Regression models for categorical and count data:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Los Angeles ; London ; New Delhi ; Singapore ; Washington DC ; Melbourne
Sage
[2021]
|
| Schriftenreihe: | The Sage quantitative research kit
8th volume |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Enthält Literaturverzeichnis Seite 237-242 und Index |
| Beschreibung: | xiv, 247 Seiten Diagramme |
| ISBN: | 9781529761269 |
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| adam_text | CONTENTS List ofFigures, Tables and Boxes About the Author Acknowledgements Preface 1 2 Introduction ix xv xvii xix 1 Why Study Regression Models for Categorical and Count Data? A Few Words on Terminology Outcome and Predictor Types of Variables Why Do We Need to Look Beyond Linear Regression? Regression Beyond the Linear Model: An Illustrated Introduction Linear Regression: A Reminder, With Some Mathematical Notation Regression Model and Notation Errors and Residuals Estimation and Partition of Outcome Variance Generalised Linear Models What s the Same and What s Different How You Might Use This Book 2 3 3 3 4 4 8 8 9 9 10 11 13 Logistic Regression 15 What Is Logistic Regression? Probabilities and Conditional Probabilities Simple Example of Data With a Binary Outcome Analysis of a 2 x 2 Table: Probabilities, Odds and Odds Ratios Probabilities Risk Ratio and Absolute Risk Difference Odds Log Odds: The Logit Transformation Odds Ratio Logistic Regression: The Model 16 17 18 20 20 20 21 23 25 26
vi REGRESSION MODELS FOR CATEGORICAL AND COUNT DATA Logistic Regression With a Single Categorical Predictor Predicted Probabilities Estimated Odds Ratio From a Logistic Regression Model Don t the Numbers Look Familiar? Logistic Regression With Two Categorical Predictors A Simple Model With Two Categorical Predictors Modelling an Interaction Illustrating the Models With and Without an Interaction Odds Ratios Predicted Probabilities Logistic Regression With a Numeric Predictor Logistic Regression: Assumptions and Estimation The Binomial Distribution The Logistic Curve Maximum Likelihood Estimation: How the Coefficients Are Found Confidence Intervals Model Comparison and Hypothesis Tests Likelihood Ratio Test Wald Test (or z-Test) Logistic Regression: An Example With Multiple Predictors Model Evaluation Residuals in Logistic Regression Model Calibration: Graphical Exploration The Hosmer-Lemeshow Test of Model Calibration Model Quality Indices for Logistic Regression Interpretation of Effect Sizes and Graphical Illustration Things That Might Go Wrong: Estimation Problems Logistic Regression in Action Exploring the Relationship Between Age and Attending Pop Concerts Logistic Regression of Pop Concert Attendance on Six Predictors Non-Binary Categorical Variables 3 * 28 29 30 31 32 32 33 34 35 36 37 43 43 45 47 48 50 50 52 53 57 57 58 60 63 65 67 70 71 73 75 Ordinal Logistic Regression: The Generalised Ordered Logit Model 79 Modelling Ordinal Outcomes: Proportional Odds or Non-Proportional Odds? Calculating Predicted Probabilities The Proportional Odds Ordinal Logistic Regression
Model Testing the Proportional Odds Assumption: Brant s Test Generalised Ordinal Logit Models: Full, Partial and Non-Proportional Odds 80 87 88 94 96
CONTENTS vii A Case Where the Proportional Odds Assumption Is Not Met 96 The Non-Proportional Odds Model 98 The Partial Proportional Odds Model 99 Likelihood Ratio Test Comparing Proportional Odds, Partial Proportional Odds and Non-Proportional Odds Models 4 101 Ordinal Logistic Regression in Action 102 Multinomial Logistic Regression 111 Example Data for Multinomial Logistic Regression 112 Relative Risks 114 Relative Risk Ratios 116 A Simple Example of Multinomial Logistic Regression 117 The Multinomial Logistic Regression Model 119 Predicted Probabilities 121 Interpreting and Illustrating the Results From a Multinomial Logistic Model 122 Example Research Question 122 Interpreting Results From a Multinomial Logistic Model 123 Illustrating Results From a Multinomial Logistic Model 124 Hypothesis Tests and Confidence Intervals 5 125 Likelihood Ratio Test for Comparison of Nested Models 126 The z-Test for an Individual Coefficient 128 Confidence Intervals 130 Test for Combining Outcome Categories 131 Multinomial Regression: Some Additional Comments 132 How to Choose the Reference Outcome Category 132 Categorical Predictors With Dummy Variables 133 Multinomial Logistic Regression in Action 134 Regression Models for Count Data 145 Distributions for Count Data 147 The Poisson Distribution 147 The Negative Binomial Distribution 151 Poisson Regression 153 Research Example: Police Operations Against Street Vendors in Latin American Capitals 154 Poisson Regression ofPolice Operations in Bogota 155 The Incidence Rate Ratio 157 Visualising the Estimated Regression Line From a Poisson
Model 158 Negative Binomial Regression 159
