Handbook of regression methods:
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| Format: | Book |
| Language: | English |
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Boca Raton ; London ; New York
CRC Press, Taylor & Francis Group
[2017]
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| Series: | A Chapman & Hall book
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | xvi, 637 Seiten Illustrationen, Diagramme |
| ISBN: | 9781498775298 |
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| 245 | 1 | 0 | |a Handbook of regression methods |c Derek S. Young, University of Kentucky, Lexington |
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press, Taylor & Francis Group |c [2017] | |
| 264 | 4 | |c © 2017 | |
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| _version_ | 1804177884359688192 |
|---|---|
| adam_text | Contents
List of Examples xiii
Preface xv
I Simple Linear Regression 1
1 Introduction 3
2 Basics of Regression Models 7
2.1 Regression Notation ...................................... 8
2.2 Population Model for Simple Linear Regression............. 8
2.3 Ordinary Least Squares ................................. 10
2.4 Measuring Overall Variation from the Sample Line......... 12
2.4.1 R2 ............................................... 12
2.5 Regression Through the Origin............................ 13
2.6 Distinguishing Regression from Correlation .............. 14
2.7 Regression Effect........................................ 16
2.7.1 Regression Fallacy................................ 17
2.8 Examples ................................................ 18
3 Statistical Inference 25
3.1 Hypothesis Testing and Confidence Intervals ............. 25
3.2 Power ................................................... 30
3.3 Inference on the Correlation Model....................... 33
3.4 Intervals for a Mean Response .......................... 35
3.5 Intervals for a New Observation ......................... 36
3.6 Examples ................................................ 41
4 Regression Assumptions and Residual Diagnostics 49
4.1 Consequences of Invalid Assumptions ..................... 50
4.2 Diagnosing Validity of Assumptions ...................... 51
4.3 Plots of Residuals Versus Fitted Values ................. 53
4.3.1 Ideal Appearance of Plots......................... 54
4.3.2 Difficulties Possibly Seen in the Plots........... 56
4.4 Data Transformations .................................... 57
4.5 Tests for Normality ................................... 59
4.5.1 Skewness and Kurtosis............................. 61
vii
viii Contents
4.6 Tests for Constant Error Variance ............. 63
4.7 Examples .................................................... 66
5 ANOVA for Simple Linear Regression 73
5.1 Constructing the ANOVA Table ............. 73
5.2 Formal Lack of Fit........................................... 77
5.3 Examples .................................................... 78
II Multiple Linear Regression 83
6 Multiple Linear Regression Models and Inference 85
6.1 About the Model.............................................. 85
6.2 Matrix Notation in Regression ............................... 87
6.3 Variance-Covariance Matrix and Correlation Matrix of 92
6.4 Testing the Contribution of Individual Predictor Variables . 94
6.5 Statistical Intervals........................................ 95
6.6 Polynomial Regression........................................ 96
6.7 Examples .................................................... 99
7 Multicollinearity 109
7.1 Sources and Effects of Multicollinearity ................... 109
7.2 Detecting and Remedying Multicollinearity .................. 110
7.3 Structural Multicollinearity................................ 114
7.4 Examples ................................................... 115
8 ANOVA for Multiple Linear Regression 121
8.1 The ANOVA Table............................................. 121
8.2 The General Linear JP-Test ................................. 122
8.3 Lack-of-Fit Testing in the Multiple Regression Setting . . . 123
8.4 Extra Sums of Squares....................................... 124
8.5 Partial Measures and Plots ................................. 125
8.6 Examples ................................................... 129
9 Indicator Variables 137
9.1 Leave-One-Out Method ....................................... 137
9.2 Coefficient Interpretations................................. 138
9.3 Interactions................................................ 140
9.4 Coded Variables ............................................ 141
9.5 Conjoint Analysis .......................................... 143
9.6 Examples ................................................... 144
Contents
IX
III Advanced Regression Diagnostic Methods 151
10 Influential Values, Outliers, and More Diagnostic Tests 153
10.1 More Residuals and Measures of Influence................. 154
10.2 Masking, Swamping, and Search Methods.................... 163
10.3 More Diagnostic Tests.................................... 164
10.4 Comments on Outliers and Influential Values ............. 167
10.5 Examples ................................................ 168
11 Measurement Errors and Instrumental Variables
Regression 179
11.1 Estimation in the Presence of Measurement Errors......... 180
11.2 Orthogonal and Deming Regression ........................ 182
11.3 Instrumental Variables Regression ....................... 184
11.4 Structural Equation Modeling ............................ 186
11.5 Dilution................................................. 188
