Modern regression methods:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1997
|
| Schriftenreihe: | Wiley series in probability and statistics
A Wiley-Interscience publication |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Systemvoraussetzungen: IBM PC |
| Beschreibung: | XIX, 515 S. graph. Darst. 1 Diskette (9 cm) |
| ISBN: | 0471529125 |
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| 245 | 1 | 0 | |a Modern regression methods |c Thomas P. Ryan |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1997 | |
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Datensatz im Suchindex
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| adam_text | CONTENTS
1 Introduction 1
1.1 Simple Linear Regression Model, 3
1.2 Uses of Regression Models, 4
1.3 Graph the Data!, 4
1.4 Estimation of /3o and /?i, 6
1.5 Inferences from Regression Equations, 9
1.5.1 Predicting Y, 10
1.5.2 Worth of the Regression Equation, 11
1.5.3 Regression Assumptions, 13
1.5.4 Inferences on/31, 15
1.5.5 Inferences on £0, 19
1.5.6 Inferences for Y, 21
1.5.6.1 Prediction Interval for Y, 21
1.5.6.2 Confidence Interval for fiy x, 23
1.5.7 ANOVA Tables, 23
1.5.8 Lack of Fit, 25
1.6 Regression Through the Origin, 27
1.7 Correlation, 29
1.8 Miscellaneous Uses of Regression, 29
1.8.1 Regression for Control, 30
1.8.2 Inverse Regression, 31
1.8.3 Regression Control Chart, 34
1.9 Fixed Versus Random Regressors, 34
1.10 Software, 35
Summary, 35
Appendix, 36
ix
X CONTENTS
References, 40
Exercises, 42
2 Diagnostics and Remedial Measures 44
2.1 Assumptions, 45
2.1.1 Independence, 45
2.1.1.1 Correlated Errors, 48
2.1.1.1.1 An Example, 49
2.1.2 Normality, 52
2.1.2.1 Supernormality Property of Residuals, 53
2.1.2.2 Standardized Deletion Residuals, 53
2.1.2.3 Methods of Constructing Simulation
Envelopes, 54
2.1.3 Constant Variance, 60
2.1.3.1 Weighted Least Squares, 60
2.1.3.1.1 Unknown Weights, 63
2.1.3.1.2 Modeling the Variance, 66
2.2 Residual Plots, 70
2.3 Transformations, 71
2.3.1 Transforming the Model, 72
2.3.2 Transforming the Regressors to Improve the
Fit, 72
2.3.2.1 Box Tidwell Transformation, 74
2.3.3 Transform Y to Obtain a Better Fit?, 76
2.3.4 Transforming to Correct Heteroscedasticity and
Nonnormality, 77
2.3.5 Which R2t, 79
2.4 Influential Observations, 79
2.4.1 An Example, 80
2.4.2 Influence Statistics, 84
2.4.3 Different Schools of Thought Regarding
Influence, 86
2.4.4 Modification of Standard Influence Measures, 86
2.4.5 Application of Influence Measures to Table 2.7
Data, 87
2.4.6 Multiple Unusual Observations, 88
2.4.7 Predicting Lifespan: An Influential Data
Problem, 88
2.5 Outliers, 89
CONTENTS xi
2.6 Measurement Error, 91
2.6.1 Measurement Error in Y, 91
2.6.2 Measurement Error in X, 91
2.7 Software, 92
Summary, 93
Appendix, 93
References, 95
Exercises, 98
3 Regression with Matrix Algebra 101
3.1 Introduction to Matrix Algebra, 101
3.1.1 Eigenvalues and Eigenvectors, 103
3.2 Matrix Algebra Applied to Regression, 106
3.2.1 Predicted Y and R2, 108
3.2.2 Estimation of a2, 109
3.2.3 Variance of Y and Y, 109
3.2.4 Centered Data, 111
3.2.5 Correlation Form, 113
3.2.6 Influence Statistics in Matrix Form, 114
Summary, 114
Appendix, 115
References, 116
Exercises, 116
4 Introduction to Multiple Linear Regression 118
4.1 An Example of Multiple Linear Regression, 119
4.1.1 Orthogonal Regressors, 122
4.1.2 Correlated Regressors, 123
4.1.2.1 Partial F Test and r Tests, 124
4.1.3 Confidence Intervals and Prediction Intervals, 126
4.2 Centering and Scaling, 128
4.2.1 Centering, 128
4.2.2 Scaling, 129
4.3 Multicollinearity and the Wrong Signs Problem, 131
