[영문] CONTENTS
1 Introduction and Overview = 1
2 Detecting Influential Observations and Outliers = 6
2.1 Theoretical Foundations = 9
Single-Row Effects = 12
Deletion = 12
Coefficients and Fitted Values. The Hat Matrix. Residuals. Covariance Matrix.
Differentiation = 24
A Geometric View = 26
Criteria for Influential Observations = 27
External Scaling. Internal Scaling. Gaps.
Partial-Regression Leverage Plots = 30
Multiple-Row Effects = 31
Deletion = 31
Studentized Residuals and Dummy Variables = 33
Differentiation = 35
Geometric Approaches = 37
Final Comments = 38
2.2 Application : an Intercountry Life-Cycle Savings Function = 39
A Diagnostic Analysis of the Model = 39
The Model and Regression Results = 40
Single-Row Diagnostics = 42
Residuals. Leverage and Hat-Matrix Diagonals. Coefficient Sensitivity. Covariance Matrix Sensitivity. Change in Fit. Internal Scaling. A Provisional Summary.
Multiple-Row Diagnostics = 51
Partial-Regression Leverage Plots : a Preliminary Analysis. Using Multiple-Row Methods. Deletion. Residuals. Differentiation. Geometry.
Final Comments = 63
Appendix 2A : Additional Theoretical Background = 64
Deletion Formulas = 64
Differentiation Formulas = 65
Theorems Related to the Hat Matrix = 66
Size of the Diagonal Elements. Distribution Theory. Dummy Variables and Singular Matrices.
Appendix 2B : Computational Elements = 69
Computational Elements for Single-Row Diagnostics = 69
Orthogonal Decompositions, the Least-Squares Solution, and Related Statistics. The Diagonal Elements of the Hat Matrix. Computing the DFBETA.
Computational Elements for Multiple-Row Diagnostics = 75
Notation and the Subset Tree. An Algorithm for the Geometric Measure, Wilks' Dummy Variables, Sequential Choleski Decomposition, and the Andrews-Pregibon Statistic. Further Elements Computed from the Triangular Factors. Inequalities Related to MDFFI
3 Detecting and Assessing Collinearity = 85
3.1 Introduction and Historical Perspective = 85
Overview = 91
Historical Perspective = 92
A Basis for a Diagnostic = 96
3.2 Technical Background = 98
The Singular-Value Decomposition = 98
Exact Linear Dependencies : Rank Deficiency = 99
The Condition Number = 100
Near Linear Dependencies : How Small is Small? = 104
The Regression-Coefficient Variance Decomposition = 105
Two Interpretive Considerations = 107
Near Collinearity Nullified by Near Orthogonality = 107
At Least Two Variates Must Be Involved = 108
An Example = 110
A Suggested Diagnostic Procedure = 112
The Diagnostic Procedure = 112
Examining the Near Dependencies = 113
What is “Large” or “High,” = 114
The Ill Effects of Collinearity = 114
Computational Problems = 114
Statistical Problems = 115
Harmful Versus Degrading Collinearity = 115
3.3 Experimental Experience = 117
The Experimental Procedure = 117
The Choice of the X's = 119
Experimental Shortcomings = 119
The Need for Column Scaling = 120
The Experimental Report = 121
The Individual Experiments = 121
The Results = 125
3.4 Summary Interpretation, and Examples of Diagnosing Actual Data for Collinearity = 152
Interpreting the Diagnostic Results : a Summary of the Experimental Evidence = 152
Experience with a Single Near Dependency = 153
Experience with Coexisting Near Dependencies = 154
Employing the Diagnostic Procedure = 156
The Steps = 157
Forming the Auxiliary Regressions = 159
Software = 160
Applications with Actual Data = 160
The Bauer Matrix = 161
The Consumption Function = 163
The Friedman Data = 167
An Equation of the IBM Econometric Model = 169
Appendix 3A : The Condition Number and Invertibility = 173
Appendix 3B : Parameterization and Scaling = 177
The Effects on the Collinearity Diagnostics Due to Linear Transformations of the Data = 177
Each Parameterization is a Different Problem = 178
A More General Analysis = 180
Column Scaling = 183
Appendix 3C : The Weakness of Correlation Measures in Providing Diagnostic Information = 185
Appendix 3D : The Harm Caused by Collinearity = 186
The Basic Harm = 187
The Effect of Collinearity = 190
4 Applications and Remedies = 192
4.1 A Remedy for Collinearity : the Consumption Function with Mixed Estimation = 193
Corrective Measures = 193
Introduction of New Data = 193
Bayesian-Type Techniques = 194
Pure Bayes. Mixed-Estimation. Ridge Regression.
