Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Foreword
Preface
Acknowledgments
Author
Part I Prerequisites
1 Introduction
1.1 Data-Driven Decision-Making
1.2 Variable and Data Types
1.2.1 Random Variable
1.2.2 Measurement Scale and Data Types
1.2.3 Data Sources
1.3 Models and Modeling
1.4 Statistical Approaches to Model-Building
1.4.1 Step 1: Define Problem
1.4.2 Step 2: Develop Conceptual Model
1.4.3 Step 3: Design Study
1.4.4 Step 4: Collect Data
1.4.5 Step 5: Examine Data
1.4.6 Step 6: Select a Suitable Model
1.4.7 Step 7: Estimate Parameters
1.4.8 Step 8: Verify Model
1.4.9 Step 9: Validate Model
1.4.10 Step 10: Interpret Results
1.5 Multivariate Models
1.6 Illustrative Problems
1.7 Case Descriptions
1.7.1 Case 1: Job Stress Assessment Among Employees in Coke Plant
1.7.2 Case 2: Job Demand Analysis of Underground Coal Mine Workers
1.7.3 Case 3: Study of the Process and Quality Characteristics and Their Relationships in Worm Gear Manufacturing
1.7.4 Case 4: Study of the Process and Quality Characteristics in Cast Iron Melting Process
1.7.5 Case 5: Employees Safety Practices in Mines
1.7.6 Case 6: Modeling Causal Relationships of Job Risk Perception of EOT Crane Operators
1.8 Aims of the Book
1.9 Organization of the Book
Exercises
2 Basic Univariate Statistics
2.1 Population and Parameter
2.2 Defining Population: the Probability Distributions
2.2.1 Univariate Normal Distribution
2.3 Sample and Statistics
2.3.1 Measures of Central Tendency
2.3.2 Measures of Dispersion
2.4 Sampling Distribution
2.4.1 Standard Normal Distribution
2.4.2 Chi-Square Distribution
2.4.3 T-Distribution
2.4.4 F-Distribution
2.5 Central Limit Theorem
2.6 Estimation
2.6.1 Confidence Interval for Single Population Mean
2.6.2 Confidence Interval for Single Population Variance
2.6.3 Confidence Interval for the Difference Between Two-Population Means
2.6.4 Confidence Interval for the Ratio Of Two-Population Variances
2.7 Hypothesis Testing
2.7.1 Hypothesis Testing Concerning Single Population Mean
2.7.2 Hypothesis Testing Concerning Single Population Variance
2.7.3 Hypothesis Testing Concerning Equality Of Two-Population Means
Scenario I
Scenario II
Scenario III
2.7.4 Hypothesis Testing Concerning Equality of Two-Population Variances
2.8 Learning Summary
Exercises
Notes
3 Basic Computations
3.1 Matrix Algebra
3.1.1 Data as a Matrix
3.1.2 Row and Column Vectors
3.1.3 Orthogonal Vectors
3.1.4 Linear Dependency of a Set of Vectors
3.1.5 The Gram-Schmidt Orthogonalization Process
3.1.6 Projection of One Vector On Another
3.1.7 Basic Matrices
3.1.8 Basic Matrix Operations
3.1.9 Determinants
3.1.10 Rank of a Matrix
3.1.11 Inverse of a Matrix
3.1.12 Eigenvalues and Eigenvectors
3.1.13 Spectral Decomposition
3.1.14 Singular Value Decomposition (SVD)
3.1.15 Positive Definite Matrices
3.2 Methods of Least Squares
3.2.1 Ordinary Least Squares (OLS)
3.2.2 Weighted Least Squares (WLS)
3.2.3 Iteratively Reweighted Least Squares (IRLS)
3.2.4 Generalized Least Squares (GLS)
3.3 Maximum Likelihood Method
3.3.1 Probability Function
3.3.2 Likelihood Function
3.3.3 Maximum Likelihood Estimation
3.4 Generation of Random Variable
3.4.1 Generation of Univariate Normal Observations
3.4.2 Generating Multivariate Normal Observations
3.5 Resampling Methods
3.5.1 Jackknife
3.5.2 Bootstrap
3.6 Learning Summary
Exercises
Part II Foundations of Multivariate Statistics
4 Multivariate Descriptive Statistics
4.1 Multivariate Observations
4.2 Mean Vectors
4.3 Covariance Matrix
4.4 Correlation Matrix
4.5 Types of Correlation
4.5.1 Correlation Between Two Ordinal Variables
Spearman’s Rho
Gamma Coefficient
4.5.2 Correlation Between Two Nominal Variables
