Course 2007-2008 a.y.

Course Objectives

The key aim of this course is providing the students with basic skills in multivariate data analysis. In particular, students learn techniques and methods useful to analyze and synthesize rich data sets (e.g. cluster and factor analyses), with respect to both the number of variables and the number of observations. All methods are taught through hands-on classes, during which the students analyze a number of databases relevant to their studies (e.g. R&D data, patent data, investment data etc.).

Course Content Summary

Introduction

• Matrix algebra.
• Multivariate random variables. Moments of multivariate distributions. Multivariate samples, summary statistics for multivariate samples. Geometric interpretation of data matrices. Total and generalized variance and their geometric interpretation.

Factorial Techniques

• Principal component (PC) analysis. PC transformation. Property of PCs and their interpretation. Evaluation of results. Sample PC.
• Factor analysis. The Factor model: definition and assumptions. Parameter estimates: the principal component and the principal factor methods. Interpretation of factors: factors rotation. Factor Scores.
• Association for qualitative variables. Simple and multiple correspondence analysis. Profiles and Chi-square metric. Indicator matrices and Burt matrix. Factors and their interpretation. Graphical representation and analysis of results.

Dissimilarity matrices and clustering

• Cluster analysis. Distance and dissimilarity matrices. Hierarchical classification methods. Choice of the number of cluster. Partitioning methods: the k-means method. Evaluation of results.
• Multidimensional scaling (MDS). Representing one or more dissimilarity matrices in a factorial plane. Relationship with factor analysis and cluster analysis.

Detailed Description of Assessment Methods

The course grade is based on:

• The analysis of a real data set (Pc-lab session 4 hours)
• A written exam (concerning the methodological issues discussed during the course).

The two exams will be discussed with the instructor during an oral exam.

Textbooks

• R.A. JOHNSON, D.W. WICHERN, Applied Multivariate Statistical Analysis, Prentice Hall, 2002, 5^th ed.

or:

• J. LATTIN, J.D. CARROLL, P.E. GREEN, Analyzing Multivariate Data, Thomson, 2003