Modern regression methods:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2009
|
| Edition: | 2. ed. |
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIX, 642 S. graph. Darst. |
| ISBN: | 9780470081860 |
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| 245 | 1 | 0 | |a Modern regression methods |c Thomas P. Ryan |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2009 | |
| 300 | |a XIX, 642 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in probability and statistics | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Regression analysis | |
| 650 | 0 | 7 | |a Regressionsanalyse |0 (DE-588)4129903-6 |2 gnd |9 rswk-swf |
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| adam_text | Contents
Preface
ix
1.
Introduction
1
1.1
Simple
Linear
Regression
Model,
3
1.2
Uses of Regression Models,
4
1.3
Graph the Data!,
5
1.4
Estimation of
ßo
and
β ,
6
1.4.1
Orthogonal Regression,
11
1.5
Inferences from Regression Equations,
11
1.5.1
Predicting
Υ,
12
1.5.2
Worth of the Regression Equation,
13
1.5.3
Regression Assumptions,
15
1.5.4
Inferences on
β ,
17
1.5.5
Inferences on
ßo, 21
1.5.6
Inferences for
У,
22
1.5.6.1
Prediction Interval for
Υ
, 22
1.5.6.2
Confidence Interval for
μγ χ
, 25
1.5.7 ANOVA
Tables,
25
1.5.8
Lack of Fit,
26
1.6
Regression Through the Origin,
29
1.7
Additional Examples,
30
1.8
Correlation,
31
1.9
Miscellaneous Uses of Regression,
32
1.9.1
Regression for Control,
32
1.9.2
Inverse Regression,
33
1.9.3
Regression Control Chart,
37
1.9.4
Monitoring Linear Profiles,
37
vi
CONTENTS
1.10
Fixed Versus Random
Regressors,
37
1.11
Missing Data,
38
1.12
Spurious Relationships,
38
1.13
Software,
39
1.14
Summary,
40
Appendix,
41
References,
45
Exercises,
48
2.
Diagnostics and Remedial Measures
60
2.1
Assumptions,
61
2.1.1
Independence,
61
2.1.1.1
Correlated Errors,
64
2.1.1.1.1
An Example,
65
2.1.1.1.2
Corrective Action,
68
2.1.2
Normality,
68
2.1.2.1
Supernormality Property of Residuals,
69
2.1.2.2
Standardized Deletion Residuals,
70
2.1.2.3
Methods of Constructing Simulation
Envelopes,
70
2.1.3
Constant Variance,
77
2.1.3.1
Weighted Least Squares,
77
2.1.3.1.1
Unknown Weights,
81
2.1.3.1.2
Modeling the Variance,
83
2.1.3.2
A Heteroscedastic Alternative,
87
2.2
Residual Plots,
88
2.3
Transformations,
89
2.3.1
Transforming the Model,
89
2.3.2
Transforming the Regressors to Improve the Fit,
91
2.3.2.1
Box-Tidwell Transformation,
92
2.3.3
Transform
Y
to Obtain a Better Fit?,
95
2.3.4
Transforming to Correct Heteroscedasticity and
Nonnormality,
96
2.3.5
Which R2,
97
2.4
Influential Observations,
98
2.4.1
An Example,
99
2.4.2
Influence Statistics,
103
2.4.3
Different Schools of Thought Regarding Influence,
104
2.4.4
Modification of Standard Influence Measures,
105
CONTENTS
VU
2.4.5 Application
of Influence Measures to Table
2.7
Data,
105
2.4.6
Multiple Unusual Observations,
106
2.4.7
Predicting
Lifespan (?):
An Influential Data Problem,
107
2.5
Outliers,
108
2.6
Measurement Error, 111
2.6.1
Measurement Error in
Υ
,
111
2.6.2
Measurement Error in X
, 112
2.7
Software,
112
2.8
Summary,
114
Appendix,
114
References,
116
Exercises,
120
3.
Regression with Matrix Algebra
128
3.1
Introduction to Matrix Algebra,
128
3.1.1
Eigenvalues and Eigenvectors,
130
3.2
Matrix Algebra Applied to Regression,
133
3.2.1
Predicted
Y
and R2,
135
3.2.2
Estimation of
σ62,
136
3.2.3
Variance of
Y
and
f
, 136
3.2.4
Centered Data,
138
3.2.5
Correlation Form,
139
3.2.6
Influence Statistics in Matrix Form,
140
3.3
Summary,
141
Appendix,
141
References,
142
Exercises,
143
4.
Introduction to Multiple Linear Regression
146
4.1
An Example of Multiple Linear Regression,
147
4.1.1
Orthogonal Regressors,
150
4.1.2
Correlated Regressors,
151
4.1.2.1
Partial-F Tests and
ŕ-Tests,
153
4.1.2.2
Individual Regressor Effects,
155
4.1.3
Confidence Intervals and Prediction Intervals,
156
4.2
Centering And Scaling,
158
4.2.1
Centering,
158
4.2.2
Scaling,
159
viii CONTENTS
4.3
Interpreting Multiple Regression Coefficients,
161
4.3.1
Multicollinearity and the Wrong Signs Problem,
167
4.3.2
So Are Individual Regression Coefficients
Interpretable?,
168
4.3.3
Inflated Variances,
169
4.3.4
Detecting Multicollinearity,
169
4.3.5
Variance Proportions,
173
4.3.6
What to Do About Multicollinearity?,
174
4.4
Indicator Variables,
175
4.5
Separation or Not?,
176
4.6
Alternatives to Multiple Regression,
176
4.7
Software,
176
4.8
Summary,
177
References,
178
Exercises,
181
5.