4.5.3 Correlation Between One Continuous and One Ordinal Variable
4.5.4 Correlation Between One Continuous and One Nominal Variable
4.5.5 Correlation Between One Ordinal and Another Nominal Variable
4.6 Correlation With Dependence Structure
4.6.1 Part Correlation
4.6.2 Partial Correlation
4.7 Learning Summary
Exercises
5 Multivariate Normal Distribution
5.1 Statistical Distance
5.2 Bivariate Normal Density Function
5.3 Multivariate Normal Density Function
5.4 Constant Density Contours
5.5 Properties of Multivariate Normal Density Function
5.6 Assessing Multivariate Normality
5.6.1 Tests of Univariate Normality
5.6.2 Tests of Multivariate Normality
5.6.3 Remedy to Violation of Multivariate Normality
5.7 Learning Summary
Exercises
6 Multivariate Inferential Statistics
6.1 Estimation of Parameters of Multivariate Normal Distribution
6.2 Sampling Distribution of X– and S
6.3 Multivariate Central Limit Theorem
6.4 Hotelling’s T2 Distribution
6.5 Inference About Single Population Mean Vector
6.5.1 Confidence Region
6.5.2 Simultaneous Confidence Intervals
Scenario 1: Sampling From When Is Known
Scenario 2: S Is Unknown and Sample Size Is Large
Scenario 3: S Is Unknown and N Is Small to Medium
6.5.3 Hypothesis Testing
Scenario 1: X ~ Np (., S) and Is Known
Scenario 2: and Is Unknown But N Is Large
Scenario 3: , and Is Unknown But N Is Small to Medium
6.6 Inference About Equality of Two-Population Mean Vectors
6.6.1 Confidence Region
Scenario 1: Sampling From Multivariate Normal Populations With Known
Scenario 2: Sampling From Multivariate Normal Populations With Unknown But Equal
Scenario 3: Sampling From Multivariate Normal Populations With Unknown and Unequal and Large Samples
6.6.2 Simultaneous Confidence Intervals
Scenario 1: Sampling From Multivariate Normal Populations With Known SA and SB
Scenario 2: Sampling From Multivariate Normal Populations With Unknown But Equal S
Scenario 3: Sampling From Multivariate Normal Populations With Unknown, Unequal and Large Samples
6.6.3 Hypothesis Testing
Scenario 1: Sampling From Multivariate Normal Populations With Known SA and SB
Scenario 2: Sampling From Multivariate Normal Population With Unknown But Equal S
Scenario 3: Sampling From Multivariate Normal Population With Unknown, Unequal S and Large Samples
6.7 Confidence Region and Hypothesis Testing for Covariance Matrix S
6.7.1 Confidence Region for S
6.7.2 Hypothesis Testing for S
6.8 Sampling From Non-Normal Population
6.9 Learning Summary
Exercises
Part III Multivariate Models
7 Multivariate Analysis of Variance
7.1 Analysis of Variance (ANOVA)
7.1.1 Conceptual Model
7.1.2 Assumptions
Bartlett Test
7.1.3 Total Sum Squares Decomposition
7.1.4 Hypothesis Testing
7.1.5 Estimation of Parameters
100(1–a)% Confidence Interval (CI) and Simultaneous Confidence Interval (SCI) for
100(1–a)% CI and Simultaneous Confidence Interval (SCI) for
7.1.6 Model Adequacy Tests
Test of Normality
Test of Independence
Test of Homogeneity of Variances
Modified Leven Test
7.1.7 Interpretation of Results
7.2 Multivariate Analysis of Variance (MANOVA)
7.2.1 Conceptual Model
7.2.2 Assumptions
Box’s M Test
7.2.3 Total Sum Squares and Cross Product (SSCP) Decomposition
7.2.4 Hypothesis Testing
Multivariate Test Statistics Used in MANOVA
7.2.5 Estimation of Parameters
100(1 – .)% Simultaneous CI
7.2.6 Model Adequacy Tests
7.2.7 Test of Assumptions
Test of Normality
Test of Independence
Test of Homogeneity of Covariance Matrices
7.3 Two-Way MANOVA
7.3.1 Two-Way ANOVA
7.3.2 Two-Way MANOVA
7.3.3 Hypothesis Testing
Factor F1 (Wilks’ Lambda, )
Factor F2 (Wilks’ Lambda, )
Interaction F12 (Wilks’ Lambda, )
7.4 Case Study
7.5 Learning Summary
Exercises
