Matrix-Based Introduction to Multivariate Data Analysis

ISBN-13: 9789811095955 / Angielski / Miękka / 2018 / 301 str.

Kohei Adachi

Recenzje

"Kohei Adachi's elegant piece ... striking a good balance between technical details, geometric intuition, and examples from real data. ... Every chapter in this book has exercises that can be used as homework problems or for self-study. ... cover topics that every student and user of statistics should understand, and they can be used in an undergraduate- or master-level multivariate statistical course. ... I highly recommend this book and believe it will reach diverse audiences." (Lin Liu, Biometrics, Vol. 77 (4), December, 2021)

Spis treści

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.

O autorze

Kohei Adachi, Graduate School of Human Sciences, Osaka University

Blurb

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.