Applied regression analysis and generalized linear models:
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| Previous Title: | Fox, John Applied regression analysis, linear models, and related methods |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
Los Angeles [u.a.]
Sage
2008
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XXI, 665 S. zahlr. graph. Darst. |
| ISBN: | 9780761930426 |
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| _version_ | 1804139247553216512 |
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| adam_text | Titel: Applied regression analysis and generalized linear models
Autor: Fox, John
Jahr: 2008
Contents
Preface xiv
1 Statistical Models and Social Science 1
1.1 Statistical Models and Social Reality 1
1.2 Observation and Experiment 4
1.3 Populations and Samples 8
Exercise 9
Summary 9
Recommended Reading 10
PART I DATA CRAFT 11
2 What Is Regression Analysis? 13
2.1 Preliminaries 15
2.2 Naive Nonparametric Regression 17
2.3 Local Averaging 21
Exercise 24
Summary 25
3 Examining Data 26
3.1 Univariate Displays 28
3.1.1 Histograms 28
3.1.2 Nonparametric Density Estimation 30
3.1.3 Quantile-Comparison Plots 34
3.1.4 Boxplots 37
3.2 Plotting Bivariate Data 40
3.3 Plotting Multivaríate Data 43
3.3.1 Scatterplot Matrices 44
3.3.2 Coded Scatterplots 45
3.3.3 Three-Dimensional Scatterplots 45
3.3.4 Conditioning Plots 46
Summary 47
Recommended Reading 49
4 Transforming Data 50
4.1 The Family of Powers and Roots 50
4.2 Transforming Skewness 54
4.3 Transforming Nonlinearity 57
4.4 Transforming Nonconstant Spread 63
4.5 Transforming Proportions 66
4.6 Estimating Transformations as Parameters* 68
Exercises 71
Summary 72
Recommended Reading 72
PART II LINEAR MODELS AND LEAST SQUARES 75
5 Linear Least-Squares Regression 77
5.1 Simple Regression 78
5.1.1 Least-Squares Fit 78
5.1.2 Simple Correlation 82
5.2 Multiple Regression 86
5.2.1 Two Explanatory Variables 86
5.2.2 Several Explanatory Variables 90
5.2.3 Multiple Correlation 92
5.2.4 Standardized Regression Coefficients 94
Exercises 96
Summary 98
6 Statistical Inference for Regression 100
6.1 Simple Regression 100
6.1.1 The Simple-Regression Model 100
6.1.2 Properties of the Least-Squares Estimator 102
6.1.3 Confidence Intervals and Hypothesis Tests 104
6.2 Multiple Regression 105
6.2.1 The Multiple-Regression Model 105
6.2.2 Confidence Intervals and Hypothesis Tests 106
6.3 Empirical Versus Structural Relations 110
6.4 Measurement Error in Explanatory Variables* 112
Exercises 115
Summary 118
7 Dummy-Variable Regression 120
7.1 A Dichotomous Factor 120
7.2 Polytomous Factors 124
7.2.1 Coefficient Quasi-Variances* 129
7.3 Modeling Interactions 131
7.3.1 Constructing Interaction Regressors 132
7.3.2 The Principle of Marginality 135
7.3.3 Interactions With Polytomous Factors 135
7.3.4 Interpreting Dummy-Regression Models With Interactions 136
7.3.5 Hypothesis Tests for Main Effects and Interactions 137
7.4 A Caution Concerning Standardized Coefficients 140
Exercises 140
Summary 141
8 Analysis of Variance 143
8.1 One-Way Analysis of Variance 143
8.2 Two-Way Analysis of Variance 149
8.2.1 Patterns of Means in the Two-Way Classification 149
8.2.2 The Two-WayANOVA Model 154
8.2.3 Fitting the Two-Way ANOVA Model to Data 156
8.2.4 Testing Hypotheses in Two-Way ANOVA 158
8.2.5 Equal Cell Frequencies 161
8.2.6 Some Cautionary Remarks 162
8.3 Higher-Way Analysis of Variance 163
8.3.1 The Three-Way Classification 163
8.3.2 Higher-Order Classifications 166
8.3.3 Empty Cells in ANOVA 172
8.4 Analysis of Covariance 173
8.5 Linear Contrasts of Means 176
Exercises 180
Summary 185
9 Statistical Theory for Linear Models* 187
9.1 Linear Models in Matrix Form 187
9.1.1 Dummy Regression and Analysis of Variance 188
9.1.2 Linear Contrasts 191
9.2 Least-Squares Fit 192
9.3 Properties of the Least-Squares Estimator 194
9.3.1 The Distribution of the Least-Squares Estimator 195
9.3.2 The Gauss-Markov Theorem 196
9.3.3 Maximum-Likelihood Estimation 197
9.4 Statistical Inference for Linear Models 198
9.4.1 Inference for Individual Coefficients 198
