445 a Population Model for PCA 446 b Number of Components and Component Structure 449 c Principal Components with Covariates 453 d Sample PCA 455 e Plotting Components 458 83 Principal Component Analysis Examples 460 b Semantic Differential Ratings Example 832 461 c Performance Assessment Program Example 833 465 84 Statistical Tests in Principal Component Analysis 468 b Tests Using a Correlation Matrix 472 85 Regression on Principal Components 474 a GMANOVA Model 475 86 Multivariate Regression on Principal Components Example 476 87 Canonical Correlation Analysis 477 b Sample CCA 482 c Tests of Significance 483 d Association and Redundancy 485 e Partial Part and Bipartial Canonical Correlation 487 f Predictive Validity in Multivariate Regression using CCA 490 g Variable Selection and Generalized Constrained CCA 491 a Rohwer CCA Example 881 492 b Partial and Part CCA Example 882 494 89 Exploratory Factor Analysis 496 a Population Model for EFA 497 b Estimating Model Parameters 502 c Determining Model Fit 506 d Factor Rotation 507 e Estimating Factor Scores 509 f Additional Comments 510 810 Exploratory Factor Analysis Examples 511 b Di Vesta and Walls Example 8102 512 Cluster Analysis and Multidimensional Scaling 515 92 Proximity Measures 516 b Similarity Measures 519 c Clustering Variables 522 a Agglomerative Hierarchical Clustering Methods 523 b Nonhierarchical Clustering Methods 530 c Number of Clusters 531 d Additional Comments 533 a Protein Consumption Example 941 534 b Nonhierarchical Method Example 942 536 c Teacher Perception Example 943 538 d Cedar Project Example 944 541 a Classical Metric Scaling 542 b Nonmetric Scaling 544 c Additional Comments 547 96 Multidimensional Scaling Examples 548 a Classical Metric Scaling Example 961 549 b Teacher Perception Example 962 550 c Nation Example 963 553 Structural Equation Models 556 102 Path Diagrams Basic Notation and the General Approach 558 103 Conﬁrmatory Factor Analysis 567 104 Confirmatory Factor Analysis Examples 575 b Performance Assessment 5Factor Model Example 1042 578 105 Path Analysis 580 106 Path Analysis Examples 586 b Nonrecursive Model Example 1062 590 107 Structural Equations with Manifest and Latent Variables 594 108 Structural Equations with Manifest and Latent Variables Example 595 109 Longitudinal Analysis with Latent Variables 600 1010 Exogeniety in Structural Equation Models 604 Appendix A 609 References 625 Author Index 667 Subject Index 675 Urheberrecht

### Verweise auf dieses Buch

 Planung von Just-in-time-Belieferungen mit lokalen SuchverfahrenKarsten-Patrick UrbanKeine Leseprobe verfügbar - 2004
 Nonlinear Time Series Analysis of Business CyclesEingeschränkte Leseprobe - 2006
Alle Ergebnisse von Google Books &raquo;

### Über den Autor (2007)

"This book is more than an up-to-date textbook on multivariate analysis. It could enable SAS users to take full and informed advantage of the many options offered in the SAS procedures. For non-SAS users, the clear statement of the models should enable them to fit and interpret them with other software."

ISI Short Book Reviews, Vol. 23/2, August 2003