11.6 Examples ................................................ 188
12 Weighted Least Squares and Robust Regression
Procedures 195
12.1 Weighted Least Squares................................. 195
12.2 Robust Regression Methods................................ 197
12.3 Theil-Sen and Passing-Bablok Regression.................. 201
12.4 Resistant Regression Methods............................. 202
12.5 Resampling Techniques for ¡3 203
12.6 Examples ................................................ 210
13 Correlated Errors and Autoregressive Structures 219
13.1 Overview of Time Series and Autoregressive Structures . . 219
13.2 Properties of the Error Terms............................ 221
13.3 Testing and Remedial Measures for Autocorrelation .... 224
13.4 Advanced Methods......................................... 230
13.4.1 ARIMA Models..................................... 230
13.4.2 Exponential Smoothing............................ 233
13.4.3 Spectral Analysis................................ 234
13.5 Examples ................................................ 236
14 Crossvalidation and Model Selection Methods 249
14.1 Crossvalidation.......................................... 249
14.2 PRESS ................................................... 251
14.3 Best Subset Procedures .................................. 252
14.4 Statistics from Information Criteria . .................. 254
14.5 Stepwise Procedures for Identifying Models .............. 255
14.6 Example.................................................. 256
X
Contents
IV Advanced Regression Models 261
15 Mixed Models and Some Regression Models for Designed
Experiments 263
15.1 Mixed Effects Models ................................... 263
15.2 ANCOVA.................................................. 265
15.3 Response Surface Regression ............................ 268
15.4 Mixture Experiments .................................... 273
15.5 Examples ............................................... 276
16 Biased Regression, Regression Shrinkage, and Dimension
Reduction 287
16.1 Regression Shrinkage and Penalized Regression........... 287
16.2 Principal Components Regression ........................ 292
16.3 Partial Least Squares .................................. 294
16.4 Other Dimension Reduction Methods and Sufficiency . . . 296
16.5 Examples ............................................... 301
17 Piecewise, Nonparametric, and Local Regression Methods 307
17.1 Piecewise Linear Regression............................. 307
17.2 Local Regression Methods................................ 310
17.3 Splines ................................................ 318
17.4 Other Nonparametric Regression Procedures .............. 324
17.5 Examples ............................................... 327
18 Regression Models with Censored Data 335
18.1 Overview of Survival and Reliability Analysis........... 335
18.2 Censored Regression Model............................... 337
18.3 Survival (Reliability) Regression ...................... 339
18.4 Cox Proportional Hazards Regression .................... 343
18.5 Diagnostic Procedures................................... 344
18.6 Truncated Regression Models............................. 347
18.7 Examples ............................................... 350
19 Nonlinear Regression 361
19.1 Nonlinear Regression Models ............................ 361
19.2 Nonlinear Least Squares................................. 364
19.2.1 A Few Algorithms................................ 365
19.3 Approximate Inference Procedures........................ 367
19.4 Examples ............................................... 370
20 Regression Models with Discrete Responses 375
20.1 Logistic Regression..................................... 375
20.1.1 Binary Logistic Regression...................... 376
20.1.2 Nominal Logistic Regression..................... 383
20.1.3 Ordinal Logistic Regression .................... 384
Contents xi
20.2 Poisson Regression........................................ 385
20.3 Negative Binomial Regression.............................. 390
20.4 Specialized Models Involving Zero Counts.................. 396
20.5 Examples ................................................. 398
21 Generalized Linear Models 413
21.1 The Generalized Linear Model and Link Functions........... 413
21.2 Gamma Regression ......................................... 418
21.3 Inverse Gaussian (Normal) Regression ..................... 419
21.4 Beta Regression .......................................... 420
21.5 Generalized Estimating Equations ......................... 422
21.6 Examples ................................................. 426
22 Multivariate Multiple Regression 439
22.1 The Model ................................................ 439
22.2 Estimation and Statistical Regions........................ 441
22.3 Reduced Rank Regression................................... 446
22.4 Seemingly Unrelated Regressions........................... 447
22.5 Examples ................................................. 449
23 Semiparametric Regression 455
23.1 Single-Index Models ...................................... 456
23.2 (Generalized) Additive Models ............................ 457
23.3 (Generalized) Partial Linear Models ...................... 458
23.4 (Generalized) Partial Linear Partial Additive Models .... 460
23.5 Varying-Coefficient Models ............................... 460
23.6 Projection Pursuit Regression............................. 461
23.7 Examples ................................................. 462
