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2nd Edition

# Foundations of Factor Analysis

By

## Stanley A Mulaik

ISBN 9781420099614
Published September 25, 2009 by Chapman and Hall/CRC
548 Pages 50 B/W Illustrations

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## Book Description

Providing a practical, thorough understanding of how factor analysis works, Foundations of Factor Analysis, Second Edition discusses the assumptions underlying the equations and procedures of this method. It also explains the options in commercial computer programs for performing factor analysis and structural equation modeling. This long-awaited edition takes into account the various developments that have occurred since the publication of the original edition.

New to the Second Edition

• A new chapter on the multivariate normal distribution, its general properties, and the concept of maximum-likelihood estimation
• More complete coverage of descriptive factor analysis and doublet factor analysis
• A rewritten chapter on analytic oblique rotation that focuses on the gradient projection algorithm and its applications
• Discussions on the developments of factor score indeterminacy
• A revised chapter on confirmatory factor analysis that addresses philosophy of science issues, model specification and identification, parameter estimation, and algorithm derivation

Presenting the mathematics only as needed to understand the derivation of an equation or procedure, this textbook prepares students for later courses on structural equation modeling. It enables them to choose the proper factor analytic procedure, make modifications to the procedure, and produce new results.

Introduction
Factor Analysis and Structural Theories
Brief History of Factor Analysis as a Linear Model
Example of Factor Analysis
Mathematical Foundations for Factor Analysis
Introduction
Scalar Algebra
Vectors
Matrix Algebra
Determinants
Treatment of Variables as Vectors
Maxima and Minima of Functions
Composite Variables and Linear Transformations
Introduction
Composite Variables
Unweighted Composite Variables
Differentially Weighted Composites
Matrix Equations
Multiple and Partial Correlations
Multiple Regression and Correlation
Partial Correlations
Determinantal Formulas
Multiple Correlation in Terms of Partial Correlation
Multivariate Normal Distribution
Introduction
Univariate Normal Density Function
Multivariate Normal Distribution
Maximum-Likelihood Estimation
Fundamental Equations of Factor Analysis
Analysis of a Variable into Components
Use of Matrix Notation in Factor Analysis
Methods of Factor Extraction
Diagonal Method of Factoring
Centroid Method of Factoring
Principal-Axes Methods
Common-Factor Analysis
Preliminary Considerations
First Stages in a Factor Analysis
Fitting the Common-Factor Model to a Correlation Matrix
Other Models of Factor Analysis
Introduction
Component Analysis
Image Analysis
Canonical-Factor Analysis
Problem of Doublet Factors
Metric Invariance Properties
Image-Factor Analysis
Psychometric Inference in Factor Analysis
Factor Rotation
Introduction
Thurstone’s Concept of a Simple Structure
Oblique Graphical Rotation
Orthogonal Analytic Rotation
Introduction
Quartimax Criterion
Varimax Criterion
Transvarimax Methods
Simultaneous Orthogonal Varimax and Parsimax
Oblique Analytic Rotation
General
Oblimin Family
Harris–Kaiser Oblique Transformations
Weighted Oblique Rotation
Oblique Procrustean Transformations
Rotating Using Component Loss Functions
Conclusions
Factor Scores and Factor Indeterminacy
Introduction
Scores on Component Variables
Indeterminacy of Common-Factor Scores
Further History of Factor Indeterminacy
Other Estimators of Common Factors
Factorial Invariance
Introduction
Invariance under Selection of Variables
Invariance under Selection of Experimental Populations
Comparing Factors across Populations
Confirmatory-Factor Analysis
Introduction
Example of Confirmatory-Factor Analysis
Mathematics of Confirmatory-Factor Analysis
Designing Confirmatory Factor-Analysis Models
Some Other Applications
Conclusion
References
Subject Index
Author Index

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## Author(s)

### Biography

Stanley A. Mulaik is a Professor Emeritus in the School of Psychology at the Georgia Institute of Technology.

## Reviews

"The author does a good job in explaining basic formal and mathematical concepts. … a useful text for psychologists and scientists from other fields that deal with similar data. The book covers a wide range of topics related to exploratory factor analysis and is useful to readers interested in that topic."
Statistical Papers (2014) 55

"I must say that I am very happy that the author has taken the challenge to update and revise this precious book into the second edition. It will be an important source for decades to come. … there are good grounds for the new edition … it digs deep into the foundations of factor analysis … the topics are explained clearly, and mathematics is taught, as it is needed to understand a derivation of an equation or some procedure. … the book is worth having nearby … ."
International Statistical Review (2010), 78