Regression analysis: a constructive critique
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Thousand Oaks, Calif.
Sage Publ.
2004
|
| Schriftenreihe: | Advanced quantitative techniques in the social sciences
11 |
| Schlagworte: | |
| Online-Zugang: | Table of contents Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 239-250) and index |
| Beschreibung: | XIX, 259 S. Ill. |
| ISBN: | 0761929045 |
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| adam_text | Contents
Series Editor s Introduction xi
Preface xvii
1. Prologue: Regression Analysis as Problematic 1
2. A Grounded Introduction to Regression Analysis 5
2.1 Some Examples of Regression Analysis 5
2.1.1 Abortion and Subsequent Crime 5
2.1.2 Mandatory Basic Education
for Welfare Recipients 6
2.1.3 Gender and Academic Salaries 7
2.1.4 Climate Change and Water Resources in India 8
2.1.5 Deforestation and Soil Erosion in the Yangtze
River Valley 8
2.1.6 Epidemics of Hepatitis C 9
2.1.7 Onward and Upward 9
2.2 What Is Regression Analysis? 10
2.2.1 A Simple Illustration 10
2.2.2 Controlling for a Third Variable 13
2.2.3 Imposing a Smoother 16
2.3 Getting From Data to Stories 18
3. Simple Linear Regression 21
3.1 Introduction 21
3.2 Describing a Conditional Relationship
With a Straight Line 22
3.3 Defining the “Best” Line 24
3.4 Some Useful Formulas 27
3.5 Standardized Slopes 28
3.6 Using Transformations for a Nonlinear Fit 30
3.7 What About the Variance Function? 35
3.8 Summary and Conclusions 37
4. Statistical Inference for Simple Linear Regression 39
4.1 The Role of Sampling 39
4.1.1 Random Sampling 39
4.1.2 Strategy I: Treating the Data as Population 42
4.1.3 Strategy II: Treating the Data as If They Were
Generated by Random Sampling From a Population 44
4.1.4 Strategy III: Inventing an Imaginary Population 51
4.1.5 Strategy IV: Model-Based Sampling—Inventing
a Friendly Natural Process Responsible for the Data 53
4.1.6 A Note on Randomization Inference 56
4.1.7 Summing Up 58
4.2 Simple Linear Regression Under Random Sampling 58
4.2.1 Estimating the Population Regression Line 58
4.2.2 Estimating the Standard Errors 61
4.2.3 Estimation Under Model-Based Sampling 62
4.2.4 Some Things That Can Go Wrong 62
4.2.5 Tests and Confidence Intervals 65
4.3 Statistical Power 69
4.4 Stochastic Predictors 69
4.5 Measurement Error 73
4.6 Can Resampling Techniques Help? 74
4.6.1 Percentile Confidence Intervals 76
4.6.2 Hypothesis Testing 77
4.6.3 Bootstrapping Regression 77
4.6.4 Possible Benefits From Resampling 78
4.7 Summary and Conclusions 79
5. Causal Inference for the Simple Linear Model 81
5.1 Introduction 81
5.2 Some Definitions: What’s a Causal Effect? 82
5.2.1 The Neyman-Rubin Model 84
5.2.2 Thinking About Causal Effects
as Response Schedules 88
5.2.3 What’s an Intervention? 90
5.3 Studying Cause and Effect With Data 97
5.3.1 Using Nonstatistical Solutions
for Making Causal Inferences 97
5.3.2 Using Statistical Solutions for Making
Causal Inferences 98
5.3.3 Using the Simple Linear Model
for Making Causal Inferences 99
5.4 Summary and Conclusions 101
6. The Formalities of Multiple Regression 103
6.1 Introduction
6.2 Terms and Predictors ^03
6.3 Some Notation for Multiple Regression 105
6.4 Estimation 105
6.5 How Multiple Regression “Holds Constant” 107
6.6 Summary and Conclusions 110
7. Using and Interpreting Multiple Regression 111
7.1 Introduction 111
7.2 Another Formal Perspective on Holding Constant 111
7.3 When Does Holding Constant Make Sense? 113
7.4 Standardized Regression Coefficients:
Once More With Feeling 117
7.5 Variances of the Coefficient Estimates 119
7.6 Summary and Conclusions 122