Application to the Consumption-Function Data = 196
Prior Restrictions = 197
Ignored Information = 199
Summary of Prior Data = 200
Regression Results and Variance-Decomposition Proportions for Mixed-Estimation Consumption-Function Data = 200
4.2 Row-Deletion Diagnostics with Mixed-Estimation of the U.S. Consumption Function = 204
A Diagnostic Analysis of the Consumption-Function Data = 204
Single-Row Diagnostics = 205
Residuals. Leverage and Hat-Matrix Diagonals. Coefficient Sensitivity.
Summary = 207
A Reanalysis after Remedial Action for Ill Conditioning = 207
The Row Diagnostics = 208
A Suggested Research Strategy = 210
4.3 An Analysis of an Equation Describing the Household Demand for Corporate Bonds = 212
An Examination of Parameter Instability and Sensitivity = 215
Tests for Overall Structural Instability = 215
Sensitivity Diagnostics = 217
Residuals. Leverage and Coefficient Sensitivity.
The Monetary Background = 219
A Use of Ridge Regression = 219
Summary = 228
4.4 Robust Estimation of a Hedonic Housing-Price Equation = 229
The Model = 231
Robust Estimation = 232
Partial Plots = 235
Single-Row Diagnostics = 237
Multiple-Row Diagnostics = 241
Summary = 243
Appendix 4A : Harrison and Rubinfeld Housing-Price Data = 245
5 Research Issues and Directions for Extensions = 262
5.1 Issues in Research Strategy = 263
5.2 Extensions of the Diagnostics = 266
Extensions to Systems of Simultaneous Equations = 266
Influential-Data Diagnostics = 266
Collinearity Diagnostics = 268
Extensions to Nonlinear Models = 269
Influential-Data Diagnostics = 269
Collinearity Diagnostics = 272
Additional Topics = 274
Bounded-Influence Regression = 274
Multiple-Row Procedures = 274
Transformations = 275
Time Series and Lags = 276
Bibliography = 277
Author Index = 285
Subject Index = 287
1 Introduction and Overview = 1
2 Detecting Influential Observations and Outliers = 6
2.1 Theoretical Foundations = 9
Single-Row Effects = 12
Deletion = 12
Coefficients and Fitted Values. The Hat Matrix. Residuals. Covariance Matrix.
Differentiation = 24
A Geometric View = 26
Criteria for Influential Observations = 27
External Scaling. Internal Scaling. Gaps.
Partial-Regression Leverage Plots = 30
Multiple-Row Effects = 31
Deletion = 31
Studentized Residuals and Dummy Variables = 33
Differentiation = 35
Geometric Approaches = 37
Final Comments = 38
2.2 Application : an Intercountry Life-Cycle Savings Function = 39
A Diagnostic Analysis of the Model = 39
The Model and Regression Results = 40
Single-Row Diagnostics = 42
Residuals. Leverage and Hat-Matrix Diagonals. Coefficient Sensitivity. Covariance Matrix Sensitivity. Change in Fit. Internal Scaling. A Provisional Summary.
Multiple-Row Diagnostics = 51
Partial-Regression Leverage Plots : a Preliminary Analysis. Using Multiple-Row Methods. Deletion. Residuals. Differentiation. Geometry.
Final Comments = 63
Appendix 2A : Additional Theoretical Background = 64
Deletion Formulas = 64
Differentiation Formulas = 65
Theorems Related to the Hat Matrix = 66
Size of the Diagonal Elements. Distribution Theory. Dummy Variables and Singular Matrices.
Appendix 2B : Computational Elements = 69
Computational Elements for Single-Row Diagnostics = 69
Orthogonal Decompositions, the Least-Squares Solution, and Related Statistics. The Diagonal Elements of the Hat Matrix. Computing the DFBETA.