4.3.1 Inflated Variances, 132
4.3.2 Detecting Multicollinearity, 132
4.3.3 Variance Proportions, 136
4.3.4 What to Do about Multicollinearity?, 137
Jdi CONTENTS
4.4 Software, 138
Summary, 139
References, 139
Exercises, 140
5 Plots in Multiple Regression 144
5.1 Beyond Standardized Residual Plots, 144
5.1.1 Partial Residual Plots, 145
5.1.2 CCPRPlot, 147
5.1.3 Augmented Partial Residual Plot, 147
5.1.4 CERES Plots, 148
5.2 Some Examples, 149
5.3 Which Plot?, 162
5.3.1 Relationships Between Plots, 162
5.3.2 True Model Contains Nonlinear Terms, 165
5.4 Recommendations, 166
5.5 Partial Regression Plots, 168
5.5.1 Examples, 170
5.5.2 Detrended Added Variable Plot, 171
5.5.3 Partial Regression Plots Used to Detect Influential
Observations, 172
5.6 Other Plots for Detecting Influential Observations, 176
5.7 Lurking Variables, 176
5.8 Explanation of Two Data Sets Relative to R2, 177
5.9 Software, 178
Summary, 178
References, 179
Exercises, 180
6 Transformations in Multiple Regression 183
6.1 Transforming Regressors, 183
6.2 Transforming Y, 187
6.2.1 Transformation Needed But Not Suggested, 187
6.2.2 Transformation Needed and Suggested, 189
6.2.3 Transformation Apparently Successful, 190
6.3 Further Comments on the Normality Issue, 191
6.4 Box Cox Transformation, 192
6.5 Box Cox Revisited, 195
CONTENTS xiii
6.6 Combined Box Cox and Box Tidwell Approach, 196
6.6.1 Table 6.2 Data, 196
6.6.2 Table 6.3 Data, 198
6.6.3 Table 6.4 Data, 198
6.6.4 Minitab Tree Data, 203
6.6.4.1 Other Analyses of the Tree Data, 204
6.6.5 Stack Loss Data, 207
6.7 Other Transformation Methods, 211
6.7.1 Transform Both Sides, 212
6.8 Transformation Diagnostics, 213
6.8.1 Diagnostics after a Transformation, 214
6.9 Software, 214
Summary, 215
References, 215
Exercises, 217
7 Selection of Regressors 220
7.1 Forward Selection, 221
7.2 Backward Elimination, 222
7.3 Stepwise Regression, 222
7.3.1 Significance Levels, 222
7.4 All Possible Regressions, 223
7.4.1 Criteria, 224
7.4.1.1 Mallow s Cp, 224
7.4.1.1.1 Cp and Influential Data, 227
7.4.1.2 Minimum a2, 228
7.4.1.3 r Statistics, 228
7.4.1.4 Other Criteria, 228
7.5 Examples, 228
7.6 Variable Selection for Nonlinear Terms, 229
7.6.1 Negative Cp Values, 232
7.7 Must We Select a Subset?, 233
7.8 Model Validation, 233
7.9 Software, 234
Summary, 235
Appendix, 236
References, 237
Exercises, 238
xiv CONTENTS
8 Polynomial and Trigonometric Terms 240
8.1 Polynomial Terms, 240
8.1.1 Orthogonal Polynomial Regression, 242
8.1.1.1 When to Stop?, 243
8.1.2 An Example, 243
8.2 Polynomial Trigonometric Regression, 245
8.2.1 Orthogonality of Trigonometric Terms, 246
8.2.2 Practical Considerations, 247
8.2.3 Examples, 247
8.2.4 Multiple Independent Variables, 250
8.3 Software, 251
Summary, 251
References, 252
Exercises, 253
9 Logistic Regression 255
9.1 Introduction, 255
9.2 One Regressor, 255
9.2.1 Estimating /30 and ft, 258
9.2.1.1 Method of Maximum Likelihood, 258
9.2.1.2 Exact Logistic Regression, 262
9.3 Simulated Example, 262
9.3.1 Complete and Quasicomplete Separation, 263
9.3.2 Overlap: Modifying Table 9.1, 265
9.4 Measuring the Worth of the Model, 266
9.4.1 R2 in Logistic Regression, 266
9.4.2 Deviance, 267
9.4.3 Other Measures of Model Fit, 268
9.5 Determining the Worth of the Individual Regressors, 269
9.5.1 Wald Test, 269
9.5.2 Likelihood Ratio Test, 270
9.5.3 Scores Test, 270
9.5.4 Exact Conditional Scores Test, 270
9.5.5 Exact p Value, 271
9.6 Confidence Intervals, 272
9.6.1 Confidence Interval for j8,, 272
9.6.2 Confidence Interval for Change in Odds Ratio, 273
9.6.3 Confidence Interval for w, 273
CONTENTS XV
9.6.4 Exact Confidence Intervals, 274