Plots in Multiple Regression
190
5.1
Beyond Standardized Residual Plots,
190
5.1.1
Partial Residual Plots,
191
5.1.2
CCPRPlot,
193
5.1.3
Augmented Partial Residual Plots,
194
5.1.4
CERES Plots,
194
5.2
Some Examples,
196
5.3
Which Plot?,
208
5.3.1
Relationships Between Plots,
209
5.3.2
True Model Contains Nonlinear Terms,
211
5.4
Recommendations,
212
5.5
Partial Regression Plots,
213
5.5.1
Examples,
216
5.5.2
Detrended Added Variable Plot,
217
5.5.3
Partial Regression Plots Used to Detect Influential
Observations,
218
5.6
Other Plots For Detecting Influential Observations,
222
5.7
Recent Contributions to Plots in Multiple Regression,
223
5.8
Lurking Variables,
225
5.9
Explanation of Two Data Sets Relative to
Ŕ1,
225
5.10
Software,
226
5.11
Summary,
227
References,
228
Exercises,
230
CONTENTS ix
6. Transformations in Multiple Regression 234
6.1
Transforming Regressors,
234
6.2
Transforming
Y,
238
6.2.1 Transformation
Needed But Not Suggested,
238
6.2.2
Transformation Needed and Suggested,
240
6.2.3
Transformation Apparently Successful,
241
6.3
Further Comments on the Normality Issue,
242
6.4
Box
-Сох
Transformation,
243
6.5
Box-Tidwell Revisited,
247
6.6
Combined
Box
-Сох
and Box-Tidwell Approach,
247
6.6.1
Table
6.2
Data,
248
6.6.2
Table
6.3
Data,
249
6.6.3
Table
6.4
Data,
250
6.6.4
MINITAB Tree Data,
250
6.6.4.1
Other Analyses of the Tree Data,
253
6.6.5
Stack Loss Data,
255
6.6.6
Palm Beach County Data,
257
6.7
Other Transformation Methods,
258
6.7.1
Transform Both Sides (TBS),
259
6.8
Transformation Diagnostics,
260
6.8.1
Diagnostics After a Transformation,
261
6.9
Software,
261
6.10
Summary,
262
References,
262
Exercises,
265
7.
Selection of Regressors
269
7.1
Forward Selection,
270
7.2
Backward Elimination,
271
7.3
Stepwise Regression,
272
7.3.1
Significance Levels,
272
7.4
All Possible Regressions,
272
7.4.1
Criteria,
273
7.4.1.1
Mallows s Cp,
273
7.4.1.1.1
Cp and Influential Data,
276
7.4.1.2
Minimuma2,
277
7.4.1.3
r-Statistics,
277
7.4.1.4
Other Criteria,
277
x
CONTENTS
7.5
Newer Methods,
277
7.5.1
Robust Variable Selection,
278
7.6
Examples,
279
7.7
Variable Selection for Nonlinear Terms,
280
7.7.1
Negative Cp Values,
282
7.8
Must We Use a Subset?,
283
7.9
Model Validation,
284
7.10
Software,
284
7.11
Summary,
285
Appendix,
286
References,
287
Exercises,
290
8.
Polynomial and Trigonometric Terms
296
8.1
Polynomial Terms,
296
8.1.1
Orthogonal Polynomial Regression,
299
8.1.1.1
When to Stop?,
299
8.1.2
An Example,
300
8.2
Polynomial-Trigonometric Regression,
302
8.2.1
Orthogonality of Trigonometric Terms,
303
8.2.2
Practical Considerations,
303
8.2.3
Examples,
303
8.2.4
Multiple Independent Variables,
307
8.3
Software,
307
8.4
Summary,
307
References,
308
Exercises,
309
9.