24 Data Mining 477
24.1 Classification and Support Vector Regression ............. 478
24.2 Prediction Trees and Related Methods...................... 483
24.3 Some Ensemble Learning Methods for Regression............. 488
24.4 Neural Networks .......................................... 492
24.5 Examples ................................................. 493
25 Miscellaneous Topics 503
25.1 Multilevel Regression Models ............................. 503
25.2 Functional Linear Regression Analysis..................... 510
25.3 Regression Depth.......................................... 515
25.4 Mediation and Moderation Regression....................... 517
25.5 Meta-Regression Models.................................... 522
25.6 Regression Methods for Analyzing Survey Data.............. 526
25.7 Regression with Missing Data and Regression Imputation . 533
25.8 Bayesian Regression ...................................... 538
25.9 Quantile Regression ...................................... 542
xii Contents
25.10 Monotone Regression ................................... 544
25.11 Generalized Extreme Value Regression Models ........... 546
25.12 Spatial Regression .................................... 548
25.13 Circular Regression ................................... 554
25.14 Rank Regression ....................................... 557
25.15 Mixtures of Regressions ............................... 560
25.16 Copula Regression ..................................... 563
25.17 Tensor Regression ..................................... 565
V Appendices 571
Appendix A Steps for Building a Regression Model 573
Appendix B Refresher on Matrices and Vector Spaces 575
Appendix C Some Notes on Probability and Statistics 579
Bibliography 583
Index
615
Contents
List of Examples xiii
Preface xv
I Simple Linear Regression 1
1 Introduction 3
2 Basics of Regression Models 7
2.1 Regression Notation ...................................... 8
2.2 Population Model for Simple Linear Regression............. 8
2.3 Ordinary Least Squares ................................. 10
2.4 Measuring Overall Variation from the Sample Line......... 12
2.4.1 R2 ............................................... 12
2.5 Regression Through the Origin............................ 13
2.6 Distinguishing Regression from Correlation .............. 14
2.7 Regression Effect........................................ 16
2.7.1 Regression Fallacy................................ 17
2.8 Examples ................................................ 18
3 Statistical Inference 25
3.1 Hypothesis Testing and Confidence Intervals ............. 25
3.2 Power ................................................... 30
3.3 Inference on the Correlation Model....................... 33
3.4 Intervals for a Mean Response .......................... 35
3.5 Intervals for a New Observation ......................... 36
3.6 Examples .............................................. 41 4
4 Regression Assumptions and Residual Diagnostics 49
4.1 Consequences of Invalid Assumptions ..................... 50
4.2 Diagnosing Validity of Assumptions ...................... 51
4.3 Plots of Residuals Versus Fitted Values ................. 53
4.3.1 Ideal Appearance of Plots......................... 54
4.3.2 Difficulties Possibly Seen in the Plots........... 56
4.4 Data Transformations .................................... 57
4.5 Tests for Normality ................................... 59
4.5.1 Skewness and Kurtosis............................. 61
vii
viii Contents
4.6 Tests for Constant Error Variance ............. 63
4.7 Examples .................................................... 66
5 ANOVA for Simple Linear Regression 73
5.1 Constructing the ANOVA Table ............. 73
5.2 Formal Lack of Fit........................................... 77
5.3 Examples .................................................... 78
II Multiple Linear Regression 83
6 Multiple Linear Regression Models and Inference 85
6.1 About the Model.............................................. 85
6.2 Matrix Notation in Regression ............................... 87
6.3 Variance-Covariance Matrix and Correlation Matrix of 92
6.4 Testing the Contribution of Individual Predictor Variables . 94
6.5 Statistical Intervals........................................ 95
6.6 Polynomial Regression........................................ 96
6.7 Examples .................................................... 99
7 Multicollinearity 109
7.1 Sources and Effects of Multicollinearity ................... 109
7.2 Detecting and Remedying Multicollinearity .................. 110
7.3 Structural Multicollinearity................................ 114
7.4 Examples ................................................... 115
8 ANOVA for Multiple Linear Regression 121
8.1 The ANOVA Table............................................. 121
8.2 The General Linear JP-Test ................................. 122
8.3 Lack-of-Fit Testing in the Multiple Regression Setting . . . 123
8.4 Extra Sums of Squares....................................... 124
8.5 Partial Measures and Plots ................................. 125
8.6 Examples ................................................... 129
9 Indicator Variables 137
9.1 Leave-One-Out Method ....................................... 137
9.2 Coefficient Interpretations................................. 138
9.3 Interactions................................................ 140
9.4 Coded Variables ............................................ 141
9.5 Conjoint Analysis .......................................... 143
