名称：
Statistical Factor Analysis and Related Methods.

Theory and Applications
ALEXANDER BASTLEVSKY
Department of Mathematics & Statistics
The University of Winnipeg
Winnipeg, Manitoba
Canada

*大小：755页.
*格式：PDF。
*目录：
Contents
1. Preiiminaries
1.1 Introduction
1.2 Rules for Univariate Distributions
1.2.1 The Chi-Squared Distribution
1.2.2 The F Distribution
1.2.3 The f Distribution
1.3.1 Point Estimation: Maximum Likelihood
1.3.2 The Likelihood Ratio Criterion
1.4 Notions of Multivariate Distributions
1.5 Statistics and the Theory of Measurement
1.5.1 The Algebraic Theory of Measurement
1.5.2 Admissiblc Transformations and the Classification
of Scales
1 S.3 Scale Classification and Meaningful Statistics
1.5.4 Units of Measurc and Dimensional Analysis for
Ratio Scales
1.3 Estimation
1.6 Statistical Entropy
1.7 Complex Random Variables
Exercises
2. Matrixes, Vector Spaces
2.1 Introduction
2.2 Linear, Quadratic Forms
2.3 Multivariate Differentiation
2.3.1 Derivative Vectors
2.3.2 Derivative Matrices
2.4 Grammian Association Matrices
2.4.1 The inner Product Matrix
2.4.2 The Cosine Matrix
2.4.3 The Covariance Matrix
2.4.4 The Correlation Matrix
2.5 Transformation of Coordinates
2.5.1 Orthogonal Rotations
2.5.2 Oblique Rotations
Latent Roots and Vectors of Grammian Matrices
Elements of Multivariate Normal Theory
2.8.1 The Multivariate Normal Distribution
2.8.2 Sampling from the Multivariatc Normal
2.9 Thc Ktonecker Product
2.10 Simultaneous Decomposition of Two Grammian Matrices
2.1 1 The Complex Muitivariate Normal Distribution
2.11.1 Complex Matrices, Hermitian Forms
2.11.2 The Complex Multivariate Normat
2.6
2.7 Rotation of Quadratic Forms
2.8
Exercises
3. The Ordinary Principal Components Model
3. t Introduction
3.2 Principal Components in the Population
3.3 Isotropic Variation
3.4 Principal Components in the Sample
3.4. I Introduction
3.4.2 The General Model
3.4.3 The Effect of Mean and Variances on PCs
3.5 Principal Components and Projections
3.6 Principal Components by Least Squares
3.7 Nonlinearity in the Variables
3.8 Alternative Scaling Criteria
3.8.1 Introduction
3.8.2 Standardized Regression Loadings
3.8.3 Ratio Index Loadings
3.8.4 Probability Index Loadings
Exercises
4. Statistical Testing of the Ordinary Principal Components Model
4.1 Introduction
4.2 Testing Covariance and Correlation Matrices
4.2.1 Testing for CompIete Independence
4.2.2 Testing Sphericity
4.2.3 Other lests for Covariance Matrices
4.3 Testing Principal Components by Maximum Likelihood
4.3.1 Testing Equality of all Latent Roots
4.3.2 Testing Subsets of Principal Components
4.3.3 Testing Residuals
4.3.4 Testing Individual Principal Components
4.3.5 Information Criteria of Maximum Likelihood
Estimation of the Number of Components
4.4 Other Methods of Choosing Principal Components
4.4.1 Estirnatcs Bascd on Resampling
4.4.2 Residual Correlations Test
4.4.3 Informal Rules of Thumb
4.5 Discarding Redundant Variables
4.6 Assessing Normality
4.6.1 Assessing for Univariate Normality
4.6.2 Testing for Multivariate Normality
4.6.3 Retrospective Testing for Multivariate Normality
4.7 Robustness, Stability, and Missing Data
4.7.1 Robustness
4.7.2 Sensitivity of Principal Components
4.7.3 Missing Data
Exercises
5. Extensions of the Ordinary Principal Components Model
5.1 introduction
5.2 Principal Components of Singular Matrices
5.2. I Singular Grammian Matrices
5.2.2 Rectangular Matrices and Generalized Inverses
5.3 Principal Components as Clusters: Linear
Transformations in Exploratory Research
5.3. i Orthogonal Rotations
5.3.2 Oblique Rotations
5.3.3 Grouping Variables
5.4 Alternative Modes for Principal Components
5.4.1 Q-Mode Analysis
5.4.2 Multidimensional Scaling and Principal
Coordinates
5.4.3 Three-Mode Analysis
5.4.4 Joint Plotting of Loadings and Scores
5.5 Other Methods for Multivariable and Multigroup
Principal Components
5.5.1 The Canonical Correlation Model
5.5.2 Modification of Canonical Correlation
5.5.3 Canonical Correlation for More than Two Sets
of Variables
5.5.4 Multigroup Principal Components
5.6 Weighted Principal Components
5.7 Principal Components in the Complex Field
5.8 Miscellaneous Statistical Applications
5.8.1 Further Optimality Properties
5.8.2 Screening Data
5 3.3 Principal Components of Discrimination and
Classification
5.8.4 Mahalanobis Distance and thc Multivariate TTest
5.9 Special Types of Continuous Data
5.9.1 Proportions and Compositional Data
5.9.2 Estimating Components of a Mixture
5.9.3 Directional Data
Exercises