Logistic Regression
312
9.1
Introduction,
312
9.2
One Regressor,
313
9.2.1
Estimating
ß0
and
βλ
, 315
9.2.1.1
Method of Maximum Likelihood,
315
9.2.1.2
Exact Logistic Regression,
319
9.3
A Simulated Example,
320
9.3.1
Complete and Quasicomplete Separation,
320
9.3.2
Overlap: Modifying Table
9.1, 325
9.4
Detecting Complete Separation, Quasicomplete Separation and
Near Separation,
326
CONTENTS XJ
9.5
Measuring the Worth of the Model,
326
9.5.1
R2 in Logistic Regression,
327
9.5.2
Deviance,
328
9.5.3
Other Measures of Model Fit,
329
9.6
Determining the Worth of the Individual Regressors,
330
9.6.1 Wald
Test,
330
9.6.2
Likelihood Ratio Test,
331
9.6.3
Scores Test,
331
9.6.4
Exact Conditional Scores Test,
332
9.6.5
Exact p-Value,
333
9.7
Confidence Intervals,
333
9.7.1
Confidence Interval for
βχ,
333
9.7.2
Confidence Interval for Change in Odds Ratio,
334
9.7.3
Confidence Interval for
π,
334
9.7.4
Exact Confidence Intervals,
335
9.7.4.1
Exact Confidence Interval for
βχ,
335
9.7.4.2
Exact Confidence Interval for Change in
Odds Ratio,
336
9.8
Exact Prediction,
336
9.8.1
Exact Confidence Interval for
7Γ,
337
9.9
An Example With Real Data,
337
9.9.1
Hosmer-Lemeshow Goodness-of-Fit Tests,
340
9.9.2
Which Residuals?,
343
9.9.3
Application to Table
9.4
Data,
345
9.9.3.1
Pearson Residuals,
346
9.9.3.2
Deviance Residuals,
348
9.9.4
Other Diagnostics,
349
9.9.5
Partial Residual Plot,
350
9.9.6
Added Variable Plot,
351
9.9.7
Confidence Intervals for Table
9.3
Data,
352
9.10
An Example of Multiple Logistic Regression,
352
9.10.1
Correct Classification Rate for Full Data Set,
355
9.10.2
Influential Observations,
356
9.10.3
Which Variables?,
357
9.10.3.1
Algorithmic Approaches to Variable
Selection,
359
9.10.3.2
What About Nonlinear Terms?,
361
9.11
Multicollinearity in Multiple Logistic
Regression,
362
xii CONTENTS
9.12 Osteogenic
Sarcoma
Data
Set,
366
9.13
Missing Data,
369
9.14 Sample
Size
Determination, 369
9.15 Polytomous
Logistic
Regression, 370
9.16
Logistic
Regression
Variations,
372
9.17 Alternatives
to Logistic
Regression, 373
9.18 Software
for Logistic
Regression, 373
9.19
Summary,
375
Appendix, 375
References,
376
Exercises,
381
10. Nonparametric Regression 385
10.1
Relaxing
Regression
Assumptions,
386
10.1.1
Bootstrapping,
386
10.2 Monotone Regression, 387
10.3
Smoothers,
390
10.3.1
Running Line,
393
10.3.1.1
Inferences for Running Line,
397
10.3.2
Kernel Regression,
398
10.3.2.1
Inferences in Kernel Regression,
399
10.3.3
Local Regression,
400
10.3.3.1
Inferences and Diagnostics,
403
10.3.4
Splines,
403
10.3.4.1
Piecewise Linear Regression
(Linear Splines),
403
10.3.4.1.1
Model Representation,
405
10.3.4.2
Splines with Polynomial Terms,
405
10.3.4.3
Smoothing Splines,
407
10.3.4.4
Splines Compared to Local
Regression,
408
10.3.5
Other Smoothers,
409
10.3.6
Which Smoother?,
409
10.3.7
Smoothers for Multiple Regressors,
409
10.4
Variable Selection,
410
10.5
Important Considerations in Smoothing,
410
10.6
Sliced Inverse Regression,
410
10.7
Projection Pursuit Regression,
411
10.8
Software,
411
CONTENTS
XIII
10.9
Summary,
412
Appendix,
413
References,
414
Exercises,
418
11.
Robust Regression
421
11.1
The Need for Robust Regression,
421
11.2
Types of Outliers,
423
11.3
Historical Development of Robust Regression,
426
11.3.1
Breakdown Point,
427
11.3.2
Efficiency,
427
11.3.3
Classes of Estimators,
428
11.3.3.1
M-Estimators,
428
11.3.3.2
Bounded Influence Estimators,
428
11.3.3.3
High Breakdown Point Estimators,
429
11.3.3.4
Two-Stage Procedures,
429
11.3.3.5
MM-Estimator (Three Stages),
429
11.4
Goals of Robust Regression,
430
11.5
Proposed High Breakdown Point Estimators,
430
11.5.1
Least Median of Squares,
430
11.5.2
Least Trimmed Squares,
432
11.5.2.1
LTS
Applications,
434
11.5.3
S-Estimators,
434
11.6
Approximating HBP Estimator Solutions,
435
11.6.1
Application to Hawkins-Bradu-Kass Data Set,
436
11.6.2
Another Application: One Regressor,
440
11.6.3
A Proposed Sequential Procedure,
441
11.6.4
Application to Multiple Regression,
442
11.7
Other Methods for Detecting Multiple Outliers,
446
11.8
Bounded Influence Estimators,
446
11.8.1
Shortcomings of Bounded Influence Estimators,
449
11.8.2
Application of Welsh Estimator,
450
11.9
Multistage Procedures,
452
11.10
Other Robust Regression Estimators,
454
11.11
Applications,
456
11.12
Software for Robust Regression,
456
11.13
Summary,
457
References,
458
Exercises,
462
XIV
CONTENTS
12.
Ridge Regression
466
12.1
Introduction,
466
12.2
How Do We Determine it?,
470
12.3
An Example,
471
12.4
Ridge Regression for Prediction?,
476
12.5
Generalized Ridge Regression,
477
12.6
Inferences in Ridge Regression,
477
12.7
Some Practical Considerations,
477
12.8
Robust Ridge Regression?,
478
12.9
Recent Developments in Ridge Regression,
478
12.10
Other Biased Estimators,
479
12.11
Software,
480
12.12
Summary,
480
Appendix,
481
References,
482
Exercises,
485
13.
