732G08 Multivariate Methods

1 Course information

The aim of this course is that the student should acquire knowledge in so called multivariate statistical methods, which is a generic term for statistical methods where several random variables are studied simultaneously.

This area includes generalisations of the usual statistical inference, as inference of multidimensional expectations. A problem we will look into is how to measure distances between random variables, which will depend on the purpose. Other questions that will appear are: How can variables/observations be grouped?, do groups of random variables correlate to each other?, can the number of variables be reduced?,  can observations be allocated to a certain groups by the given random variables?,  can a picture/map be drawn from given distances between data?

This is some of the issues that will be discussed and/or analysed

Instructions will be given as distance teaching. This involve that we just meet once at the start of the course and once at the end of the course for oral examination. It is possible to book a time at the teacher’s room. All necessary information during the course will be given through the Internet.  The student collect information by herself through books, notes via It´s Learning (the course-platform). The student also solves recommended exercises by hand and by the computer.

Literature: The main literature is the book by Manly B, Multivariate Methods, and a Swedish compendium by Danielsson S, Grundläggande inferens vid multivariat normalfördelning.  Instead of this Swedish compendium (if you do not speak Swedish) you should find a book containing theory about multivariate normal-distribution. I can recommend Chatfield, Collins, Introduction to Multivariate Analysis, but it is quit old. There will be some hardcopies available.

The book written by Manly is ordered to the bookstore in Kårallen at campus Linköping.  By experience I know that it is often delayed. I recommend therefore that you visit the web-site pricerunner.com and search the book there and of course other interesting books you think you will need. The ISBN for Manly is 1-58488-414-2. The compendium written by Danielsson can only be bought in Kårallen.

Examination will be done by six reports and an oral examination.

2 Plan of the course

The course stretches from week 34 to week 42. The plan below is a short summery of which theory that will be studied each week.

V34:       First meeting, get acquainted to It´Learning

V35        Matrix algebra, Multivariate normal distribution

V36:       Hotellings T²,  Bonferroni,  multivariate distances, test of variation

V37:       Principal component analysis,  factor analyses

V38:       Discriminant-analyses

V39:       Canonical correlation

V40:       Cluster analyses, Multi-dimensional scaling

V41:       Summary of the course, oral examination

V42:        oral examination

3 Weekly plans

Knowledge in some specific areas will be acquired each week. A detailed plan will be given each week. At the end of each week (w35-40) a report should be handed to the teacher. This report is a part of the examination. The report should be written in a word processor and sent to the teacher via It's Learning.

3.1 How to write the report

The list below is a guidance for what should be included in and how to write the report. About 20 pages. Exclude unnecessary computer output.

For example include:

• Formulate the problem.

• Present the dataset.

• Describe which method that should be suitable to use.

• Describe which assumptions that must be fulfilled.

o       Study the data graphically.

o       Correlation between variables?

o       Is Normal- distribution a necessary assumption?

o       Reasonable approximations

• Are the assumptions fulfilled? If not, how is the problem solved in the best way and why.

• Apply the method after possible adjustments.

• Interpret and draw conclusions

4 Exercises

Connected with each item there will be some kind of exercise which solution in some cases will be handed to the teacher. These exercises are not a part of the examination.

5 Course platform

The tool used on the Internet is It's Learning. All communication between teacher and student is done on the Internet via  It's Learning. Send all mail through this platform and you are guaranteed an answer within 24 hours. More information will be found when you logged on  It's Learning. The address is https://www.itslearning.com.

6 Grading

It is possible to get ECTS grades on this course. To get grade C you must hand in the six reports and get them accepted. For grade A the deliveries must be of very high quality and delivered in time and a complementary oral examination.

7 Computer programs

All students should use at least to different kinds of statistical computer programs. There are three programs available: MINITAB, SAS and SPSS.  These three programs can be used at the university. The following holds for use at home:

MINITAB: Borrow a CD from the teacher and install it. No charge.

SPSS: Buy a CD at Bokakademin Kårallen. Charge about 100 SEK

SAS: Borrow  the CDs from the teacher and install it.