8. Some Popular Extensions of Multiple Regression 125
8.1 Introduction 125
8.2 Model Selection and Stepwise Regression 126
8.2.1 Model Selection by Removing Terms 127
8.2.2 Tests to Compare Models 128
8.2.3 Selecting Terms Without Testing 130
8.2.4 Stepwise Selection Methods 132
8.2.5 Some Implications 133
8.3 Using Categorical Terms: Analysis of Variance
and Analysis of Covariance 135
8.3.1 An Extended Example 135
8.4 Back to the Variance Function:
Weighted Least Squares 141
8.4.1 Visualizing Lack of Fit 141
8.4.2 Weighted Least Squares as a Possible Fix 142
8.4.3 Evaluating the Mean Function 145
8.5 Locally Weighted Regression Smoother 147
8.6 Summary and Conclusions 148
9. Some Regression Diagnostics 151
9.1 Introduction 151
9.2 Transformations of the Response Variable 152
9.2.1 Box-Cox Procedures 152
9.2.2 Inverse Fitted Value Response Plots 153
9.3 Leverage and Influence 159
9.3.1 Influential Cases and Cook’s Distance 159
9.4 Cross-Validation 162
9.5 Misspeciflcation Tests 163
9.5.1 Instrumental Variables 164
9.5.2 Tests for Exogeneity 167
9.6 Conclusions 168
10. Further Extensions of Regression Analysis 171
10.1 Regression Models for Longitudinal Data 171
10.1.1 Multiple Linear Regression for Time Series Data 172
10.2 Regression Analysis With Multiple
Time Series Data * 77
10.2.1 Fixed Effects Models 178
10.2.2 Random Effects Models 178
10.2.3 Estimation 18®
10.3 Multilevel Models 18®
10.4 The Generalized Linear Model 183
10.4.1 GLM Structure 183
10.4.2 Normal Models 184
10.4.3 Poisson Models 184
10.4.4 Poisson Models for Contingency Tables 186
10.4.5 Binomial Regression 186
10.5 Multiple Equation Models 188
10.5.1 Causal Inference Once Again 191
10.5.2 A Final Observation 196
10.6 Meta-Analysis 196
10.7 Conclusions 200
11. What to Do 203
11.1 How Did We Get Into This Mess? 203
11.2 Three Cheers for Description 206
11.2.1 What’s Description? 207
11.2.2 Advocacy Settings 207
11.2.3 Descriptive Regressions as Part of a Broad
Research Program 209
11.2.4 Spotting Provocative Associations 210
11.2.5 Some Other Benefits of Description 212
11.3 Two Cheers for Statistical Inference 218
11.3.1 Working With Near-Random Samples 220
11.3.2 Working With Data From Nature 222
11.3.3 Working With a Nearly Correct Model 222
11.4 One Cheer for Causal Inference 223
11.4.1 Special-Purpose Estimators 226
11.4.2 Propensity Scores 230
11.4.3 Sensitivity Analysis of the Selection Process 231
11.4.4 Bounding Treatment Effects 232
11.4.5 Some Forecasts 234
11.5 Some Final Observations 234
11.5.1 A Police Story 234
11.5.2 Regression Analysis as Too Little, Too Late 237
References
Index
About the Author
239
251
259
|
| adam_txt |
Contents
Series Editor's Introduction xi
Preface xvii
1. Prologue: Regression Analysis as Problematic 1
2. A Grounded Introduction to Regression Analysis 5
2.1 Some Examples of Regression Analysis 5
2.1.1 Abortion and Subsequent Crime 5
2.1.2 Mandatory Basic Education
for Welfare Recipients 6
2.1.3 Gender and Academic Salaries 7
2.1.4 Climate Change and Water Resources in India 8
2.1.5 Deforestation and Soil Erosion in the Yangtze
River Valley 8
2.1.6 Epidemics of Hepatitis C 9
2.1.7 Onward and Upward 9
2.2 What Is Regression Analysis? 10
2.2.1 A Simple Illustration 10
2.2.2 Controlling for a Third Variable 13
2.2.3 Imposing a Smoother 16
2.3 Getting From Data to Stories 18
3. Simple Linear Regression 21
3.1 Introduction 21
3.2 Describing a Conditional Relationship
With a Straight Line 22
3.3 Defining the “Best” Line 24
3.4 Some Useful Formulas 27
3.5 Standardized Slopes 28
3.6 Using Transformations for a Nonlinear Fit 30
3.7 What About the Variance Function? 35