Computational Elements for Multiple-Row Diagnostics = 75
Notation and the Subset Tree. An Algorithm for the Geometric Measure, Wilks' Dummy Variables, Sequential Choleski Decomposition, and the Andrews-Pregibon Statistic. Further Elements Computed from the Triangular Factors. Inequalities Related to MDFFI
3 Detecting and Assessing Collinearity = 85
3.1 Introduction and Historical Perspective = 85
Overview = 91
Historical Perspective = 92
A Basis for a Diagnostic = 96
3.2 Technical Background = 98
The Singular-Value Decomposition = 98
Exact Linear Dependencies : Rank Deficiency = 99
The Condition Number = 100
Near Linear Dependencies : How Small is Small? = 104
The Regression-Coefficient Variance Decomposition = 105
Two Interpretive Considerations = 107
Near Collinearity Nullified by Near Orthogonality = 107
At Least Two Variates Must Be Involved = 108
An Example = 110
A Suggested Diagnostic Procedure = 112
The Diagnostic Procedure = 112
Examining the Near Dependencies = 113
What is “Large” or “High,” = 114
The Ill Effects of Collinearity = 114
Computational Problems = 114
Statistical Problems = 115
Harmful Versus Degrading Collinearity = 115
3.3 Experimental Experience = 117
The Experimental Procedure = 117
The Choice of the X's = 119
Experimental Shortcomings = 119
The Need for Column Scaling = 120
The Experimental Report = 121
The Individual Experiments = 121
The Results = 125
3.4 Summary Interpretation, and Examples of Diagnosing Actual Data for Collinearity = 152
Interpreting the Diagnostic Results : a Summary of the Experimental Evidence = 152
Experience with a Single Near Dependency = 153
Experience with Coexisting Near Dependencies = 154
Employing the Diagnostic Procedure = 156
The Steps = 157
Forming the Auxiliary Regressions = 159
Software = 160
Applications with Actual Data = 160
The Bauer Matrix = 161
The Consumption Function = 163
The Friedman Data = 167
An Equation of the IBM Econometric Model = 169
Appendix 3A : The Condition Number and Invertibility = 173
Appendix 3B : Parameterization and Scaling = 177
The Effects on the Collinearity Diagnostics Due to Linear Transformations of the Data = 177
Each Parameterization is a Different Problem = 178
A More General Analysis = 180
Column Scaling = 183
Appendix 3C : The Weakness of Correlation Measures in Providing Diagnostic Information = 185
Appendix 3D : The Harm Caused by Collinearity = 186
The Basic Harm = 187
The Effect of Collinearity = 190
4 Applications and Remedies = 192
4.1 A Remedy for Collinearity : the Consumption Function with Mixed Estimation = 193
Corrective Measures = 193
Introduction of New Data = 193
Bayesian-Type Techniques = 194
Pure Bayes. Mixed-Estimation. Ridge Regression.
Application to the Consumption-Function Data = 196
Prior Restrictions = 197
Ignored Information = 199
Summary of Prior Data = 200
Regression Results and Variance-Decomposition Proportions for Mixed-Estimation Consumption-Function Data = 200
4.2 Row-Deletion Diagnostics with Mixed-Estimation of the U.S. Consumption Function = 204
A Diagnostic Analysis of the Consumption-Function Data = 204
Single-Row Diagnostics = 205
Residuals. Leverage and Hat-Matrix Diagonals. Coefficient Sensitivity.
Summary = 207
A Reanalysis after Remedial Action for Ill Conditioning = 207
The Row Diagnostics = 208
A Suggested Research Strategy = 210
4.3 An Analysis of an Equation Describing the Household Demand for Corporate Bonds = 212
An Examination of Parameter Instability and Sensitivity = 215
Tests for Overall Structural Instability = 215
Sensitivity Diagnostics = 217
Residuals. Leverage and Coefficient Sensitivity.
The Monetary Background = 219
A Use of Ridge Regression = 219
Summary = 228
4.4 Robust Estimation of a Hedonic Housing-Price Equation = 229
The Model = 231
Robust Estimation = 232
Partial Plots = 235
Single-Row Diagnostics = 237
Multiple-Row Diagnostics = 241
Summary = 243
Appendix 4A : Harrison and Rubinfeld Housing-Price Data = 245
5 Research Issues and Directions for Extensions = 262
5.1 Issues in Research Strategy = 263
5.2 Extensions of the Diagnostics = 266
Extensions to Systems of Simultaneous Equations = 266
Influential-Data Diagnostics = 266
Collinearity Diagnostics = 268
Extensions to Nonlinear Models = 269
Influential-Data Diagnostics = 269
Collinearity Diagnostics = 272
Additional Topics = 274
Bounded-Influence Regression = 274
Multiple-Row Procedures = 274
Transformations = 275
Time Series and Lags = 276
Bibliography = 277
Author Index = 285
Subject Index = 287