University of Plymouth, 2009. – 189 p. – ISBN: N/AThe objective of Multivariate Statistics with R is to cover a basic core of multivariate material in such a way that the core mathematical principles are covered, and to provide access to current applications and developments.
The author notes that numerous multivariate statistics books, but this book emphasises the applications (and introduces contemporary applications) with a little more mathematical detail than happens in many such "application/software" based books.
Chapters cover:
Multivariate data including graphical and dynamic graphical methods (Chernoff's Faces, scatterplots, 3d scatterplots, and other methods), animated exploration
Matrix manipulation: Vectors, Matrices, Crossproduct matrix, Matrix inversion, Eigen values and eigen vectors, Singular Value Decomposition, Extended Cauchy-Schwarz Inequality, and Partitioning
Measures of distance: Mahalanobis Distance, Definitions, Distance between points, Quantitative variables - Interval scaled, Distance between variables, Quantitative variables: Ratio Scaled, Dichotomous data, Qualitative variables, Different variables, Properties of proximity matrices
Cluster analysis: Introduction to agglomerative hierarchical cluster analysis, Cophenetic Correlation, Divisive hierarchical clustering, K-means clustering, K-centroids
Multidimensional scaling: Metric Scaling, Visualising multivariate distance, Assessing the quality of fit
Multivariate normality: Exceptations and moments of continuous random functions, Multivariate normality (including R estimation), Transformations
Inference for the mean: Two sample Hotellin's T2 test, Constant Density Ellipses, Multivariate Analysis of Variance
Discriminant analysis: Fisher discrimination, Accuracy of discrimination, Importance of variables in discrimination, Canonical discriminant functions, Linear discrimation
Principal component analysis: Derivation of Principal Components, Some properties of principal components, Ilustration of Principal Components, Principal Components Regression, "Model" criticism for principal components analysis, Sphericity, How many components to retain, Intrepreting the principal components
Canonical Correlation: Canonical variates, Interpretation, Computer example
Factor analysis: Role of factor analysis, The factor analysis model, Principal component extraction, Maximum likelihood solutions, Rotation, Factor scoring
