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Statistical Factor Analysis and Related Methods: Theory and Applications (Wiley Series in Probability & Mathematical Statistics)

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Synopses & Reviews

Publisher Comments:

Despite their evident popularity among research workers in virtually every scientific endeavor, factor analysis and the wider class of procedures known as latent variable models continue to be regarded with skepticism by many mathematical statisticians who point out what they perceive as the arbitrariness and subjectivity of their methods. Statistical Factor Analysis and Related Methods redresses this imbalance by highlighting the value of these multivariate methods for today’s statisticians. Reflecting the importance of factor analysis as a useful data analytic tool and as an invaluable aid to other statistical models, this volume includes cluster and discriminant analysis, least square regression, time/frequency domain stochastic processes, discrete random variables, and graphical data displays. In bridging the gap between the mathematical and statistical theory of factor analysis, this new work represents the first unified treatment of the theory and practice of factor analysis and latent variable models. The book defines factor analysis in broader terms than is typical of the literature, essentially regarding it as the class of models which includes ordinary principal components, weighted principal components, maximum likelihood factor analysis, certain multidimensional scaling models, dual scaling, correspondent analysis, canonical correlation, and the latest class/latent profile analysis. Such usage underscores the common structural features of certain models and the essential similarities among them, which are not readily apparent when dealing solely with empirical applications. Statistical Factor Analysis and Related Methods assumes readers will have a fundamental background in calculus, linear algebra, and introductory statistics while providing basic coverage in these fields in the first two chapters for those who may lack such grounding. In addition, these chapters offer an accessible review of some of the more difficult material in multivariate sampling, measurement and information theory, latent roots and latent vectors in the real and complex normal distribution. A volume whose arrival is long overdue, Statistical Factor Analysis and Related Methods will serve the needs of statisticians and researchers in the empirical sciences who want to gain a deeper understanding of latent variable models as well as the needs of senior undergraduate and graduate students in statistics and related disciplines.

Book News Annotation:

Provides a unified treatment of both the theory and practice of factor analysis and latent variables models, for senior undergraduate and graduate students with a good background in statistics and mathematics, as well as for research workers in the empirical sciences who may wish to better acquaint themselves with the theory of latent variables. Although stress is placed on mathematical and statistical theory, this is generally reinforced by examples taken from the various areas of the natural and social sciences as well as engineering and medicine.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Synopsis:

Statistical Factor Analysis and Related Methods Theory and Applications In bridging the gap between the mathematical and statistical theory of factor analysis, this new work represents the first unified treatment of the theory and practice of factor analysis and latent variable models. It focuses on such areas as:
  • The classical principal components model and sample-population inference
  • Several extensions and modifications of principal components, including Q and three-mode analysis and principal components in the complex domain
  • Maximum likelihood and weighted factor models, factor identification, factor rotation, and the estimation of factor scores
  • The use of factor models in conjunction with various types of data including time series, spatial data, rank orders, and nominal variable
  • Applications of factor models to the estimation of functional forms and to least squares of regression estimators

Description:

Includes bibliographical references (p. 690-731) and index.

About the Author

About the author ALEXANDER BASILEVSKY is Professor of Mathematics and Statistics at the University of Winnipeg. He frequently serves as a professional consultant to both government and industry. In addition to numerous scholarly papers and government reports, Professor Basilevsky is the author of Applied Matrix Algebra in Statistical Sciences and coauthor of An Analysis of the U.S. Income Maintenance Experiments. He is a member of the Canadian Statistical Association, the American Statistical Association, and the Statistical Association of Manitoba, of which he is former president-at-large. Professor Basilevsky received his PhD in statistics/econometrics from the University of Southampton, England.

Table of Contents

Preliminaries.

Matrixes, Vector Spaces.

The Ordinary Principal Components Model.

Statistical Testing of the Ordinary Principal Components Model.

Extensions of the Ordinary Principal Components Model.

Factor Analysis.

Factor Analysis of Correlated Observations.

Ordinal and Nominal Random Data.

Other Models for Discrete Data.

Factor Analysis and Least Squares Regression.

Exercises.

References.

Index.

Product Details

ISBN:
9780471570820
Subtitle:
Theory and Applications
Author:
Basilevsky, Alexander
Author:
Basilevsky
Author:
Basilevsky, Alexander T.
Author:
Basilevsky, A.
Publisher:
Wiley-Interscience
Location:
New York :
Subject:
Probability
Subject:
Statistics - Multivariate analysis
Subject:
Factor analysis
Subject:
Probability & Statistics - General
Subject:
Probability & Statistics - Multivariate Analysis
Subject:
Statistics
Subject:
Probability & Mathematical Statistics
Subject:
Mathematics - General
Copyright:
Edition Description:
WOL online Book (not BRO)
Series:
Wiley Series in Probability and Statistics
Series Volume:
232
Publication Date:
June 1994
Binding:
Online electronic file accessible through online networks
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Yes
Pages:
768
Dimensions:
244 x 160.5 x 42 mm 38.4 oz

Related Subjects

Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Statistical Factor Analysis and Related Methods: Theory and Applications (Wiley Series in Probability & Mathematical Statistics) New Hardcover
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$156.50 In Stock
Product details 768 pages Wiley-Interscience - English 9780471570820 Reviews:
"Synopsis" by , Statistical Factor Analysis and Related Methods Theory and Applications In bridging the gap between the mathematical and statistical theory of factor analysis, this new work represents the first unified treatment of the theory and practice of factor analysis and latent variable models. It focuses on such areas as:
  • The classical principal components model and sample-population inference
  • Several extensions and modifications of principal components, including Q and three-mode analysis and principal components in the complex domain
  • Maximum likelihood and weighted factor models, factor identification, factor rotation, and the estimation of factor scores
  • The use of factor models in conjunction with various types of data including time series, spatial data, rank orders, and nominal variable
  • Applications of factor models to the estimation of functional forms and to least squares of regression estimators
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