9.4.2 Inference for Several Coefficients 200
9.4.3 General Linear Hypotheses 202
9.4.4 Joint Confidence Regions 203
9.5 Multivariate Linear Models 207
9.6 Random Regressors 210
9.7 Specification Error 212
Exercises 213
Summary 217
Recommended Reading 219
10 The Vector Geometry of Linear Models* 220
10.1 Simple Regression 220
10.1.1 Variables in Mean-Deviation Form 222
10.1.2 Degrees of Freedom 224
10.2 Multiple Regression 226
10.3 Estimating the Error Variance 231
10.4 Analysis-of-Variance Models 233
Exercises 235
Summary 236
Recommended Reading 238
PART III LINEAR-MODEL DIAGNOSTICS 239
11 Unusual and Influential Data 241
11.1 Outliers, Leverage, and Influence 241
11.2 Assessing Leverage: Hat-Values 244
11.3 Detecting Outliers: Studentized Residuals 246
11.3.1 Testing for Outliers in Linear Models 247
11.3.2 Anscombe s Insurance Analogy 248
11.4 Measuring Influence 250
11.4.1 Influence on Standard Errors 252
11.4.2 Influence on Collinearity 253
11.5 Numerical Cutoffs for Diagnostic Statistics 254
11.5.1 Hat-Values 254
11.5.2 Studentized Residuals 254
11.5.3 Measures of Influence 255
11.6 Joint Influence 255
11.6.1 Added-Variable Plots 255
11.6.2 Forward Search 259
11.7 Should Unusual Data Be Discarded? 260
11.8 Some Statistical Details* 261
11.8.1 Hat-Values and the Hat-Matrix 261
11.8.2 The Distribution of the Least-Squares Residuals 262
11.8.3 Deletion Diagnostics 262
11.8.4 Added-Variable Plots and Leverage Plots 263
Exercises 264
Summary 265
Recommended Reading 266
12 Diagnosing Non-Normality, Nonconstant Error Variance, and Nonlinearity 267
12.1 Non-Normally Distributed Errors 268
12.1.1 Confidence Envelopes by Simulated Sampling* 271
12.2 Nonconstant Error Variance 272
12.2.1 Residual Plots 272
12.2.2 Weighted-Least-Squares Estimation* 274
12.2.3 Correcting OLS Standard Errors for Nonconstant Variance* 275
12.2.4 How Nonconstant Error Variance Affects the OLS Estimator* 276
12.3 Nonlinearity 277
12.3.1 Component-Plus-Residual Plots 278
12.3.2 Component-Plus-Residual Plots for Models With Interactions 282
12.3.3 When Do Component-Plus-Residual Plots Work? 284
12.4 Discrete Data 287
12.4.1 Testing for Nonlinearity ( Lack of Fit ) 287
12.4.2 Testing for Nonconstant Error Variance 290
12.5 Maximum-Likelihood Methods* 291
12.5.1 Box-Cox Transformation of y 292
12.5.2 Box-Tidwell Transformation of the Xs 294
12.5.3 Nonconstant Error Variance Revisited 296
12.6 Structural Dimension 298
Exercises 301
Summary 305
Recommended Reading 306
13 Collinearity and Its Purported Remedies 307
13.1 Detecting Collinearity 308
13.1.1 Principal Components* 313
13.1.2 Generalized Variance Inflation* 322
13.2 Coping With Collinearity: No Quick Fix 323
13.2.1 Model Respecification 323
13.2.2 Variable Selection 324
13.2.3 Biased Estimation 325
13.2.4 Prior Information About the Regression Coefficients 328
13.2.5 Some Comparisons 329
Exercises 330
Summary 331
PART IV GENERALIZED LINEAR MODELS 333
14 Logit and Probit Models for Categorical Response Variables 335
14.1 Models for Dichotomous Data 335
14.1.1 The Linear-Probability Model 337
14.1.2 Transformations of n: Logit and Probit Models 339
14.1.3 An Unobserved-Variable Formulation 343
14.1.4 Logit and Probit Models for Multiple Regression 344
14.1.5 Estimating the Linear Logit Model* 352
14.2 Models for Polytomous Data 355
14.2.1 The Polytomous Logit Model 355
14.2.2 Nested Dichotomies 361
14.2.3 Ordered Logit and Probit Models 363
14.2.4 Comparison of the Three Approaches 368
14.3 Discrete Explanatory Variables and Contingency Tables 370
14.3.1 The Binomial Logit Model* 372
Exercises 375
Summary 377
Recommended Reading 378
15 Generalized Linear Models 379
15.1 The Structure of Generalized Linear Models 379
15.1.1 Estimating and Testing GLMs 385
15.2 Generalized Linear Models for Counts 387
15.2.1 Models for Overdispersed Count Data 391
15.2.2 Loglinear Models for Contingency Tables 394
15.3 Statistical Theory for Generalized Linear Models* 402
15.3.1 Exponential Families 402
15.3.2 Maximum-Likelihood Estimation of Generalized Linear Models 404