8 Multiple Linear Regression
8.1 Conceptual Model
8.2 Assumptions
8.3 Estimation of Model Parameters
8.4 Sampling Distribution of
8.5 Confidence Region (CR) and Simultaneous Confidence Intervals (SCI) for
8.6 Sampling Distribution of
8.7 Assessment of Overall Fit of the Model
8.8 Test of Individual Regression Parameters
8.9 Interpretation of Regression Parameters
8.10 Test of Assumptions
8.10.1 Test of Linearity
8.10.2 Homoscedasticity Or Constant Error Variance
8.10.3 Uncorrelated Error Terms
8.10.4 Normality of Error Terms
8.11 Remedy Against Violation of Assumptions
8.11.1 Remedies Against Linearity
8.11.2 Remedies Against Non-Normality and Heteroscedasticity
8.12 Diagnostic Issues in MLR
8.12.1 Outliers
8.12.2 Leverage Points
8.12.3 Influential Observations
8.12.4 Multicollinearity
Variance Inflation Factor (VIF)
Tolerance Statistic
Eigenvalue Structure of the Correlation Matrix, R
Multicollinearity Condition Number (MCN)
8.13 Prediction With MLR
8.14 Model Validation
8.15 Case Study
8.16 Learning Summary
Exercises
Notes
9 Multivariate Multiple Linear Regression
9.1 Conceptual Model
9.2 Assumptions
9.3 Estimation of Parameters
9.4 Sampling Distribution of
9.5 Assessment of Overall Fit of The Model
9.6 Test of Subset of Regression Parameters
9.7 Test of Individual Regression Parameters
9.8 Interpretation and Diagnostics
9.9 Case Study
9.10 Learning Summary
Exercises
10 Path Model
10.1 Conceptual Model
10.2 Assumptions
10.3 Estimation of Parameters for Recursive Model
10.3.1 Normal Equation Approach
10.3.2 Reduced Form Approach
10.4 Estimation of Parameters for Non-Recursive Model
10.4.1 Model Identification
10.4.2 Estimation of Parameters
Instrumental Variable (IV) Method
Two Stage Least Squares (2SLS)
Three Stage Least Squares (3SLS)
Maximum Likelihood Estimation
10.5 Overall Fit AND SPECIFICATION TESTS
10.5.1 Tests for Endogeneity
10.5.2 Tests for Over-Identifying Restrictions
Anderson-Rubin Test
Sargan Test
10.5.3 Heteroscedasticity-Robust Tests
10.5.4 Tests for Identifying Weak Instruments
10.5.5 Coefficients of Determination (R2)
10.6 Test of Individual Path Coefficients
10.7 Case Study
10.8 Learning Summary
Exercises
Notes
11 Principal Component Analysis
11.1 Conceptual Model
11.2 Extracting Principal Components
11.3 Sampling Distribution of and
11.4 Adequacy Tests for PCA
11.4.1 Bartlett’s Sphericity Test
11.4.2 Number of PCs to Be Extracted
Cumulative Percentage of Total Variation
Kaiser’s Rule (Eigenvalue Criteria)
The Average Root
The Broken Stick Method
Scree Plot
11.4.3 Hypothesis Testing Concerning Insignificant Eigenvalues
11.5 Principal Component Scores
11.6 Validation
11.7 Case Study
11.8 Learning Summary
Exercises
12 Exploratory Factor Analysis
12.1 Conceptual Model
12.2 Assumptions
12.3 Some Useful Results
12.4 Factor Extraction Methods
12.4.1 The Principal Component Method
12.4.2 The Principal Factor Method
12.4.3 The Maximum Likelihood Method
12.4.4 Choice of Methods of Estimation
12.4.5 Degrees of Freedom
12.5 Model Adequacy Tests
12.6 Number of Factors
12.7 Factor Rotation
12.8 Factor Scores
12.8.1 Estimation By Principal Component Scores
12.8.2 Estimation By Least Squares Approach
12.8.3 Estimation By Regression Method
12.9 Difference With Principal Component Analysis
12.10 Validation
12.11 Case Study
12.11.1 Background
12.11.2 Variables And Data
12.11.3 Data Analysis
12.11.4 Results And Discussion
12.11.5 Conclusions
12.12 Learning Summary
Exercises
Notes
1 Factor Analysis Is Not a Causal Model. It Is an Interdependence Model That Is Used to Identify and Quantify Hidden Factors, Usually Lesser in Dimensions. The Use of ‘Cause’ Here Is to Explain the Inner Meaning of a Factor.