9.6.4.1 Exact Confidence Interval for j8i, 274
9.6.4.2 Exact Confidence Interval for Change in
Odds Ratio, 275
9.6.4.3 Exact Confidence Interval for x, 275
9.7 An Example with Real Data, 275
9.7.1 Hosmer Lemeshow Goodness of Fit Tests, 278
9.7.2 Which Residuals?, 281
9.7.3 Application to Table 9.3 Data, 284
9.7.3.1 Pearson Residuals, 284
9.7.3.2 Deviance Residuals, 286
9.7.4 Other Diagnostics, 287
9.7.5 Partial Residual Plot, 288
9.7.6 Added Variable Plot, 290
9.7.7 Confidence Intervals for Table 9.3 Data, 290
9.8 An Example of Multiple Logistic Regression, 291
9.8.1 Correct Classification Rate for Full Data
Set, 294
9.8.2 Influential Observations, 295
9.8.3 Which Variables?, 296
9.8.3.1 Algorithmic Approaches to Variable
Selection, 298
9.8.3.2 What about Nonlinear Terms?, 299
9.9 Multicollinearity in Multiple Logistic Regression, 300
9.10 Osteogenic Sarcoma Data Set, 303
9.11 Sample Size Determination, 306
9.12 Alternatives to Logistic Regression, 306
9.13 Software for Logistic Regression, 306
Summary, 307
Appendix, 308
References, 308
Exercises, 311
10 Nonparametric Regression 314
10.1 Relaxing Regression Assumptions, 314
10.1.1 Bootstrapping, 315
10.2 Monotone Regression, 316
10.3 Smoothers, 319
10.3.1 Running Line, 322
xvi CONTENTS
10.3.1.1 Modified Running Line, 325
10.3.1.2 Inferences for Running Line, 328
10.3.2 Kernel Regression, 329
10.3.2.1 Inferences in Kernel Regression, 330
10.3.3 Local Regression, 331
10.3.3.1 Inferences and Diagnostics, 333
10.3.4 Splines, 334
10.3.4.1 Piecewise Linear Regression (Linear
Splines), 334
10.3.4.1.2 Model Representation, 335
10.3.4.2 Splines with Polynomial Terms, 335
10.3.4.3 Smoothing Splines, 337
10.3.4.4 Splines Compared to Local Regression, 338
10.3.5 Other Smoothers, 339
10.3.6 Which Smoother?, 339
10.3.7 Smoothers for Multiple Regression, 340
10.4 Software, 340
Summary, 341
Appendix, 342
References, 343
Exercises, 345
11 Robust Regression 348
11.1 Need for Robust Regression, 348
11.2 Types of Outliers, 350
11.3 Historical Development of Robust Regression, 353
11.3.1 Breakdown Point, 353
11.3.2 Efficiency, 354
11.3.3 Classes of Estimators, 354
11.3.3.1 M Estimators, 354
11.3.3.2 Bounded Influence Estimators, 355
11.3.3.3 High Breakdown Point
Estimators, 355
11.3.3.4 Two Stage Procedures, 356
11.4 Goals of Robust Regression, 356
11.5 Proposed High Breakdown Point Estimators, 356
11.5.1 Least Median of Squares, 356
11.5.1.1 Computational Aspects, 357
11.5.1.2 Illustrative Examples, 358
CONTENTS xvii
11.5.1.3 Exact LMS, 361
11.5.2 Least Trimmed Squares, 362
11.5.3 S Estimators, 363
11.5.3.1 Are 5 Estimators Any
Better?, 364
11.5.3.2 Computing S Estimators, 364
11.6 Approximating HBP Estimator Solutions, 365
11.6.1 Application to Hawkins Bradu Kass Data
Set, 367
11.6.2 Another Application: One Regressor, 370
11.6.3 Application to Multiple Regression, 375
11.7 LTS Running Line Smoother, 378
11.8 Bounded Influence Estimators, 378
11.8.1 Shortcomings of Bounded Influence
Estimators, 381
11.8.2 Applications, 383
11.9 Multistage Procedures, 384
11.10 Software, 387
Summary, 388
Appendix, 388
References, 389
Exercises, 391
12 Ridge Regression 396
12.1 Introduction, 396
12.2 How Do We Determine kl, 400
12.3 An Example, 401
12.4 Ridge Regression for Prediction?, 406
12.5 Generalized Ridge Regression, 407
12.6 Inferences in Ridge Regression, 408
12.7 Some Practical Considerations, 408
12.8 Robust Ridge Regression?, 409
12.9 Other Biased Estimators, 409
12.10 Software, 410
Summary, 410
Appendix, 411
References, 413
Exercises, 414
xviii CONTENTS
13 Nonlinear Regression 416
13.1 Introduction, 416