15.3.3 Hypothesis Tests 408
15.3.4 Effect Displays 411
15.4 Diagnostics for Generalized Linear Models 412
15.4.1 Outlier, Leverage, and Influence Diagnostics 412
15.4.2 Nonlinearity Diagnostics 415
Exercises 417
Summary 421
Recommended Reading 424
PART V EXTENDING LINEAR AND GENERALIZED LINEAR MODELS 425
16 Time-Series Regression and Generalized Least Squares* 427
16.1 Generalized Least-Squares Estimation 428
16.2 Serially Correlated Errors 429
16.2.1 The First-Order Autoregressive Process 430
16.2.2 Higher-Order Autoregressive Processes 433
16.2.3 Moving-Average and Autoregressive-Moving-Average Processes 434
16.2.4 Partial Autocorrelations 436
16.3 GLS Estimation With Autocorrelated Errors 438
16.3.1 Empirical GLS Estimation 439
16.3.2 Maximum-Likelihood Estimation 440
16.4 Diagnosing Serially Correlated Errors 440
16.5 Concluding Remarks 444
Exercises 446
Summary 449
Recommended Reading 450
17 Nonlinear Regression 451
17.1 Polynomial Regression 452
17.1.1 A Closer Look at Quadratic Surfaces* 455
17.2 Piece-Wise Polynomials and Regression Splines 455
17.3 Transformable Nonlinearity 460
17.4 Nonlinear Least Squares* 463
17.4.1 Minimizing the Residual Sum of Squares 464
17.4.2 An Illustration: U.S. Population Growth 467
Exercises 469
Summary 474
Recommended Reading 475
18 Nonparametric Regression 476
18.1 Nonparametric Simple Regression: Scatterplot Smoothing 476
18.1.1 Kernel Regression 476
18.1.2 Local-Polynomial Regression 479
18.1.3 Smoothing Splines* 495
18.2 Nonparametric Multiple Regression 496
18.2.1 Local-Polynomial Multiple Regression 496
18.2.2 Additive Regression Models 508
18.3 Generalized Nonparametric Regres sion 517
18.3.1 Local Likelihood Estimation* 517
18.3.2 Generalized Additive Models 519
Exercises 523
Summary 526
Recommended Reading 529
19 Robust Regression* 530
19.1 M Estimation 530
19.1.1 Estimating Location 530
19.1.2 M Estimation in Regression 535
19.2 Bounded-Influence Regression 539
19.3 Quantile Regression 540
19.4 Robust Estimation of Generalized Linear Models 543
19.5 Concluding Remarks 544
Exercises 544
Summary 546
Recommended Reading 547
20 Missing Data in Regression Models 548
20.1 Missing Data Basics 549
20.1.1 An Illustration 550
20.2 Traditional Approaches to Missing Data 552
20.3 Maximum-Likelihood Estimation for Data Missing at Random* 556
20.3.1 The EM Algorithm 558
20.4 Bayesian Multiple Imputation 561
20.4.1 Inference for Individual Coefficients 563
20.4.2 Inference for Several Coefficients* 565
20.4.3 Practical Considerations 567
20.4.4 Example: A Regression Model for Infant Mortality 568
20.5 Selection Bias and Censoring 570
20.5.1 Truncated- and Censored-Normal Distributions 571
20.5.2 Heckman s Selection-Regression Model 573
20.5.3 Censored-Regression Models 578
Exercises 580
Summary 584
Recommended Reading 586
21 Bootstrapping Regression Models 587
21.1 Bootstrapping Basics 587
21.2 Bootstrap Confidence Intervals 594
21.2.1 Normal-Theory Intervals 594
21.2.2 Percentile Intervals 595
21.2.3 Improved Bootstrap Intervals 596
21.3 Bootstrapping Regression Models 597
21.4 Bootstrap Hypothesis Tests* 599
21.5 Bootstrapping Complex Sampling Designs 601
21.6 Concluding Remarks 602
Exercises 603
Summary 605
Recommended Reading 606
22 Model Selection, Averaging, and Validation 607
22.1 Model Selection 607
22.1.1 Model Selection Criteria 608
22.1.2 An Illustration: Baseball Salaries 618
22.1.3 Comments on Model Selection 620
22.2 Model Averaging* 622
22.2.1 Application to the Baseball Salary Data 624
22.2.2 Comments on Model Averaging 624
22.3 Model Validation 626
22.3.1 An Illustration: Refugee Appeals 628
22.3.2 Comments on Model Validation 630
Exercises 630
Summary 632
Recommended Reading 634
Appendix A: Notation 636
References 638
Author Index 648
Subject Index 652
Data Set Index 664
About the Author 665
|
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| discipline | Soziologie Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV035586866 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:41:03Z |
| institution | BVB |