13 Confirmatory Factor Analysis
13.1 Conceptual Model
13.2 Estimation of Parameters
13.2.1 Model Identification
13.2.2 Model Estimation
13.3 Model Adequacy Tests
13.3.1 Absolute Fit Indices
Goodness of Fit Index (GFI)
Root Mean Square Residual (RMSR)
Standardized Root Mean Square Residual (SRMSR)
Root Mean Square Error of Approximation (RMSEA)
13.3.2 Relative Fit Indices (RFI)
Tucker Lewis Index (TLI)
Normed Fit Index (NFI)
Comparative Fit Index (CFI)
General Normed Fit Index (GNFI)
Relative Non-Centrality Index (RNI)
13.3.3 Parsimony Fit Indices
Adjusted Goodness of Fit Index (AGFI)
Parsimony Normed Fit Index (PNFI)
13.4 Test of Parameters
13.5 Fit Indices for Individual Factors
13.5.1 Construct Validity
13.5.2 Unidimensionality
13.5.3 Reliability
13.6 Model Respecification
13.7 Case Study
13.7.1 Background
13.7.2 Variables and Data
13.7.3 Analysis and Results
Overall Fit of The Proposed Model
Test of Model Parameters
Test of Fit of Individual Factors
13.7.4 Model Re-Specifications
13.7.5 Discussions and Insights
13.8 Learning Summary
Exercises
14 Structural Equation Modeling
14.1 Prerequisite and Modeling Strategy
14.2 Variables, Relationships, Terminologies, and Notations
14.3 Model Equations and Dispersion Matrices
14.3.1 Structural Model Equations
14.3.2 Exogenous Factor Model Equations
14.3.3 Endogenous Factor Model Equations
14.4 Assumptions
14.5 Fundamental Relationships
14.5.1 Fundamental Relationships for the Structural Model
14.5.2 Fundamental Relationships for the Complete SEM Model
14.6 Parameter Estimation
14.6.1 Model Identification
Measurement Model Identification
Structural Model Identification
14.6.2 Model Estimation
14.6.3 Direct, Indirect, and Total Effects
14.7 Evaluating Model Fit
14.8 Test of Model Parameters
14.9 Other Important Issues in SEM
14.9.1 Sample Size
14.9.2 Input Matrix
14.9.3 Estimation Process
14.9.4 Model Respecification
14.10 Case Study
14.10.1 Background
14.10.2 Variables and Data
14.10.3 Conceptual Model
14.10.4 Measurement Model
Overall Fit of the Measurement Model
Parameter Estimation
Test of Model Parameters
14.10.5 Structural Model
Model Identification
Model Respecification
Overall Fit of the Structural Model
Test of Model Parameters
Direct, Indirect, and Total Effects
14.10.6 Discussions and Insights
14.11 Learning Summary
Exercises
Bibliography
Appendix A1: Cumulative Standard Normal Distribution
Appendix A2: Percentage Points of Student’s T-Distribution
Appendix A3: Percentage Points of the Chi-Square Distribution
Appendix A4: Percentage Points of the F-Distribution (α = 0.10)
Appendix A5: Percentage Points of the F-Distribution (α = 0.05)
Appendix A6: Percentage Points of the F-Distribution (α = 0.01)
Index