## Applied Multivariate Statistics

 Professor: Dr. Markus Kalisch Lectures: Mo 13-15, HG G 3 Tutor: Laura Buzdugan Alan Muro Jimenez

Start of lectures: Monday, February 18, 2013.

Exercises: Details for the exercises can be foundĀ  here.

### Overview

Multivariate Statistics studies the joint distribution of two or more random variables.

Many procedures rely on the multivariate normal distribution. As in univariate statistics, differences between two or more groups of observations are examined (discriminant analysis), and effects of explanatory variables on several target variables are modeled (regression). In addition, there are methods for reducing dimension (principal component analysis, ordination) and formation of groups (cluster analysis).

The course gives an overview of problems and methods. A selection will be treated more in depth.

### Content and time schedule

 Date Subject (1st hour) Subject (2nd hour) Reading 18.02.13 Introduction Visualization 1 AMR Ch 1 & 2 25.02.13 Visualisation & Outlier Detection Exercise 1 Shading; 04.03.13 Imputation & Multiple Imputation Imputation & Multiple Imputation Overview, missForest, MICE 11.03.13 MDS Exercise 2 AMR Ch 4, 18.03.13 PCA PCA AMR Ch 3 25.03.13 Supervised Learning 1: LDA & QDA Exercise 3 ESL Ch 4 (contains more than we need) 08.04.13 Exploratory Factor Analysis (EFA) Revision AMR Ch 5 22.04.13 Extending univariate methods Exercise 4 MSA Ch 5 & 8 (contains much more than we need); 29.04.13 Cluster Analysis Cluster Analysis AMR Ch 6; Notes on mclust (contains much more than we need) 06.05.13 Supervised Learning 2: Trees Supervised Learning 2: Random Forest ESL Ch 9.2, 15 13.05.13 Repeated Measures Repeated Measures AMR Ch 8 27.05.13 Exercise 5 Exercise 6/7

### Exercises

Details for the exercises can be found here.

Exercise for revision including solution (pdf)

### Lecture notes

There will be no script to this lecture, but slides for the lecture presentations can be downloaded from here.

Slides:

### Video Tutorials

We offer short video tutorials on how to use R to apply the methods mentioned in the lecture. Note, that this is still at an experimental stage - feedback is welcome!

Datasets are either in the above folder or in the folder for data sets.

### Literature

• (AMR) B. Everitt et.al., "An Introduction to Applied Multivariate Analysis with R", Springer, 2011.
• (ESL) Hastie et.al., "The Elements of Statistical Learning", Springer, 2009.
• (MSA) More mathematical treatment of fundamental methods: Anderson, "An Introduction to Multivariate Statistical Analysis", Wiley, 2nd Edition (not available online, but ETH library has hardcopies)
• (ISR) Good for reviewing R: P. Dalgaard, "Introductory Statistics with R"; Springer
• Book for the nlme-package in R explaining mixed effects models in more detail: J.C. Pinheiro, D.M. Bates, "Mixed-Effects Models in S and S-PLUS", Spinger

The books AMR, ESL, and JSR are available online via nebis.

### Exam

It will be an oral exam (30min). You have to be abel to solve case studies in R on a computer and explain different concepts of multivariate statistics seen in the lecture. You may bring a one page summary (DIN A4, text on both sides).

Office hours: Fr, 19.7. and Fr, 26.7. from 9.00 to 10.00 in my office (HG G 15.2)

### Misc

• Nice GapMinder Videos
• Background on bias in admission of UC Berkeley (Simpson's Paradox) (this is a paper in Science, one of the most prestigous journals in the world; by this, you can get an impression, how delicate the matter was...)
• More details on Wilks test and Multivariate Regression can be found in W.J. Krzanowski, "Principles of Multivariate Analysis", Oxford Science Publications, 1.Edition, Ch 15.2

Wichtiger Hinweis:
Diese Website wird in älteren Versionen von Netscape ohne graphische Elemente dargestellt. Die Funktionalität der Website ist aber trotzdem gewährleistet. Wenn Sie diese Website regelmässig benutzen, empfehlen wir Ihnen, auf Ihrem Computer einen aktuellen Browser zu installieren. Weitere Informationen finden Sie auf
folgender Seite.

Important Note:
The content in this site is accessible to any browser or Internet device, however, some graphics will display correctly only in the newer versions of Netscape. To get the most out of our site we suggest you upgrade to a newer browser.