9.6 Examples ................................................... 144
Contents
IX
III Advanced Regression Diagnostic Methods 151
10 Influential Values, Outliers, and More Diagnostic Tests 153
10.1 More Residuals and Measures of Influence................. 154
10.2 Masking, Swamping, and Search Methods.................... 163
10.3 More Diagnostic Tests.................................... 164
10.4 Comments on Outliers and Influential Values ............. 167
10.5 Examples ................................................ 168
11 Measurement Errors and Instrumental Variables
Regression 179
11.1 Estimation in the Presence of Measurement Errors......... 180
11.2 Orthogonal and Deming Regression ........................ 182
11.3 Instrumental Variables Regression ....................... 184
11.4 Structural Equation Modeling ............................ 186
11.5 Dilution................................................. 188
11.6 Examples ................................................ 188
12 Weighted Least Squares and Robust Regression
Procedures 195
12.1 Weighted Least Squares................................. 195
12.2 Robust Regression Methods................................ 197
12.3 Theil-Sen and Passing-Bablok Regression.................. 201
12.4 Resistant Regression Methods............................. 202
12.5 Resampling Techniques for ¡3 203
12.6 Examples ................................................ 210
13 Correlated Errors and Autoregressive Structures 219
13.1 Overview of Time Series and Autoregressive Structures . . 219
13.2 Properties of the Error Terms............................ 221
13.3 Testing and Remedial Measures for Autocorrelation .... 224
13.4 Advanced Methods......................................... 230
13.4.1 ARIMA Models..................................... 230
13.4.2 Exponential Smoothing............................ 233
13.4.3 Spectral Analysis................................ 234
13.5 Examples ................................................ 236
14 Crossvalidation and Model Selection Methods 249
14.1 Crossvalidation.......................................... 249
14.2 PRESS ................................................... 251
14.3 Best Subset Procedures .................................. 252
14.4 Statistics from Information Criteria . .................. 254
14.5 Stepwise Procedures for Identifying Models .............. 255
14.6 Example.................................................. 256
X
Contents
IV Advanced Regression Models 261
15 Mixed Models and Some Regression Models for Designed
Experiments 263
15.1 Mixed Effects Models ................................... 263
15.2 ANCOVA.................................................. 265
15.3 Response Surface Regression ............................ 268
15.4 Mixture Experiments .................................... 273
15.5 Examples ............................................... 276
16 Biased Regression, Regression Shrinkage, and Dimension
Reduction 287
16.1 Regression Shrinkage and Penalized Regression........... 287
16.2 Principal Components Regression ........................ 292
16.3 Partial Least Squares .................................. 294
16.4 Other Dimension Reduction Methods and Sufficiency . . . 296
16.5 Examples ............................................... 301
17 Piecewise, Nonparametric, and Local Regression Methods 307
17.1 Piecewise Linear Regression............................. 307
17.2 Local Regression Methods................................ 310
17.3 Splines ................................................ 318
17.4 Other Nonparametric Regression Procedures .............. 324
17.5 Examples ............................................... 327
18 Regression Models with Censored Data 335
18.1 Overview of Survival and Reliability Analysis........... 335
18.2 Censored Regression Model............................... 337
18.3 Survival (Reliability) Regression ...................... 339
18.4 Cox Proportional Hazards Regression .................... 343
18.5 Diagnostic Procedures................................... 344
18.6 Truncated Regression Models............................. 347
18.7 Examples ............................................... 350
19 Nonlinear Regression 361
19.1 Nonlinear Regression Models ............................ 361
19.2 Nonlinear Least Squares................................. 364
19.2.1 A Few Algorithms................................ 365
19.3 Approximate Inference Procedures........................ 367
19.4 Examples ............................................... 370
20 Regression Models with Discrete Responses 375
20.1 Logistic Regression..................................... 375
20.1.1 Binary Logistic Regression...................... 376
20.1.2 Nominal Logistic Regression..................... 383
20.1.3 Ordinal Logistic Regression .................... 384
Contents xi
20.2 Poisson Regression........................................ 385
20.3 Negative Binomial Regression.............................. 390
20.4 Specialized Models Involving Zero Counts.................. 396
20.5 Examples ................................................. 398
21 Generalized Linear Models 413
21.1 The Generalized Linear Model and Link Functions........... 413
21.2 Gamma Regression ......................................... 418
21.3 Inverse Gaussian (Normal) Regression ..................... 419
21.4 Beta Regression .......................................... 420
21.5 Generalized Estimating Equations ......................... 422
