Matrix-Based Introduction to Multivariate Data Analysis, Softcover reprint of the original 1st ed. 2016

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Language: English
Cover of the book Matrix-Based Introduction to Multivariate Data Analysis

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This book enables readers who may not be familiar with matrices to understand a variety of multivariate analysis procedures in matrix forms. Another feature of the book is that it emphasizes what model underlies a procedure and what objective function is optimized for fitting the model to data. The author believes that the matrix-based learning of such models and objective functions is the fastest way to comprehend multivariate data analysis. The text is arranged so that readers can intuitively capture the purposes for which multivariate analysis procedures are utilized: plain explanations of the purposes with numerical examples precede mathematical descriptions in almost every chapter.
 This volume is appropriate for undergraduate students who already have studied introductory statistics. Graduate students and researchers who are not familiar with matrix-intensive formulations of multivariate data analysis will also find the book useful, as it is based on modern matrix formulations with a special emphasis on singular value decomposition among theorems in matrix algebra.
 The book begins with an explanation of fundamental matrix operations and the matrix expressions of elementary statistics, followed by the introduction of popular multivariate procedures with advancing levels of matrix algebra chapter by chapter. This organization of the book allows readers without knowledge of matrices to deepen their understanding of multivariate data analysis.

Part 1. Elementary Statistics with Matrices.- 1 Introduction to Matrix Operations.- 2 Intra-variable Statistics.- 3 Inter-variable Statistics.- Part 2. Least Squares Procedures.- 4 Regression Analysis.- 5 Principal Component Analysis (Part 1).- 6 Principal Component Analysis 2 (Part 2).- 7 Cluster Analysis.- Part 3. Maximum Likelihood Procedures.- 8 Maximum Likelihood and Normal Distributions.- 9 Path Analysis.- 10 Confirmatory Factor Analysis.- 11 Structural Equation Modeling.- 12 Exploratory Factor Analysis.- Part 4. Miscellaneous Procedures.- 13 Rotation Techniques.- 14 Canonical Correlation and Multiple Correspondence Analyses.- 15 Discriminant Analysis.- 16 Multidimensional Scaling.- Appendices.- A1 Geometric Understanding of Matrices and Vectors.-  A2 Decomposition of Sums of Squares.-  A3 Singular Value Decomposition (SVD).- A4 Matrix Computation Using SVD.- A5 Supplements for Probability Densities and Likelihoods.- A6 Iterative Algorithms.- References.- Index.
Kohei Adachi, Graduate School of Human Sciences, Osaka University

Enables even readers without knowledge of matrices to grasp their operations to learn multivariate data analysis in matrix forms

Emphasizes what model underlies an analysis procedure and what function is optimized for estimating model parameters as the fastest way to understand the procedure

Introduces plain numerical illustrations of the purposes for which procedures are utilized, followed by mathematical descriptions for an intuitive understanding of those purposes

Includes supplementary material: sn.pub/extras