Applied Multivariate AnalysisUnivariate 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. |
Contents
| 7 | |
Multivariate Distributions and the Linear Model | 79 |
Multivariate Regression Models | 185 |
Seemingly Unrelated Regression Models 311 | 310 |
Multivariate Random and Mixed Models | 351 |
Discriminant and Classification Analysis 419 | 418 |
Principal Component Canonical Correlation and Exploratory | 445 |
Cluster Analysis and Multidimensional Scaling | 515 |
Structural Equation Models 557 | 556 |
Appendix | 609 |
| 625 | |
Author Index | 667 |
Other editions - View all
Common terms and phrases
analysis analyze approximate assume B₁ calculated cell chi-square chi-square distribution clusters coefficients column components confidence intervals contrasts correlation matrix covariance matrix covariance structure criterion critical value data set defined degrees of freedom dependent variables design matrix diag diagonal discussed eigenvalues elements equal equation error evaluate example F distribution F statistic F tests factor fixed effects function given GMANOVA model independent interaction Letting LFR model linear model MANOVA MANOVA design methods mixed model ML estimate multivariate normal distribution multivariate normality multivariate test normal distribution null hypothesis observations obtained orthogonal outliers p-value parameters population PROC GLM PROC MIXED procedure Q-Q plots rank regression model represent roots sample significant simultaneous confidence intervals subspace Table Theorem treatment univariate variance Wishart distribution zero μ₁ σ²