Statistical Factor Analysis Rel Method: Theory and Applications: 232 (Wiley Series in Probability and Statistics) - Hardcover

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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.

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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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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.