730—Multivariate Analysis. (3) (Prereq: STAT 713) A survey of the theory and applications of the fundamental techniques for analyzing multivariate data.

Usually Offered: Fall semesters, Even years

Purpose: To provide graduate students who have training in mathematical statistics with a solid introduction to the theory and implementation of the fundamental methods of multivariate statistics, and to give an overview of some recent developments. Major topics include procedures such as principal component and factor analysis, discriminant analysis, multivariate analysis of variance, cluster analysis, and multidimensional scaling.

Required Text:
Mardia, K.V., Kent, J.T., and Bibby, J.M. (1980). Multivariate Analysis. New York: Academic Press.

Selected Other Useful Books:
Everitt, B. (2005). An R and S-PLUS Companion to Multivariate Analysis. London: Springer. 
Stevens, J.P. (2009). Applied Multivariate Statistics for the Social Sciences. Fifth Edition. New York: Routledge. 
Venables, W.N., and Ripley, B.D. (2002). Modern Applied Statistics with S. Fourth Edition.. New York: Springer.

 

Topics Covered	Chapters	Time
Foundations of Multivariate Analysis: Properties of Random Vectors, Theory of The Multivariate Normal Distribution, Multivariate Regression Analysis	1-6	6 weeks
Principal Components and Exploratory Factor Analysis, Introduction to Confirmatory Factor Analysis and Structural Equation Modeling	8-9	2.3 weeks
Canonical Correlation Analysis	10	0.3 weeks
Discriminant Analysis and Multivariate Analysis of Variance	11-12	2.3 weeks
Classification and Regression Trees and Random Decision Forests	-	1 week
Hierarchical Clustering, Model Based Clustering, and Multidimensional Scaling	13-14	1.3 weeks
Hierarchical Linear Models (a.k.a. Multi-level Models or Random Coefficients Regression)	-	0.7 weeks

Contact Faculty: Brian Habing