Nonlinear Regression
488
13.1
Introduction,
488
13.2
Linear Versus Nonlinear Regression,
489
13.3
A Simple Nonlinear Example,
489
13.3.1
Iterative Estimation,
491
13.4
Relative Offset Convergence Criterion,
493
13.5
Adequacy of the Estimation Approach,
494
13.6
Computational Considerations,
495
13.7
Determining Model Adequacy,
496
13.7.1
Lack-of-Fit Test,
496
13.7.2
Residual Plots,
497
13.7.3
Multicollinearity Diagnostics,
498
13.7.4
Influence and Unusual Data Diagnostics,
499
13.7.4.1
Leverage,
499
13.7.4.2
Influence,
499
13.8
Inferences,
501
13.8.1
Confidence Intervals,
501
13.8.2
Prediction Interval,
502
13.8.3
Hypothesis Tests,
502
13.9
An Application,
502
13.9.1
When Is a Linear Fit Not Good Enough?,
507
CONTENTS
XV
13.10 Rational
Functions,
510
13.11 Robust Nonlinear Regression, 510
13.12 Applications, 510
13.13
Teaching
Tools, 511
13.14
Recent
Developments, 511
13.15 Software, 511
13.15.1
SAS
Software, 511
13.15.1.1
Cautions,
512
13.15.2 SPSS, 512
13.15.3 BMDP, 512
13.15.4 S-PlusandÄ, 512
13.15.5 MINITAB, 513
13.16
Summary,
513
Appendix, 513
References,
516
Exercises,
520
14.
Experimental
Designs
for
Regression 525
14.1
Objectives for Experimental
Designs, 525
14.2
Equal Leverage Points,
525
14.2.1
Simple Linear Regression,
526
14.2.2
Multiple Linear Regression,
526
14.2.2.1
Construction of Equileverage Designs
—
Two Regressors,
527
14.2.2.1.1
Inverse Projection
Approach,
531
14.3
Other Desirable Properties of Experimental Designs,
537
14.3.1
D-Optimality,
537
14.3.2
G-Optimality,
538
14.3.3
Other Optimality Criteria,
539
14.4
Model Misspecification,
540
14.5
Range of Regressors,
541
14.6
Algorithms for Design Construction,
541
14.7
Designs for Polynomial Regression,
541
14.8
Designs for Logistic Regression,
542
14.9
Designs for Nonlinear Regression,
542
14.10
Software,
543
14.11
Summary,
543
References,
544
Exercises,
547
XVi
CONTENTS
15.
Miscellaneous Topics in Regression
550
15.1
Piecewise Regression and Alternatives,
550
15.2
Semiparametric Regression,
550
15.3
Quantile Regression,
552
15.4
Poisson
Regression,
556
15.4.1
Exact
Poisson
Regression,
560
15.4.2
Zero-Inflated
Poisson
Regression,
561
15.4.3
Zero-Truncated
Poisson
Regression,
562
15.5
Negative Binomial Regression,
562
15.5.1
Zero-Inflated Negative Binomial Regression,
563
15.5.2
Zero-Truncated Negative Binomial Regression,
563
15.6
Cox Regression,
564
15.7
Probit
Regression,
564
15.8
Censored Regression and Truncated Regression,
565
15.8.1
Tobit Regression,
566
15.9
Constrained Regression,
566
15.10
Interval Regression,
567
15.11
Random Coefficient Regression,
567
15.12
Partial Least Squares Regression,
568
15.13
Errors-in-Variables Regression,
568
15.14
Regression with Life Data,
568
15.15
Use of Regression in Survey Sampling,
569
15.16
Bayesian Regression,
569
15.17
Instrumental Variables Regression,
570
15.18
Shrinkage Estimators,
571
15.19
Meta-Regression,
571
15.20
Classification and Regression Trees (CART),
571
15.21
Multivariate Regression,
572
References,
572
Exercises,
576
16.
Analysis of Real Data Sets
577
16.1
Analyzing Buchanan s Presidential Vote in Palm Beach
County in 2000,
577
16.2
Water Quality Data,
578
16.3
Predicting
Lifespan?, 588
16.4
Scottish Hill Races Data,
591
16.5
Leukemia Data,
593
16.5.1
У
Binary,
593
16.5.2
ľ
Continuous,
598
CONTENTS XVII
16.6
Dosage
Response
Data,
599
16.7
A
Strategy for Analyzing Regression Data,
602
16.8
Summary,
604
References,
604
Exercises,
606
Answers to Selected Exercises
609
Statistical Tables
617
Author Index
625
Subject Index
637
|
| adam_txt |
Contents
Preface
ix
1.