| isbn | 9780761930426 |
| language | English |
| lccn | 2007047617 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017642158 |
| oclc_num | 176927374 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-473 DE-BY-UBG DE-945 DE-11 DE-83 DE-20 DE-188 DE-634 DE-824 DE-B768 DE-384 |
| owner_facet | DE-19 DE-BY-UBM DE-473 DE-BY-UBG DE-945 DE-11 DE-83 DE-20 DE-188 DE-634 DE-824 DE-B768 DE-384 |
| physical | XXI, 665 S. zahlr. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Sage |
| record_format | marc |
| spelling | Fox, John 1947- Verfasser (DE-588)132520346 aut Applied regression analysis and generalized linear models John Fox 2. ed. Los Angeles [u.a.] Sage 2008 XXI, 665 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Sozialwissenschaften Linear models (Statistics) Models, Theoretical Regression Analysis Regression analysis Social sciences Statistical methods Statistics as Topic Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Sozialwissenschaften (DE-588)4055916-6 gnd rswk-swf Lineares Regressionsmodell (DE-588)4127971-2 gnd rswk-swf Lineares Modell (DE-588)4134827-8 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s Lineares Modell (DE-588)4134827-8 s DE-604 Lineares Regressionsmodell (DE-588)4127971-2 s Sozialwissenschaften (DE-588)4055916-6 s 1\p DE-604 Statistik (DE-588)4056995-0 s 2\p DE-604 1. Auflage Fox, John Applied regression analysis, linear models, and related methods http://www.loc.gov/catdir/enhancements/fy0834/2007047617-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0834/2007047617-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0834/2007047617-t.html Table of contents only HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017642158&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fox, John 1947- Applied regression analysis and generalized linear models Sozialwissenschaften Linear models (Statistics) Models, Theoretical Regression Analysis Regression analysis Social sciences Statistical methods Statistics as Topic Regressionsanalyse (DE-588)4129903-6 gnd Statistik (DE-588)4056995-0 gnd Sozialwissenschaften (DE-588)4055916-6 gnd Lineares Regressionsmodell (DE-588)4127971-2 gnd Lineares Modell (DE-588)4134827-8 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4056995-0 (DE-588)4055916-6 (DE-588)4127971-2 (DE-588)4134827-8 |
| title | Applied regression analysis and generalized linear models |
| title_auth | Applied regression analysis and generalized linear models |
| title_exact_search | Applied regression analysis and generalized linear models |
| title_full | Applied regression analysis and generalized linear models John Fox |
| title_fullStr | Applied regression analysis and generalized linear models John Fox |
| title_full_unstemmed | Applied regression analysis and generalized linear models John Fox |
| title_old | Fox, John Applied regression analysis, linear models, and related methods |
| title_short | Applied regression analysis and generalized linear models |
| title_sort | applied regression analysis and generalized linear models |
| topic | Sozialwissenschaften Linear models (Statistics) Models, Theoretical Regression Analysis Regression analysis Social sciences Statistical methods Statistics as Topic Regressionsanalyse (DE-588)4129903-6 gnd Statistik (DE-588)4056995-0 gnd Sozialwissenschaften (DE-588)4055916-6 gnd Lineares Regressionsmodell (DE-588)4127971-2 gnd Lineares Modell (DE-588)4134827-8 gnd |
| topic_facet | Sozialwissenschaften Linear models (Statistics) Models, Theoretical Regression Analysis Regression analysis Social sciences Statistical methods Statistics as Topic Regressionsanalyse Statistik Lineares Regressionsmodell Lineares Modell |
| url | http://www.loc.gov/catdir/enhancements/fy0834/2007047617-b.html http://www.loc.gov/catdir/enhancements/fy0834/2007047617-d.html http://www.loc.gov/catdir/enhancements/fy0834/2007047617-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017642158&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT foxjohn appliedregressionanalysisandgeneralizedlinearmodels |