13.2 Linear Versus Nonlinear Regression, 416
13.3 Simple Nonlinear Example, 417
13.3.1 Iterative Estimation, 419
13.4 Relative Offset Convergence Criterion, 420
13.5 Adequacy of the Estimation Approach, 422
13.6 Computational Considerations, 423
13.7 Determining Model Adequacy, 424
13.7.1 Lack of Fit Test, 424
13.7.2 Residual Plots, 425
13.7.3 Multicollinearity Diagnostics, 426
13.7.4 Influence and Unusual Data
Diagnostics, 427
13.7.4.1 Leverage, 427
13.7.4.2 Influence, 427
13.8 Inferences, 429
13.8.1 Confidence Intervals, 430
13.8.2 Prediction Interval, 430
13.8.3 Hypothesis Tests, 430
13.9 An Application, 431
13.10 Robust Nonlinear Regression, 436
13.11 Software, 436
13.11.1 SAS Software, 436
13.11.1.1 Cautions, 437
13.11.2 SPSS, 437
13.11.3 BMDP, 437
13.11.4 Minitab, 438
Summary, 438
Appendix, 438
References, 441
Exercises, 443
14 Experimental Designs for Regression 446
14.1 Objectives for Experimental Designs, 446
14.2 Equal Leverage Points, 446
14.2.1 Simple Linear Regression, 447
14.2.2 Multiple Linear Regression, 447
CONTENTS xix
14.2.2.1 Construction of Equileverage
Designs—Two Regressors, 448
14.2.2.1.1 Inverse Projection
Approach, 452
14.3 Other Desirable Properties of Experimental Designs, 458
14.3.1 D Optimality, 459
14.3.2 G Optimality, 460
14.3.3 Other Optimality Criteria, 460
14.4 Model Misspecification, 461
14.5 Range of Regressors, 462
14.6 Algorithms and Software for Design Construction, 462
14.7 Designs for Polynomial Regression, 462
14.8 Designs for Logistic Regression, 463
14.9 Designs for Nonlinear Regression, 463
Summary, 463
References, 464
Exercises, 466
15 Applications of Regression 468
15.1 Water Quality Data, 468
15.2 Predicting Lifespan, 477
15.3 Scottish Hill Races Data, 480
15.4 Leukemia Data, 482
15.4.1 Y Binary, 482
15.4.2 Y Continuous, 487
15.5 Dosage Response Data, 488
15.6 A Strategy for Analyzing Regression Data, 491
Summary, 493
References, 494
Exercises, 495
Appendix A List of Minitab Macros 498
Appendix B Statistical Tables 501
Appendix C Answers to Selected Exercises 506
Index 511
|
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| physical | XIX, 515 S. graph. Darst. 1 Diskette (9 cm) |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics A Wiley-Interscience publication |
| spelling | Ryan, Thomas P. Verfasser aut Modern regression methods Thomas P. Ryan New York [u.a.] Wiley 1997 XIX, 515 S. graph. Darst. 1 Diskette (9 cm) txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics A Wiley-Interscience publication Systemvoraussetzungen: IBM PC Analyse de régression Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Regressionsanalyse (DE-588)4129903-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007715466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ryan, Thomas P. Modern regression methods Analyse de régression Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4123623-3 |
| title | Modern regression methods |
| title_auth | Modern regression methods |
| title_exact_search | Modern regression methods |
| title_full | Modern regression methods Thomas P. Ryan |
| title_fullStr | Modern regression methods Thomas P. Ryan |
| title_full_unstemmed | Modern regression methods Thomas P. Ryan |
| title_short | Modern regression methods |
| title_sort | modern regression methods |
| topic | Analyse de régression Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd |
| topic_facet | Analyse de régression Regressieanalyse Regression analysis Regressionsanalyse Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007715466&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ryanthomasp modernregressionmethods |