3.8 Summary and Conclusions 37
4. Statistical Inference for Simple Linear Regression 39
4.1 The Role of Sampling 39
4.1.1 Random Sampling 39
4.1.2 Strategy I: Treating the Data as Population 42
4.1.3 Strategy II: Treating the Data as If They Were
Generated by Random Sampling From a Population 44
4.1.4 Strategy III: Inventing an Imaginary Population 51
4.1.5 Strategy IV: Model-Based Sampling—Inventing
a Friendly Natural Process Responsible for the Data 53
4.1.6 A Note on Randomization Inference 56
4.1.7 Summing Up 58
4.2 Simple Linear Regression Under Random Sampling 58
4.2.1 Estimating the Population Regression Line 58
4.2.2 Estimating the Standard Errors 61
4.2.3 Estimation Under Model-Based Sampling 62
4.2.4 Some Things That Can Go Wrong 62
4.2.5 Tests and Confidence Intervals 65
4.3 Statistical Power 69
4.4 Stochastic Predictors 69
4.5 Measurement Error 73
4.6 Can Resampling Techniques Help? 74
4.6.1 Percentile Confidence Intervals 76
4.6.2 Hypothesis Testing 77
4.6.3 Bootstrapping Regression 77
4.6.4 Possible Benefits From Resampling 78
4.7 Summary and Conclusions 79
5. Causal Inference for the Simple Linear Model 81
5.1 Introduction 81
5.2 Some Definitions: What’s a Causal Effect? 82
5.2.1 The Neyman-Rubin Model 84
5.2.2 Thinking About Causal Effects
as Response Schedules 88
5.2.3 What’s an Intervention? 90
5.3 Studying Cause and Effect With Data 97
5.3.1 Using Nonstatistical Solutions
for Making Causal Inferences 97
5.3.2 Using Statistical Solutions for Making
Causal Inferences 98
5.3.3 Using the Simple Linear Model
for Making Causal Inferences 99
5.4 Summary and Conclusions 101
6. The Formalities of Multiple Regression 103
6.1 Introduction
6.2 Terms and Predictors ^03
6.3 Some Notation for Multiple Regression 105
6.4 Estimation 105
6.5 How Multiple Regression “Holds Constant” 107
6.6 Summary and Conclusions 110
7. Using and Interpreting Multiple Regression 111
7.1 Introduction 111
7.2 Another Formal Perspective on Holding Constant 111
7.3 When Does Holding Constant Make Sense? 113
7.4 Standardized Regression Coefficients:
Once More With Feeling 117
7.5 Variances of the Coefficient Estimates 119
7.6 Summary and Conclusions 122
8. Some Popular Extensions of Multiple Regression 125
8.1 Introduction 125
8.2 Model Selection and Stepwise Regression 126
8.2.1 Model Selection by Removing Terms 127
8.2.2 Tests to Compare Models 128
8.2.3 Selecting Terms Without Testing 130
8.2.4 Stepwise Selection Methods 132
8.2.5 Some Implications 133
8.3 Using Categorical Terms: Analysis of Variance
and Analysis of Covariance 135
8.3.1 An Extended Example 135
8.4 Back to the Variance Function:
Weighted Least Squares 141
8.4.1 Visualizing Lack of Fit 141
8.4.2 Weighted Least Squares as a Possible Fix 142
8.4.3 Evaluating the Mean Function 145
8.5 Locally Weighted Regression Smoother 147
8.6 Summary and Conclusions 148
9. Some Regression Diagnostics 151
9.1 Introduction 151
9.2 Transformations of the Response Variable 152
9.2.1 Box-Cox Procedures 152
9.2.2 Inverse Fitted Value Response Plots 153
9.3 Leverage and Influence 159
9.3.1 Influential Cases and Cook’s Distance 159
9.4 Cross-Validation 162
9.5 Misspeciflcation Tests 163
9.5.1 Instrumental Variables 164
9.5.2 Tests for Exogeneity 167
9.6 Conclusions 168
10. Further Extensions of Regression Analysis 171
10.1 Regression Models for Longitudinal Data 171
10.1.1 Multiple Linear Regression for Time Series Data 172
10.2 Regression Analysis With Multiple
Time Series Data * 77
10.2.1 Fixed Effects Models 178
10.2.2 Random Effects Models 178
10.2.3 Estimation 18®
10.3 Multilevel Models 18®
10.4 The Generalized Linear Model 183
