Regression Diagnostics: Identifying Influential Data and Sources of Collinearity (Wiley Series in Probability and Statistics)

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity......Page 2
Preface......Page 10
Contents......Page 14
1 Introduction and Overview......Page 22
2 Detecting influential Observations and Outliers......Page 27
2.1 Theoretical Foundations......Page 30
Coefficients and Fitted Values......Page 32
The Hat Matrix......Page 37
Residuals......Page 39
Covariance Matrix......Page 43
Differentiation......Page 45
A Geometric View......Page 47
Criteria for Influential Observations......Page 48
External Scaling......Page 49
Gaps......Page 50
Partial-Regression Leverage Plots......Page 51
Deletion......Page 52
Studentized Residuals and Dummy Variables......Page 54
Differentiation......Page 56
Geometric Approaches......Page 58
Final Comments......Page 59
A Diagnostic Analysis of the Model......Page 60
The Model and Regression Results......Page 61
Residuals......Page 63
Leverage and Hat-Matrix Diagonals......Page 64
Coefficient Sensitivity......Page 66
Covariance Matrix Sensitivity......Page 67
A Provisional Summary......Page 70
Partial-Regression Leverage Plots: a Preliminary Analysis......Page 72
Using Multiple-Row Methods......Page 75
Deletion......Page 76
Residuals......Page 80
Geometry......Page 82
Final Comments......Page 84
Deletion Formulas......Page 85
Differentiation Formulas......Page 86
Size of the Diagonal Elements......Page 87
Distribution Theory......Page 88
Dummy Variables and Singular Matrices......Page 89
Orthogonal Decompositions, the Least-Squares Solution, and Related Statistics......Page 90
The Diagonal Elements of the Hat Matrix......Page 93
Computing the DFBETA......Page 94
Computational Elements for Multiple-Row Diagnostics......Page 96
Notation and the Subset Tree......Page 97
An Algorithm for the Geometric Measure, Wilks’......Page 98
A Dummy Variables, Sequential Choleski Decomposition, and the Andrews-Pregibon......Page 101
Further Elements Computed from the Triangular Factors......Page 102
Inequalities Related to MDFFIT......Page 103
3.1 Introduction and Historical Perspective......Page 106
Overview......Page 112
Historical Perspective......Page 113
A Basis for a Diagnostic......Page 117
The Singular-Value Decomposition......Page 119
Exact Linear Dependencies: Rank Deficiency......Page 120
The Condition Number......Page 121
Near Linear Dependencies: How Small is Small?......Page 125
The Regression-Coefficient Variance Decomposition......Page 126
Near Collinearity Nullified by Near Orthogonality......Page 128
At Least Two Variates Must Be Involved......Page 129
An Example......Page 131
The Diagnostic Procedure......Page 133
Examining the Near Dependencies......Page 134
Computational Problems......Page 135
Harmful Versus Degrading Collinearity......Page 136
The Experimental Procedure......Page 138
Experimental Shortcomings......Page 140
The Need for Column Scaling......Page 141
The Individual Experiments......Page 142
The Results......Page 146
Interpreting the Diagnostic Results: a Summary of the Experimental Evidence......Page 173
Experience with a Single Near Dependency......Page 174
Experience with Coexisting Near Dependencies......Page 175
Employing the Diagnostic Procedure......Page 177
The Steps......Page 178
Forming the Auxiliary Regressions......Page 180
Applications with Actual Data......Page 181
The Bauer Matrix......Page 182
The Consumption Function......Page 184
The Friedman Data......Page 188
An Equation of the IBM Econometric Model......Page 190
Appendix 3A: The Condition Number and Invertibility......Page 194
The Effects on the Collinearity Diagnostics Due to Linear Transformations of the Data......Page 198
Each Parameterization is a Different Problem......Page 199
A More General Analysis......Page 201
Column Scaling......Page 204
Appendix 3C: The Weakness of Correlation Measures in Providing Diagnostic Information......Page 206
Appendix 3D: The Harm Caused by Collinearity......Page 207
The Basic Harm......Page 208
The Effect of Collinearity......Page 211
4 Applications and Remedies......Page 213
Introduction of New Data......Page 214
Pure Bayes......Page 215
Mixed-Estimation......Page 216
Application to the Consumption-Function Data......Page 217
Prior Restrictions......Page 218
Ignored Information......Page 220
Regression Results and Variance-Decomposition Proportions for Mixed-Estimation Consumption-Function Data......Page 221
A Diagnostic Analysis of the Consumption-Function Data......Page 225
Coefficient Sensitivity......Page 226
A Reanalysis after Remedial Action for Ill Conditioning......Page 228
The Row Diagnostics......Page 229
A Suggested Research Strategy......Page 231
4.3 An Analysis of an Equation Describing the Household Demand for Corporate Bonds......Page 233
Tests for Overall Structural Instability......Page 236
Residuals......Page 238
Leverage and Coefficient Sensitivity......Page 239
A Use of Ridge Regression......Page 240
Summary......Page 249
4.4 Robust Estimation of a Hedonic Housing-Price Equation......Page 250
The Model......Page 252
Robust Estimation......Page 253
Partial Plots......Page 256
Single-Row Diagnostics......Page 258
Multiple-Row Diagnostics......Page 262
Summary......Page 264
Appendix 4A: Harrison and Rubinfeld Housing-Price Data......Page 266
5 Research Issues and Directions for Extensions......Page 283
5.1 Issues in Research Strategy......Page 284
Influential-Data Diagnostics......Page 287
Collinearity Diagnostics......Page 289
Influential-Data Diagnostics......Page 290
Collinearity Diagnostics......Page 293
Multiple-Row Procedures......Page 295
Transformations......Page 296
Time Series and Lags......Page 297
Bibliography......Page 298
Author Index......Page 306
Subject Index......Page 308