21.6 Examples ................................................. 426
22 Multivariate Multiple Regression 439
22.1 The Model ................................................ 439
22.2 Estimation and Statistical Regions........................ 441
22.3 Reduced Rank Regression................................... 446
22.4 Seemingly Unrelated Regressions........................... 447
22.5 Examples ................................................. 449
23 Semiparametric Regression 455
23.1 Single-Index Models ...................................... 456
23.2 (Generalized) Additive Models ............................ 457
23.3 (Generalized) Partial Linear Models ...................... 458
23.4 (Generalized) Partial Linear Partial Additive Models .... 460
23.5 Varying-Coefficient Models ............................... 460
23.6 Projection Pursuit Regression............................. 461
23.7 Examples ................................................. 462
24 Data Mining 477
24.1 Classification and Support Vector Regression ............. 478
24.2 Prediction Trees and Related Methods...................... 483
24.3 Some Ensemble Learning Methods for Regression............. 488
24.4 Neural Networks .......................................... 492
24.5 Examples ................................................. 493
25 Miscellaneous Topics 503
25.1 Multilevel Regression Models ............................. 503
25.2 Functional Linear Regression Analysis..................... 510
25.3 Regression Depth.......................................... 515
25.4 Mediation and Moderation Regression....................... 517
25.5 Meta-Regression Models.................................... 522
25.6 Regression Methods for Analyzing Survey Data.............. 526
25.7 Regression with Missing Data and Regression Imputation . 533
25.8 Bayesian Regression ...................................... 538
25.9 Quantile Regression ...................................... 542
xii Contents
25.10 Monotone Regression ................................... 544
25.11 Generalized Extreme Value Regression Models ........... 546
25.12 Spatial Regression .................................... 548
25.13 Circular Regression ................................... 554
25.14 Rank Regression ....................................... 557
25.15 Mixtures of Regressions ............................... 560
25.16 Copula Regression ..................................... 563
25.17 Tensor Regression ..................................... 565
V Appendices 571
Appendix A Steps for Building a Regression Model 573
Appendix B Refresher on Matrices and Vector Spaces 575
Appendix C Some Notes on Probability and Statistics 579
Bibliography 583
Index
615
|
| any_adam_object | 1 |
| author | Young, Derek S. |
| author_GND | (DE-588)1144552214 |
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| author_role | aut |
| author_sort | Young, Derek S. |
| author_variant | d s y ds dsy |
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| bvnumber | BV044532031 |
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| ctrlnum | (OCoLC)989867183 (DE-599)BSZ493914846 |
| dewey-full | 519.536 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.536 |
| dewey-search | 519.536 |
| dewey-sort | 3519.536 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV044532031 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:55:10Z |
| institution | BVB |
| isbn | 9781498775298 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029931303 |
| oclc_num | 989867183 |
| open_access_boolean | |
| owner | DE-706 DE-739 DE-703 DE-634 DE-521 |
| owner_facet | DE-706 DE-739 DE-703 DE-634 DE-521 |
| physical | xvi, 637 Seiten Illustrationen, Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | CRC Press, Taylor & Francis Group |
| record_format | marc |
| series2 | A Chapman & Hall book |
| spelling | Young, Derek S. Verfasser (DE-588)1144552214 aut Handbook of regression methods Derek S. Young, University of Kentucky, Lexington Boca Raton ; London ; New York CRC Press, Taylor & Francis Group [2017] © 2017 xvi, 637 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier A Chapman & Hall book Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Regression analysis Multivariate analysis Regressionsanalyse (DE-588)4129903-6 s DE-604 Erscheint auch als Online-Ausgabe, e-Book 978-1-4987-7530-4 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029931303&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029931303&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Young, Derek S. Handbook of regression methods Regressionsanalyse (DE-588)4129903-6 gnd |
| subject_GND | (DE-588)4129903-6 |
| title | Handbook of regression methods |
| title_auth | Handbook of regression methods |
| title_exact_search | Handbook of regression methods |
| title_full | Handbook of regression methods Derek S. Young, University of Kentucky, Lexington |
| title_fullStr | Handbook of regression methods Derek S. Young, University of Kentucky, Lexington |
| title_full_unstemmed | Handbook of regression methods Derek S. Young, University of Kentucky, Lexington |
| title_short | Handbook of regression methods |
| title_sort | handbook of regression methods |
| topic | Regressionsanalyse (DE-588)4129903-6 gnd |
| topic_facet | Regressionsanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029931303&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029931303&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT youngdereks handbookofregressionmethods |
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