Applied Multivariate StatisticsFall Semester 2014

University of MannheimDepartment of EconomicsChair of StatisticsToni Stocker

Applied Multivariate Statistics (AMS) - ContentIntroduction to AMS

Principal Component Analysis (PCA)

Correspondence Analysis

Matrix Algebra

Multivariate Samples

Biplots

Multidimensional Scaling (MDS)Cluster Analysis

Linear Discriminant Analysis (LDA)Binary Response Models

Factor Analysis

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Introduction to AMS

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2 All other students:should have attended two or more courses in Statistics(descriptive statistics, estimating and hypothesis testing)

Students in Economics from Mannheim: no problem

A course in Basic Econometrics is helpful but not strictly required.

The statistical software R will intensively be used throughout thiscourse. Students who are not yet familiar with R should workthrough chapters 1-5 of the R introduction (see course folder) ontheir own by September 12 at the latest.

If you are not yet sure whether you will attend this course, you mayread sections 1.1 and 1.2 in Johnson & Wichern (see p. 3) to get anidea about the purposes of this course.

Though R is easy to learn, you need to invest some time at the beginning. But you may benefit from it for a long time.

Prerequisites

General Course Information

Day Time LocationLecture Friday 10:15-11:45 L7, 3-5, P043Tutorial Friday 08:30-10:15 L7, 3-5, P043Extra-R-Tutorial Monday 12:00-13:30 t.b.a.

Office Hour: Wednesday, 3:30-5:00 p.m. or by appointment

Office: L7, 3-5, 1st floor, room 143

Phone: 0621-181-3963

Email: stocker@rumms.uni-mannheim.de

General Course Information

Tutorials start in the 2nd week.

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Time and Locations

Contact

Slides (Lecture), Assignments (Tutorials), Introduction to R (see p. 1)Material will be updated weekly (Friday) to find in course folder at Studierendenportal (ILIAS)

General Course Information

R. Johnson, D. Wichern (2007):Applied Multivariate Statistical Analysis; Pearson Intl. Ed.

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Main Reference

A. J. Izenman (2008):Modern Multivariate Statistical Techniques; Springer.

P. Hewson (2009):Multivariate Statistics with R; Open Text Book.

A. Rencher (2002):Methods of Multivariate Analysis; Wiley.

W. Hrdle, L. Simar (2003):Applied Multivariate Statistical Analysis; Wiley.

Course Material

References

Exam + Assignments:80% written exam (120 minutes) + 20% Assignmentsin terms of points to earn in total.

Example:Points

Written Exam: 60 (from 80)Assignments: 18 (from 20): Total: 78 (from 100)=> Grading will be based on 78 points (from 100)Minimum for passing: 40

Assignments:Need to submit homework and attend tutorial. To get full points (20) youneed to work at least on 10 assignments (out of 11) in a meaningful way.(See Guidelines for Assignments)

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Examination

Multivariate analysis consists of a collection of methods that can beused when several measurements are made on each individual orobject in one or more samples.

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See Renchner (2002), p.1

Objectives Dimension reduction and structural simplification

Grouping, discrimination and classification

Investigation of the dependence among variables

Visualization of high-dimensional data

(see also J+W (2007), p.2)

What is it about?

Issues of Applied Multivariate Statistics (AMS)

Close link to other areas such as Exploratory Data Analysis (EDA) and Data Mining

What is it about?

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Example 1: Dimension Reduction

Economic Indicators for the 27 European Union Countries in 2011(see WIREs Comput Stat 2012, 4:399406. doi: 10.1002/wics.1200)

What is it about?

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Example 2: Modern Graphical Techniques

What is it about?

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Example 2 ...

What is it about?

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Example 3: Factor Analysis

Consumer Preference (J&W, example 9.9, p. 508)

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179.011.085.001.079.0150.071.042.011.050.0113.096.085.071.013.0102.001.042.096.002.01

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What is it about?

Example 4: Distances

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Voting results for 15 congressmen from New Jersey(example from R package HSAUR)

Hunt(R) Sandman(R) Howard(D)Hunt(R) 0 8 15Sandman(R) 8 0 17Howard(D) 15 17 0

Extraction from the distance matrix ...

What is it about?

Example 5: Grouping

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What is it about?

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Example 5 ...

What is it about?

Example 6: Classification

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Labor Market Participation of Married Women in Switzerland (1981)(example from R package AER)

What is it about?

Example 7: Discrimination

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Heights and weights of students

What is it about?

Example 8: Correspondence Analysis

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Baccalaurat in France (Hrdle & Simar, p. 313)

What is it about?

Generally: Chapters 1-4, 8, 9, 11, 12 from Johnson and Wichern (J&W)

Timetable and Contents

Lecture 3: Matrix Algebra (part 2)

Lecture 2: Matrix Algebra (part 1)

Lecture 4: Multivariate Samples

Lecture 5: Principal Component Analysis

Lecture 1: Introduction (today)

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Lecture 6: Biplots

Lecture 7: Factor Analysis

Course Outline

What is it about?

Lecture 8: Multidimensional Scaling

Lecture 10: Linear Discriminant Analysis

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Lecture 13: Used as time buffer

Lecture 11: Binary Response Models

Lecture 12: Correspondence Analysis

Lecture 9: Cluster Analysis

Note: This is just a plan! Topics may be skipped; order

may be changed; lecture topics may overlap

What is it about?

... at the end of the semester you

know and (hopefully) understand most common methods foranalyzing multivariate data and their theoretical background

Generally: This is an introductory and applied course. Modern multivariate techniques based on machine learning algorithms will hardly be covered.

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can proficiently use R when using multivariate techniques:data import, constructing graphics, inference, model diagnosis and assessment

have experienced the possibilities and limitations ofmultivariate methods on the basis of real data examples

Main Objectives