2nd Edition

Foundations of Factor Analysis

By Stanley A Mulaik Copyright 2009
    548 Pages 50 B/W Illustrations
    by Chapman & Hall

    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.

    Factor Analysis and Structural Theories
    Brief History of Factor Analysis as a Linear Model
    Example of Factor Analysis
    Mathematical Foundations for Factor Analysis
    Scalar Algebra
    Matrix Algebra
    Treatment of Variables as Vectors
    Maxima and Minima of Functions
    Composite Variables and Linear Transformations
    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
    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
    Rationale for Finding Factors and Factor Loadings
    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
    Component Analysis
    Image Analysis
    Canonical-Factor Analysis
    Problem of Doublet Factors
    Metric Invariance Properties
    Image-Factor Analysis
    Psychometric Inference in Factor Analysis
    Factor Rotation
    Thurstone’s Concept of a Simple Structure
    Oblique Graphical Rotation
    Orthogonal Analytic Rotation
    Quartimax Criterion
    Varimax Criterion
    Transvarimax Methods
    Simultaneous Orthogonal Varimax and Parsimax
    Oblique Analytic Rotation
    Oblimin Family
    Harris–Kaiser Oblique Transformations
    Weighted Oblique Rotation
    Oblique Procrustean Transformations
    Gradient-Projection-Algorithm Synthesis
    Rotating Using Component Loss Functions
    Factor Scores and Factor Indeterminacy
    Scores on Component Variables
    Indeterminacy of Common-Factor Scores
    Further History of Factor Indeterminacy
    Other Estimators of Common Factors
    Factorial Invariance
    Invariance under Selection of Variables
    Invariance under Selection of Experimental Populations
    Comparing Factors across Populations
    Confirmatory-Factor Analysis
    Example of Confirmatory-Factor Analysis
    Mathematics of Confirmatory-Factor Analysis
    Designing Confirmatory Factor-Analysis Models
    Some Other Applications
    Subject Index
    Author Index


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

    "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