Matrix-Based Introduction to Multivariate Data Analysis

  title={Matrix-Based Introduction to Multivariate Data Analysis},
  author={Kohei Adachi},
  • K. Adachi
  • Published 12 October 2016
  • Mathematics
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… 

Selected Payback Statistical Contributions to Matrix/Linear Algebra: Some Counterflowing Conceptualizations

Matrix/linear algebra continues bestowing benefits on theoretical and applied statistics, a practice it began decades ago (re Fisher used the word matrix in a 1941 publication), through a myriad of

A unified representation of simultaneous analysis methods of reduction and clustering

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Permutimin: Factor Rotation to Simple Structure with Permutation of Variables

A new rotation technique is proposed, which can give a p-variables -factors target matrix of zero and nonzero elements, which stands for the properties to be possessed by the rotated loading matrix, called Permutimin.

Factor analysis: Latent variable, matrix decomposition, and constrained uniqueness formulations

  • K. Adachi
  • Engineering
    WIREs Computational Statistics
  • 2019
Factor analysis (FA) is a time‐honored multivariate analysis procedure for exploring the factors that underlie observed multiple variables to explain their variations. According to how the factors

Clustered Common Factor Exploration in Factor Analysis

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Principal component analysis (PCA) and factor analysis (FA) are two time-honored dimension reduction methods. In this paper, some inequalities are presented to contrast the parameters’ estimates in

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Factor Analysis Procedures Revisited from the Comprehensive Model with Unique Factors Decomposed into Specific Factors and Errors

Factor analysis (FA) procedures can be classified into three types (Adachi in WIREs Comput Stat, 2019): latent variable FA (LVFA), matrix

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An Introduction to Kristof’s Theorem for Solving Least-Square Optimization Problems Without Calculus

  • N. Waller
  • Mathematics
    Multivariate behavioral research
  • 2018
The underlying logic of Kristof's Theorem is described in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof and it is shown how Kristof’s Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics.