Mulaik Foundations of Factor Analysis, Second Edition

2. Auflage 2011
ISBN: 978-1-4200-9981-2
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 548 Seiten

Reihe: Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences

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.

Zielgruppe

Graduate students and researchers in psychology, sociology, educational measurement, marketing, organizational behavior, health science, and statistics.

Autoren/Hrsg.

Mulaik, Stanley A

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

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

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

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

Gradient-Projection-Algorithm Synthesis
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

Über Autor(innen)

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