NATIONAL CHIAO TUNG UNIVERSITY

INSTITUTE OF STATISTICS

 

MULTIVARIATE ANALYSIS

FALL 2006

 

 

 


Instructor:

Guan-Hua Huang, Ph.D.

 

Office: 423 Joint Education Hall

 

Phone: 03-513-1334

 

Email: ghuang@stat.nctu.edu.tw

Class meetings:

Tuesday 9:00-12:00 at 406 Joint Education Hall

Office hours:

By appointment

Class website:

http://www.stat.nctu.edu.tw/subhtml/source/teachers/ghuang/course/multivariate06/

Credit:

Three (3) credits

 

COURSE SUMMARY

 

The aims of this course are

 

Ÿ          To illustrate extensions of univariate statistical methodology to multivariate data.

Ÿ          To introduce students to some of the distinctive statistical methodologies which arise only in multivariate data.

Ÿ          To introduce students to some of the computational techniques required for multivariate analysis available in standard statistical packages.

 

Topics include: multivariate techniques and analyses, multivariate analysis of variance and repeated measures, discriminant analysis, factor analysis and principal component analysis, canonical correlation, cluster analysis, structural equation models.

 

HANDOUTS AND TEXTBOOKS

 

Handouts corresponding to each lecture will be available on the class website before each class. There is one required textbook for this course and reading assignments will be made primary in this book:

 

Johnson, R.A. and Wichern, D.W., 2002. Applied Multivariate Statistical Analysis, Fifth Edition. Prentice Hall, Upper Saddle River, NJ.

 

PREREQUISITES

 

Students are expected to have background on undergraduate probability, mathematical statistics, and linear regression.

 

METHOD OF STUDENT EVALUATION

 

The course grade will be based on four homework assignments (50%), one midterm exam (20%), and one final exam (30%).

 

COURSE OUTLINE

 

Readings refer to: Johnson, R.A. and Wichern, D.W., 2002. Applied Multivariate Statistical Analysis, Fifth Edition.

 

Module

Topic

Reading

1

introduction, objectives, multivariate data, matrix algebra and vector spaces

1-30, 50-111

2

statistical distance, expected values, variances and covariances of linear combinations, sample geometry

30-37, 67-79,

112-148

3

multivariate normal distribution

149-209

4

inferences about a mean vector, Hotelling's T2

210-219

5

confidence regions and simultaneous comparisons, missing data

220-238, 252-256

6

two-sample T2

272-293

7

introduction to MANOVA

293-305, 395

8

MANOVA and linear models, compositional data analysis

305-323, 327-332, 354-410.

9

profile and repeated measures analysis

272-282, 318-327

10

principal components analysis, biplots

426-458, 719-723

11

cluster analysis (hierarchical and non-hierarchical)

668-700

12

multidimensional scaling, principal coordinates analysis

700-708

13

discrimination and classification, canonical discriminant analysis, data mining

581-628, 641-646, 628-641, 731-747

14

factor analysis and the factor model, factor rotation, scores, strategy

477-524

15

path and structural equation models

524-529

16

correspondence analysis, procrustes analysis, canonical correlation analysis

709-719, 723-730, 543-580