Lecturer

prof. Laura Pagani laura.pagani@uniud.it

Credits

6 CFU

Department

Department of Economics and Statistics

Aims

To introduce students to the techniques of multivariate analysis, studying the relationships between observed variables, or the similarity / dissimilarity between statistical units. Theory will be supported by exercises, involving the analysis of real data set and processing the data using Stata statistical package for analysis or with the software opensource R.

Programme

Aspects of Multivariate Analysis.
Applications of Multivariate Techniques. The Organization of Data. Data Displays and Pictorial Representations. Distance. Final Comments.
Matrix Algebra and Random Vectors.
Some Basics of Matrix and Vector Algebra. Positive Definite Matrices. A Square-Root Matrix. Random Vectors and Matrices. Mean Vectors and Covariance Matrices. Matrix Inequalities and Maximization. Singular value decomposition.
Principal Components Analysis.
Introduction. Sample Variation by Principal Components Analysis (PCA). First PCA, the linear combination with maximal variance. Mathematical procedure. Graphing the Principal Components. The scree plot and the loadings plot. PCA in practice.
Distance Measures and Dissimilarity Indices.
Introduction. Definition of distance, some types of distance: Euclidean, city block, Minkowski and ultrametrics Use and interpretation of statistical distances, Mahalanobis distances, indices of similarity Expressions general index of similarity, the Gower index for qualitative and quantitative variables.
Cluster Analysis.
Introduction to agglomerative hierarchical cluster analysis. Nearest neighbour/Single Linkage, Furthest neighbour/Complete linkage. Alternative methods for hierarchical cluster analysis. Divisive hierarchical clustering. K-means clustering, K-centroinds. Cluster Analysis in practice.
Correspondence Analysis.
Introduction. Simple illustration of Correspondence Analysis (CA). Row and column profiles, row and column masses. Decomposition of inertia. Scatter plot in the new dimensions. The quality of representation. Supplementary points. Multiple CA. CA in practice.
Introduction to Stata.

Textbook

S. Zani e A.Cerioli , Analisi dei dati e data mining per le decisioni aziendali. Milano: Giuffrè, 2007
R. Johnson and D. Wichern, Applied Multivariate Statistical Analysis, International Edition, 6th Edition, Pearson Education, 2007.