6. Factor Analysis
6.1 Introduction
6.2
6.3 Factoring by Principal Components
The Unrestricted Random Factor Model in the
Population
6.3.1 The Homoscedastic Residuals Model
6.3.2 Unweighed tcast Squares Models
6.3.3 The Image Factor Modcl
6.3.4 The Whittle M d ~ l
Unrestricted Maximum Likelihood Factor Models
6.4.1 The Reciprocal Proportionality Model
6.4.2 The Lawley Model
6.4.3 The Rao Canonical Correlation Factor Model
6.4.4. The Gencralized Least Squares Model
6.5.1 The Double Heteroscedastic Model
6.5.2 Psychometric Models
6.4
6.5 Other Weighted Factor Models
Tests of Significance
6.6.1 The Chi-Squared Test
6.62 Information Criteria
6.6.3 Testing Loading Coefficients
The Fixed Factor Model
Estimating Factor Scores
6.8.1 Random Factors: The Regression Estimator
6.8.2 Fixed Factors: The Minimum Distance Estimator
6.8.3 Interpoint Distance in the Factor Space
Factors Representing “Missing Data:” The EM
Algorithm
Factor Rotation and Identification
Confirmatory Factor Analysis
Multigroup Factor Analysis
Latent Structure Analysis
Exercises
7. Factor Analysis of Correlated Observations
7.1 introduction
7.2 Timc Series as Random Functions
7.2.1 Constructing Indices and Indicators
7.2.2 Computing Empirical Time Functions
7.2.3 Pattern Recognition and Data Compression:
Electrocardiograph Data
7.3 Demographic Cohort Data
7.4 Spatial Correlation: Geographic Maps
7.5 The Karhunen-bbve Spectral Decomposition in the
Time Domain
7.5.1 Analysis of the Population: Continuous Space
7.5.2 Analysis of ii Sample: Discrete Space
7.5.3 Order Statistics: Testing Goodness of Fit
7.6 Estimating Dimensionality of Stochastic Processes
7.6.1 Estimating A Stationary ARMA Process
7.6.2 Timc Invariant State Space Models
7.6.3 Autoregression and Principal Coniponents
7.6.4 Kalman Filtering Using Factor Scores
7.7 Multiple Time Series in the Frequcncy Domain
7.7.1 Principle Components in the Frequency Domain
7.7.2 Factor Analysis in the Frequency Domain
7.8 Stochastic Processes in the Space Domain:
Karhunen-Ldve Decomposition
7.9 Patterned Matrices
7.9.1 Circular Matrices
7.9.2 Tridiagonal Matrices
7.9.3 Toeplitz Matrices
7.0.4 Block-Patterned Matrices
Exercises
8. Ordinal and Nominal Random Data
8.1 Introduction
8.2 Ordinal Data
8.2.1 Ordinal Variables as Intrinsically Continuous:
Factor Scaling
8.2.2 Ranks as Order Statistics
8.2.3 Ranks as Qualitative Random Variables
8.2.4 Conclusions
8.3 Nominal Random Variables: Count Data
8.3.1 Symmetric Incidence Matrices
8.3.2 Asymmetric Incidence Matrices
8.3.3 Multivariate Multinominal Data: Dummy Variables
8.4 Further Models for Discrete Data
8.4.1 Guttman Scaling
8.4.2 Maximizing Canonical Correlation
8.4.3 Two-way Contingency Tables: Optimal Scoring
8.4.4 Extensions and Other Types of Discrete Data
8.5 Related Procedures: Dual Scaling and Correspondence
Analysis
8.6 Conciusions
Exercises
9. Other Models for Discrete Data
9.1 Introduction
9.2 SeriaHy Correlated Discrete Data
9.2.1 Seriation
9.2.2 Ordination
9.2.3 Higher-Dimensional Maps
9.3 The Nonlinear “Horseshoe” Effect
9.4 Measures of Pairwise Correlation of Dichotomous
Variables
9.4.1 Euclidean Measures of Association
9.4.2 Non-Euclidean Measures of Association
9.5 Mixed Data
9.5.1 Point Biserial Correlation
9.5.2 Biserial Correlation
9.6 Threshold Models
9.7 Latent Class Analysis
Exercises
10. Factor Analysis and Least Squares Regression
10.1 Introduction
10.2 Least Squares Curve Fitting with Errors in Variables
10.2.1 Minimizing Sums of Squares of Errors in
Arbitrary Direction
10.2.2 The Maximum Likelihood Model
10.2.3 Goodness of Fit Criteria of Orthogonal-Norm
Least Squares
10.2.4 Testing Significance of Orthogonal-Norm Least
Squares
10.2.5 Nonlinear Orthogonal Curve Fitting
10.3 Least Squares Regression with Multicollinearity
10.3.1 Principal Components Regression
10.3.2 Comparing OrthogonabNorm and Y-Norm
Least Squares Regression
10.3.3 Latent Root Regression
10.3.4 Quadratic Principal Componcnts Rcgrcssion
10.4 Least Squares Regression with Errors in Variables and
Multicollinearity
10.4.1 Factor Analysis Regression: Dependent
10.4.2 Factor Analysis Regression: Dependent
10.5 Factor Analysis of Dependent Variables in MANOVA
10.6 Estimating Empirical Functional Relationships
10.7 Other Applications
Variable Excluded
Variable Included
10.7.1 Capital Stock Market Data: Arbitragc Pricing
10.7.2 Estimating Nonlinear Dimensionality: Sliced
Inverse Regression
10.7.3 Factor Analysis and Simultaneous Equations
Models
Exercises
References
Index