Applied Multivariate Analysis
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.
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Multivariate Distributions and the Linear Model
Multivariate Regression Models
Seemingly Unrelated Regression Models 311
Multivariate Random and Mixed Models
analysis analyze approximate assuming asymptotic calculated canonical correlation canonical variates cell chi-square chi-square distribution coefficients column confidence intervals consider contrasts correlation matrix covariance matrix covariance structure criterion critical value data set deﬁned degrees of freedom dependent variables design matrix diag diagonal differences discriminant discussed distances eigenvalues elements equal equation error Euclidean evaluate example F distribution F statistic F tests factor fixed effects function given GMANOVA model hypothesis independent interaction Letting linear model MANOVA methods mixed model ML estimates multivariate normal distribution multivariate normality multivariate tests observations obtained option orthogonal outliers p-value parameters plot population principal components PROC GLM PROC MIXED procedure Q-Q plots random effects rank regression model represent residuals roots sample solution subset sum of squares Table test H Theorem treatment univariate Wishart distribution zero