Introduction
1
1.1
Simple
Linear
Regression
Model,
3
1.2
Uses of Regression Models,
4
1.3
Graph the Data!,
5
1.4
Estimation of
ßo
and
β\,
6
1.4.1
Orthogonal Regression,
11
1.5
Inferences from Regression Equations,
11
1.5.1
Predicting
Υ,
12
1.5.2
Worth of the Regression Equation,
13
1.5.3
Regression Assumptions,
15
1.5.4
Inferences on
β\,
17
1.5.5
Inferences on
ßo, 21
1.5.6
Inferences for
У,
22
1.5.6.1
Prediction Interval for
Υ
, 22
1.5.6.2
Confidence Interval for
μγ\χ
, 25
1.5.7 ANOVA
Tables,
25
1.5.8
Lack of Fit,
26
1.6
Regression Through the Origin,
29
1.7
Additional Examples,
30
1.8
Correlation,
31
1.9
Miscellaneous Uses of Regression,
32
1.9.1
Regression for Control,
32
1.9.2
Inverse Regression,
33
1.9.3
Regression Control Chart,
37
1.9.4
Monitoring Linear Profiles,
37
vi
CONTENTS
1.10
Fixed Versus Random
Regressors,
37
1.11
Missing Data,
38
1.12
Spurious Relationships,
38
1.13
Software,
39
1.14
Summary,
40
Appendix,
41
References,
45
Exercises,
48
2.
Diagnostics and Remedial Measures
60
2.1
Assumptions,
61
2.1.1
Independence,
61
2.1.1.1
Correlated Errors,
64
2.1.1.1.1
An Example,
65
2.1.1.1.2
Corrective Action,
68
2.1.2
Normality,
68
2.1.2.1
Supernormality Property of Residuals,
69
2.1.2.2
Standardized Deletion Residuals,
70
2.1.2.3
Methods of Constructing Simulation
Envelopes,
70
2.1.3
Constant Variance,
77
2.1.3.1
Weighted Least Squares,
77
2.1.3.1.1
Unknown Weights,
81
2.1.3.1.2
Modeling the Variance,
83
2.1.3.2
A Heteroscedastic Alternative,
87
2.2
Residual Plots,
88
2.3
Transformations,
89
2.3.1
Transforming the Model,
89
2.3.2
Transforming the Regressors to Improve the Fit,
91
2.3.2.1
Box-Tidwell Transformation,
92
2.3.3
Transform
Y
to Obtain a Better Fit?,
95
2.3.4
Transforming to Correct Heteroscedasticity and
Nonnormality,
96
2.3.5
Which R2,
97
2.4
Influential Observations,
98
2.4.1
An Example,
99
2.4.2
Influence Statistics,
103
2.4.3
Different Schools of Thought Regarding Influence,
104
2.4.4
Modification of Standard Influence Measures,
105
CONTENTS
VU
2.4.5 Application
of Influence Measures to Table
2.7
Data,
105
2.4.6
Multiple Unusual Observations,
106
2.4.7
Predicting
Lifespan (?):
An Influential Data Problem,
107
2.5
Outliers,
108
2.6
Measurement Error, 111
2.6.1
Measurement Error in
Υ
,
111
2.6.2
Measurement Error in X
, 112
2.7
Software,
112
2.8
Summary,
114
Appendix,
114
References,
116
Exercises,
120
3.
Regression with Matrix Algebra
128
3.1
Introduction to Matrix Algebra,
128
3.1.1
Eigenvalues and Eigenvectors,
130
3.2
Matrix Algebra Applied to Regression,
133
3.2.1
Predicted
Y
and R2,
135
3.2.2
Estimation of
σ62,
136
3.2.3
Variance of
Y
and
f
, 136
3.2.4
Centered Data,
138
3.2.5
Correlation Form,
139
3.2.6
Influence Statistics in Matrix Form,
140
3.3
Summary,
141
Appendix,
141
References,
142
Exercises,
143
4.
Introduction to Multiple Linear Regression
146
4.1
An Example of Multiple Linear Regression,
147
4.1.1
Orthogonal Regressors,
150
4.1.2
Correlated Regressors,
151
4.1.2.1
Partial-F Tests and
ŕ-Tests,
153
4.1.2.2
Individual Regressor Effects,
155
4.1.3
Confidence Intervals and Prediction Intervals,
156
4.2
Centering And Scaling,
158
4.2.1
Centering,
158
4.2.2
Scaling,
159
viii CONTENTS
4.3
Interpreting Multiple Regression Coefficients,
161
4.3.1
Multicollinearity and the "Wrong Signs" Problem,
167
4.3.2
So Are Individual Regression Coefficients
Interpretable?,
168
4.3.3
Inflated Variances,
169
4.3.4
Detecting Multicollinearity,
169
4.3.5
Variance Proportions,
173
4.3.6
What to Do About Multicollinearity?,
174
4.4
Indicator Variables,
175
4.5
Separation or Not?,
176
4.6
Alternatives to Multiple Regression,
176
4.7
Software,
176
4.8
Summary,
177
References,
178
Exercises,
181
5.
