Factor Analysis and Related Methods

✍ Scribed by Roderick P. McDonald

• Publisher: Psychology Press / Routledge
• Year: 1985
• Tongue: English
• Leaves: 272
• Edition: 1
• Category: Library

✦ Synopsis

Factor Analysis is a genetic term for a somewhat vaguely delimited set of techniques for data processing, mainly applicable to the social and biological sciences. These techniques have been developed for the analysis of mutual relationships among a number of measurements made on a number of measurable entities. In the broad sense, factor analysis comprises a number of statistical models which yield testable hypotheses -- hypotheses that may confirm or disconfirm in terms of the usual statistical procedures for making tests of significance. It also comprises a number of simplifying procedures for the approximate description of data, which do not in any sense constitute disconfirmable hypotheses, except in the loose sense that they supply approximations to the data. In literature, the two types of analysis have often been confused.

This book clarifies the concepts of factor analysis for students or professionals in the social sciences who wish to know the technique, rather than the mathematics, of factor theory. Mathematical concepts are described to have an intuitive meaning for the non-mathematical reader. An account of the elements of matrix algebra, in the appendix, and the (mathematical) notes following each chapter will help the reader who wishes to receive a more advanced treatment of the subject. Factor Analysis and Related Methods should prove a useful text for graduate and advanced undergraduate students in economics, the behavioral sciences, and education. Researchers and practitioners in those fields will also find this book a handy reference.

✦ Table of Contents

Cover
Title
Copyright
Contents
Dedication
Preface
1. Introduction
1.1 Aims of the Book
1.2 Review of Basic Concepts
1.3 Multiple Regression Theory: The Foundation of Factor Analysis
1.4 Some Basic Multivariate Hypotheses
1.5 The Key Concepts of Common Factor Analysis
1.6 Mathematical Notes on Chapter 1
2. Exploratory Common Factor Analysis
2.1 The Parameters of the Common Factor Model
2.2 Estimation
2.3 Component Theory, Image Theory, Approximate Methods, and Heywood Cases
2.4 Devices for Approximating Simple Structure
2.5 Related Methods
2.6 Mathematical Notes on Chapter 2
3. The Analysis of Covariance Structures: Confirmatory Factor Analysis and Pattern Hypotheses
3.1 Introduction
3.2 Confirmatory Factor Analysis
3.3 Pattern Hypotheses and Parallel Tests
3.4 Mathematical Notes on Chapter 3
4. Models for Linear Structural Relations
4.1 Causal Relations and Causal Modeling
4.2 McArdle’s Model for Linear Structural Relations
4.3 Mathematical Notes on Chapter 4
5. The Problem of Factor Scores
5.1 Factor Analysis as a Test Construction Device
5.2 The Estimation of Common Factors
5.3 The Indeterminacy of Common Factors
5.4 Mathematical Notes on Chapter 5
6. Problems of Relationship Between Factor Analyses
6.1 The Comparison of Separate Analyses
6.2 Simultaneous Factor Analysis in Several Populations
6.3 Repeated-Measures Designs
7. Item Response Theory
7.1 The Problem of Binary (Dichotomous) Data
7.2 Item Response Theory— Latent Trait Theory
7.3 Factor Analysis and Test Theory
8. Summary
8.1 Introduction
8.2 Exploratory Common Factor Analysis
8.3 The Analysis of Covariance Structures
8.4 Models for Linear Structural Relations
8.5 The Problem of Factor Scores
8.6 Problems of Relationship Between Factor Analyses
8.7 Item Response Theory
Appendix— Some Matrix Algebra
A.1 Matrices, Vectors, Scalars
A.2 Matrix Equalities, Sums and Differences
A.3 Multiplication— Length of a Vector
A.4 The Trace of a Matrix
A.5 Special Matrices
A.6 The Inverse of a Matrix
A.7 Determinants
A.8 Partitioned Matrices
A.9 Expected Values
References
Author Index
Subject Index