10.4.1 GLM Structure 183
10.4.2 Normal Models 184
10.4.3 Poisson Models 184
10.4.4 Poisson Models for Contingency Tables 186
10.4.5 Binomial Regression 186
10.5 Multiple Equation Models 188
10.5.1 Causal Inference Once Again 191
10.5.2 A Final Observation 196
10.6 Meta-Analysis 196
10.7 Conclusions 200
11. What to Do 203
11.1 How Did We Get Into This Mess? 203
11.2 Three Cheers for Description 206
11.2.1 What’s Description? 207
11.2.2 Advocacy Settings 207
11.2.3 Descriptive Regressions as Part of a Broad
Research Program 209
11.2.4 Spotting Provocative Associations 210
11.2.5 Some Other Benefits of Description 212
11.3 Two Cheers for Statistical Inference 218
11.3.1 Working With Near-Random Samples 220
11.3.2 Working With Data From Nature 222
11.3.3 Working With a Nearly Correct Model 222
11.4 One Cheer for Causal Inference 223
11.4.1 Special-Purpose Estimators 226
11.4.2 Propensity Scores 230
11.4.3 Sensitivity Analysis of the Selection Process 231
11.4.4 Bounding Treatment Effects 232
11.4.5 Some Forecasts 234
11.5 Some Final Observations 234
11.5.1 A Police Story 234
11.5.2 Regression Analysis as Too Little, Too Late 237
References
Index
About the Author
239
251
259 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T13:50:18Z |
| indexdate | 2024-07-09T20:34:54Z |
| institution | BVB |
| isbn | 0761929045 |
| language | English |
| lccn | 2003046500 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014613474 |
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| series | Advanced quantitative techniques in the social sciences |
| series2 | Advanced quantitative techniques in the social sciences |
| spelling | Berk, Richard Verfasser (DE-588)142027235 aut Regression analysis a constructive critique Richard A. Berk Thousand Oaks, Calif. Sage Publ. 2004 XIX, 259 S. Ill. txt rdacontent n rdamedia nc rdacarrier Advanced quantitative techniques in the social sciences 11 Includes bibliographical references (p. 239-250) and index Analyse de régression Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s DE-604 Advanced quantitative techniques in the social sciences 11 (DE-604)BV023546702 11 http://www.loc.gov/catdir/toc/fy038/2003046500.html Table of contents Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014613474&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berk, Richard Regression analysis a constructive critique Advanced quantitative techniques in the social sciences Analyse de régression Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd |
| subject_GND | (DE-588)4129903-6 |
| title | Regression analysis a constructive critique |
| title_auth | Regression analysis a constructive critique |
| title_exact_search | Regression analysis a constructive critique |
| title_exact_search_txtP | Regression analysis a constructive critique |
| title_full | Regression analysis a constructive critique Richard A. Berk |
| title_fullStr | Regression analysis a constructive critique Richard A. Berk |
| title_full_unstemmed | Regression analysis a constructive critique Richard A. Berk |
| title_short | Regression analysis |
| title_sort | regression analysis a constructive critique |
| title_sub | a constructive critique |
| topic | Analyse de régression Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd |
| topic_facet | Analyse de régression Regressieanalyse Regression analysis Regressionsanalyse |
| url | http://www.loc.gov/catdir/toc/fy038/2003046500.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014613474&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023546702 |
| work_keys_str_mv | AT berkrichard regressionanalysisaconstructivecritique |