Plots in Multiple Regression
190
5.1
Beyond Standardized Residual Plots,
190
5.1.1
Partial Residual Plots,
191
5.1.2
CCPRPlot,
193
5.1.3
Augmented Partial Residual Plots,
194
5.1.4
CERES Plots,
194
5.2
Some Examples,
196
5.3
Which Plot?,
208
5.3.1
Relationships Between Plots,
209
5.3.2
True Model Contains Nonlinear Terms,
211
5.4
Recommendations,
212
5.5
Partial Regression Plots,
213
5.5.1
Examples,
216
5.5.2
Detrended Added Variable Plot,
217
5.5.3
Partial Regression Plots Used to Detect Influential
Observations,
218
5.6
Other Plots For Detecting Influential Observations,
222
5.7
Recent Contributions to Plots in Multiple Regression,
223
5.8
Lurking Variables,
225
5.9
Explanation of Two Data Sets Relative to
Ŕ1,
225
5.10
Software,
226
5.11
Summary,
227
References,
228
Exercises,
230
CONTENTS ix
6. Transformations in Multiple Regression 234
6.1
Transforming Regressors,
234
6.2
Transforming
Y,
238
6.2.1 Transformation
Needed But Not Suggested,
238
6.2.2
Transformation Needed and Suggested,
240
6.2.3
Transformation Apparently Successful,
241
6.3
Further Comments on the Normality Issue,
242
6.4
Box
-Сох
Transformation,
243
6.5
Box-Tidwell Revisited,
247
6.6
Combined
Box
-Сох
and Box-Tidwell Approach,
247
6.6.1
Table
6.2
Data,
248
6.6.2
Table
6.3
Data,
249
6.6.3
Table
6.4
Data,
250
6.6.4
MINITAB Tree Data,
250
6.6.4.1
Other Analyses of the Tree Data,
253
6.6.5
Stack Loss Data,
255
6.6.6
Palm Beach County Data,
257
6.7
Other Transformation Methods,
258
6.7.1
Transform Both Sides (TBS),
259
6.8
Transformation Diagnostics,
260
6.8.1
Diagnostics After a Transformation,
261
6.9
Software,
261
6.10
Summary,
262
References,
262
Exercises,
265
7.
Selection of Regressors
269
7.1
Forward Selection,
270
7.2
Backward Elimination,
271
7.3
Stepwise Regression,
272
7.3.1
Significance Levels,
272
7.4
All Possible Regressions,
272
7.4.1
Criteria,
273
7.4.1.1
Mallows's Cp,
273
7.4.1.1.1
Cp and Influential Data,
276
7.4.1.2
Minimuma2,
277
7.4.1.3
r-Statistics,
277
7.4.1.4
Other Criteria,
277
x
CONTENTS
7.5
Newer Methods,
277
7.5.1
Robust Variable Selection,
278
7.6
Examples,
279
7.7
Variable Selection for Nonlinear Terms,
280
7.7.1
Negative Cp Values,
282
7.8
Must We Use a Subset?,
283
7.9
Model Validation,
284
7.10
Software,
284
7.11
Summary,
285
Appendix,
286
References,
287
Exercises,
290
8.
Polynomial and Trigonometric Terms
296
8.1
Polynomial Terms,
296
8.1.1
Orthogonal Polynomial Regression,
299
8.1.1.1
When to Stop?,
299
8.1.2
An Example,
300
8.2
Polynomial-Trigonometric Regression,
302
8.2.1
Orthogonality of Trigonometric Terms,
303
8.2.2
Practical Considerations,
303
8.2.3
Examples,
303
8.2.4
Multiple Independent Variables,
307
8.3
Software,
307
8.4
Summary,
307
References,
308
Exercises,
309
9.
Logistic Regression
312
9.1
Introduction,
312
9.2
One Regressor,
313
9.2.1
Estimating
ß0
and
βλ
, 315
9.2.1.1
Method of Maximum Likelihood,
315
9.2.1.2
Exact Logistic Regression,
319
9.3
A Simulated Example,
320
9.3.1
Complete and Quasicomplete Separation,
320
9.3.2
Overlap: Modifying Table
9.1, 325
9.4
Detecting Complete Separation, Quasicomplete Separation and
Near Separation,
326
CONTENTS XJ
9.5
Measuring the Worth of the Model,
326
9.5.1
R2 in Logistic Regression,
327
9.5.2
Deviance,
328
9.5.3
Other Measures of Model Fit,
329
9.6
Determining the Worth of the Individual Regressors,
330
9.6.1 Wald
Test,
330
9.6.2
Likelihood Ratio Test,
331
9.6.3
Scores Test,
331
9.6.4
Exact Conditional Scores Test,
332
9.6.5
Exact p-Value,
333
9.7
Confidence Intervals,
333
9.7.1
Confidence Interval for
βχ,
333
9.7.2
Confidence Interval for Change in Odds Ratio,
334
9.7.3
Confidence Interval for
π,
334
9.7.4
Exact Confidence Intervals,
335
9.7.4.1
Exact Confidence Interval for
βχ,
335
9.7.4.2
Exact Confidence Interval for Change in
Odds Ratio,
336
9.8
Exact Prediction,
336
9.8.1
Exact Confidence Interval for
7Γ,
337
9.9
An Example With Real Data,
337
9.9.1
Hosmer-Lemeshow Goodness-of-Fit Tests,
340
9.9.2
Which Residuals?,
343
9.9.3
Application to Table
9.4
Data,
345
9.9.3.1
Pearson Residuals,
346
9.9.3.2
Deviance Residuals,
348
9.9.4
Other Diagnostics,
349
9.9.5
Partial Residual Plot,
350
9.9.6
Added Variable Plot,
351
9.9.7
Confidence Intervals for Table
9.3
Data,
352
9.10
An Example of Multiple Logistic Regression,
352
9.10.1
Correct Classification Rate for Full Data Set,
355
9.10.2
Influential Observations,
356
9.10.3
Which Variables?,
357
9.10.3.1
Algorithmic Approaches to Variable
Selection,
359
9.10.3.2
What About Nonlinear Terms?,
361
9.11
Multicollinearity in Multiple Logistic
Regression,
362
xii CONTENTS
9.12 Osteogenic
Sarcoma
Data
Set,
366
9.13
Missing Data,
369
9.14 Sample
Size
Determination, 369
9.15 Polytomous
Logistic
Regression, 370
9.16
Logistic
Regression
Variations,
372
9.17 Alternatives
to Logistic
Regression, 373
9.18 Software
for Logistic
Regression, 373
9.19
Summary,
375
Appendix, 375
References,
376
Exercises,
381
10. Nonparametric Regression 385
10.1
Relaxing
Regression
Assumptions,
386
10.1.1
Bootstrapping,
386
10.2 Monotone Regression, 387
10.3
Smoothers,
390
10.3.1
Running Line,
393
10.3.1.1
Inferences for Running Line,
397
10.3.2
Kernel Regression,
398
10.3.2.1
Inferences in Kernel Regression,
399
10.3.3
Local Regression,
400
10.3.3.1
Inferences and Diagnostics,
403
10.3.4
Splines,
403
10.3.4.1
Piecewise Linear Regression
(Linear Splines),
403
10.3.4.1.1
Model Representation,
405
10.3.4.2
Splines with Polynomial Terms,
405
10.3.4.3
Smoothing Splines,
407
10.3.4.4
Splines Compared to Local
Regression,
408
10.3.5
Other Smoothers,
409
10.3.6
Which Smoother?,
409
10.3.7
Smoothers for Multiple Regressors,
409
10.4
Variable Selection,
410
10.5
Important Considerations in Smoothing,
410
10.6
Sliced Inverse Regression,
410
10.7
Projection Pursuit Regression,
411
10.8
Software,
411
CONTENTS
XIII
10.9
Summary,
412
Appendix,
413
References,
414
Exercises,
418
11.
Robust Regression
421
11.1
The Need for Robust Regression,
421
11.2
Types of Outliers,
423
11.3
Historical Development of Robust Regression,
426
11.3.1
Breakdown Point,
427
11.3.2
Efficiency,
427
11.3.3
Classes of Estimators,
428
11.3.3.1
M-Estimators,
428
11.3.3.2
Bounded Influence Estimators,
428
11.3.3.3
High Breakdown Point Estimators,
429
11.3.3.4
Two-Stage Procedures,
429
11.3.3.5
MM-Estimator (Three Stages),
429
11.4
Goals of Robust Regression,
430
11.5
Proposed High Breakdown Point Estimators,
430
11.5.1
Least Median of Squares,
430
11.5.2
Least Trimmed Squares,
432
11.5.2.1
LTS
Applications,
434
11.5.3
S-Estimators,
434
11.6
Approximating HBP Estimator Solutions,
435
11.6.1
Application to Hawkins-Bradu-Kass Data Set,
436
11.6.2
Another Application: One Regressor,
440
11.6.3
A Proposed Sequential Procedure,
441
11.6.4
Application to Multiple Regression,
442
11.7
Other Methods for Detecting Multiple Outliers,
446
11.8
Bounded Influence Estimators,
446
11.8.1
Shortcomings of Bounded Influence Estimators,
449
11.8.2
Application of Welsh Estimator,
450
11.9
Multistage Procedures,
452
11.10
Other Robust Regression Estimators,
454
11.11
Applications,
456
11.12
Software for Robust Regression,
456
11.13
Summary,
457
References,
458
Exercises,
462
XIV
CONTENTS
12.
Ridge Regression
466
12.1
Introduction,
466
12.2
How Do We Determine it?,
470
12.3
An Example,
471
12.4
Ridge Regression for Prediction?,
476
12.5
Generalized Ridge Regression,
477
12.6
Inferences in Ridge Regression,
477
12.7
Some Practical Considerations,
477
12.8
Robust Ridge Regression?,
478
12.9
Recent Developments in Ridge Regression,
478
12.10
Other Biased Estimators,
479
12.11
Software,
480
12.12
Summary,
480
Appendix,
481
References,
482
Exercises,
485
13.
Nonlinear Regression
488
13.1
Introduction,
488
13.2
Linear Versus Nonlinear Regression,
489
13.3
A Simple Nonlinear Example,
489
13.3.1
Iterative Estimation,
491
13.4
Relative Offset Convergence Criterion,
493
13.5
Adequacy of the Estimation Approach,
494
13.6
Computational Considerations,
495
13.7
Determining Model Adequacy,
496
13.7.1
Lack-of-Fit Test,
496
13.7.2
Residual Plots,
497
13.7.3
Multicollinearity Diagnostics,
498
13.7.4
Influence and Unusual Data Diagnostics,
499
13.7.4.1
Leverage,
499
13.7.4.2
Influence,
499
13.8
Inferences,
501
13.8.1
Confidence Intervals,
501
13.8.2
Prediction Interval,
502
13.8.3
Hypothesis Tests,
502
13.9
An Application,
502
13.9.1
When Is a Linear Fit Not Good Enough?,
507
CONTENTS
XV
13.10 Rational
Functions,
510
13.11 Robust Nonlinear Regression, 510
13.12 Applications, 510
13.13
Teaching
Tools, 511
13.14
Recent
Developments, 511
13.15 Software, 511
13.15.1
SAS
Software, 511
13.15.1.1
Cautions,
512
13.15.2 SPSS, 512
13.15.3 BMDP, 512
13.15.4 S-PlusandÄ, 512
13.15.5 MINITAB, 513
13.16
Summary,
513
Appendix, 513
References,
516
Exercises,
520
14.
Experimental
Designs
for
Regression 525
14.1
Objectives for Experimental
Designs, 525
14.2
Equal Leverage Points,
525
14.2.1
Simple Linear Regression,
526
14.2.2
Multiple Linear Regression,
526
14.2.2.1
Construction of Equileverage Designs
—
Two Regressors,
527
14.2.2.1.1
Inverse Projection
Approach,
531
14.3
Other Desirable Properties of Experimental Designs,
537
14.3.1
D-Optimality,
537
14.3.2
G-Optimality,
538
14.3.3
Other Optimality Criteria,
539
14.4
Model Misspecification,
540
14.5
Range of Regressors,
541
14.6
Algorithms for Design Construction,
541
14.7
Designs for Polynomial Regression,
541
14.8
Designs for Logistic Regression,
542
14.9
Designs for Nonlinear Regression,
542
14.10
Software,
543
14.11
Summary,
543
References,
544
Exercises,
547
XVi
CONTENTS
15.
Miscellaneous Topics in Regression
550
15.1
Piecewise Regression and Alternatives,
550
15.2
Semiparametric Regression,
550
15.3
Quantile Regression,
552
15.4
Poisson
Regression,
556
15.4.1
Exact
Poisson
Regression,
560
15.4.2
Zero-Inflated
Poisson
Regression,
561
15.4.3
Zero-Truncated
Poisson
Regression,
562
15.5
Negative Binomial Regression,
562
15.5.1
Zero-Inflated Negative Binomial Regression,
563
15.5.2
Zero-Truncated Negative Binomial Regression,
563
15.6
Cox Regression,
564
15.7
Probit
Regression,
564
15.8
Censored Regression and Truncated Regression,
565
15.8.1
Tobit Regression,
566
15.9
Constrained Regression,
566
15.10
Interval Regression,
567
15.11
Random Coefficient Regression,
567
15.12
Partial Least Squares Regression,
568
15.13
Errors-in-Variables Regression,
568
15.14
Regression with Life Data,
568
15.15
Use of Regression in Survey Sampling,
569
15.16
Bayesian Regression,
569
15.17
Instrumental Variables Regression,
570
15.18
Shrinkage Estimators,
571
15.19
Meta-Regression,
571
15.20
Classification and Regression Trees (CART),
571
15.21
Multivariate Regression,
572
References,
572
Exercises,
576
16.
Analysis of Real Data Sets
577
16.1
Analyzing Buchanan's Presidential Vote in Palm Beach
County in 2000,
577
16.2
Water Quality Data,
578
16.3
Predicting
Lifespan?, 588
16.4
Scottish Hill Races Data,
591
16.5
Leukemia Data,
593
16.5.1
У
Binary,
593
16.5.2
ľ
Continuous,
598
CONTENTS XVII
16.6
Dosage
Response
Data,
599
16.7
A
Strategy for Analyzing Regression Data,
602
16.8
Summary,
604
References,
604
Exercises,
606
Answers to Selected Exercises
609
Statistical Tables
617
Author Index
625
Subject Index
637 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Ryan, Thomas P. 1945- |
| author_GND | (DE-588)141559098 |
| author_facet | Ryan, Thomas P. 1945- |
| author_role | aut |
| author_sort | Ryan, Thomas P. 1945- |
| author_variant | t p r tp tpr |
| building | Verbundindex |
| bvnumber | BV035063445 |
| callnumber-first | Q - Science |
| callnumber-label | QA278 |
| callnumber-raw | QA278.2 |
| callnumber-search | QA278.2 |
| callnumber-sort | QA 3278.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 840 |
| ctrlnum | (OCoLC)242573667 (DE-599)BVBBV035063445 |
| dewey-full | 519.5/36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/36 |
| dewey-search | 519.5/36 |
| dewey-sort | 3519.5 236 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035063445 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:01:25Z |
| indexdate | 2024-07-09T21:21:22Z |
| institution | BVB |
| isbn | 9780470081860 |
| language | English |
| lccn | 2008035085 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016731937 |
| oclc_num | 242573667 |
| open_access_boolean | |
| owner | DE-703 DE-634 DE-824 |
| owner_facet | DE-703 DE-634 DE-824 |
| physical | XIX, 642 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Ryan, Thomas P. 1945- Verfasser (DE-588)141559098 aut Modern regression methods Thomas P. Ryan 2. ed. Hoboken, NJ Wiley 2009 XIX, 642 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Includes bibliographical references and index 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 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016731937&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ryan, Thomas P. 1945- Modern regression methods 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_exact_search_txtP | 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 | Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd |
| topic_facet | Regression analysis Regressionsanalyse Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016731937&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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