REGRESSION MODELS FOR CATEGORICAL AND COUNT DATA viii Zero-Truncation: When No Zeroes Are Observed 164 Too Many Zeroes: Zero-Inflation and Hurdle Models 165 Zero-Inflated Count Distributions Count Distributions With Hurdles 166 167 Models for Outcomes With Excess Zeroes 168 Model Comparison and Inference Investigating Overdispersion: Poisson or Negative Binomial Model? 177 Information Criteria 180 Inference for Individual Parameters and Nested Models Within the Same Model Type 184 On Standard Errors in Count Models 186 Model Evaluation Deviance Residuals for Poisson and Negative Binomial Regression Offsets: Accounting for Population Size, Time of Exposure, or Area What Is an Offset, and Why Might We Need One? Research Example: Socio-Economic Differences in the Uptake Rate ofFree Eye Tests 6 176 186 187 190 190 191 The Practice of Modelling 197 Decision-Making in Statistical Modelling 198 Match Between the Statistical Model and the Aims of the Research 199 Most Rules Are Just Guidelines 201 Usually You Can t Be Sure That You Have Found the Best Model 201 The Importance of the Analysts Judgement 203 Some General Principles That Apply Most of the Time What If We re Not Sure About Model Assumptions: Sensitivity Analysis 205 206 How to Test a Finding: Replication and Out-of-Sample Prediction Statistical Models and Uncertainty 207 209 Two Ways of Getting It Wrong: Overfitting and Underfitting 210 Is Science in a Statistical Crisis? On p-Values and Hypothesis Tests 214 Critique of Current Practice Around Statistical Hypothesis Tests 215 What Is a Statistical Hypothesis Test
Again? 215 Misuses and Misunderstandings ofp-Values 218 Exclusive Focus on Hypothesis Tests Distracts From Other Useful Purposes of Models Beyond This Book: Other Types of Models Glossary ■ 222 224 227 References 237 Index 243
|
| adam_txt |
CONTENTS List ofFigures, Tables and Boxes About the Author Acknowledgements Preface 1 2 Introduction ix xv xvii xix 1 Why Study Regression Models for Categorical and Count Data? A Few Words on Terminology Outcome and Predictor Types of Variables Why Do We Need to Look Beyond Linear Regression? Regression Beyond the Linear Model: An Illustrated Introduction Linear Regression: A Reminder, With Some Mathematical Notation Regression Model and Notation Errors and Residuals Estimation and Partition of Outcome Variance Generalised Linear Models What's the Same and What's Different How You Might Use This Book 2 3 3 3 4 4 8 8 9 9 10 11 13 Logistic Regression 15 What Is Logistic Regression? Probabilities and Conditional Probabilities Simple Example of Data With a Binary Outcome Analysis of a 2 x 2 Table: Probabilities, Odds and Odds Ratios Probabilities Risk Ratio and Absolute Risk Difference Odds Log Odds: The Logit Transformation Odds Ratio Logistic Regression: The Model 16 17 18 20 20 20 21 23 25 26
vi REGRESSION MODELS FOR CATEGORICAL AND COUNT DATA Logistic Regression With a Single Categorical Predictor Predicted Probabilities Estimated Odds Ratio From a Logistic Regression Model Don't the Numbers Look Familiar? Logistic Regression With Two Categorical Predictors A Simple Model With Two Categorical Predictors Modelling an Interaction Illustrating the Models With and Without an Interaction Odds Ratios Predicted Probabilities Logistic Regression With a Numeric Predictor Logistic Regression: Assumptions and Estimation The Binomial Distribution The Logistic Curve Maximum Likelihood Estimation: How the Coefficients Are Found Confidence Intervals Model Comparison and Hypothesis Tests Likelihood Ratio Test Wald Test (or z-Test) Logistic Regression: An Example With Multiple Predictors Model Evaluation Residuals in Logistic Regression Model Calibration: Graphical Exploration The Hosmer-Lemeshow Test of Model Calibration Model Quality Indices for Logistic Regression Interpretation of Effect Sizes and Graphical Illustration Things That Might Go Wrong: Estimation Problems Logistic Regression in Action Exploring the Relationship Between Age and Attending Pop Concerts Logistic Regression of Pop Concert Attendance on Six Predictors Non-Binary Categorical Variables 3 * 28 29 30 31 32 32 33 34 35 36 37 43 43 45 47 48 50 50 52 53 57 57 58 60 63 65 67 70 71 73 75 Ordinal Logistic Regression: The Generalised Ordered Logit Model 79 Modelling Ordinal Outcomes: Proportional Odds or Non-Proportional Odds? Calculating Predicted Probabilities The Proportional Odds Ordinal Logistic Regression
Model Testing the Proportional Odds Assumption: Brant's Test Generalised Ordinal Logit Models: Full, Partial and Non-Proportional Odds 80 87 88 94 96
CONTENTS vii A Case Where the Proportional Odds Assumption Is Not Met 96 The Non-Proportional Odds Model 98 The Partial Proportional Odds Model 99 Likelihood Ratio Test Comparing Proportional Odds, Partial Proportional Odds and Non-Proportional Odds Models 4 101 Ordinal Logistic Regression in Action 102 Multinomial Logistic Regression 111 Example Data for Multinomial Logistic Regression 112 Relative Risks 114 Relative Risk Ratios 116 A Simple Example of Multinomial Logistic Regression 117 The Multinomial Logistic Regression Model 119 Predicted Probabilities 121 Interpreting and Illustrating the Results From a Multinomial Logistic Model 122 Example Research Question 122 Interpreting Results From a Multinomial Logistic Model 123 Illustrating Results From a Multinomial Logistic Model 124 Hypothesis Tests and Confidence Intervals 5 125 Likelihood Ratio Test for Comparison of Nested Models 126 The z-Test for an Individual Coefficient 128 Confidence Intervals 130 Test for Combining Outcome Categories 131 Multinomial Regression: Some Additional Comments 132 How to Choose the Reference Outcome Category 132 Categorical Predictors With Dummy Variables 133 Multinomial Logistic Regression in Action 134 Regression Models for Count Data 145 Distributions for Count Data 147 The Poisson Distribution 147 The Negative Binomial Distribution 151 Poisson Regression 153 Research Example: Police Operations Against Street Vendors in Latin American Capitals 154 Poisson Regression ofPolice Operations in Bogota 155 The Incidence Rate Ratio 157 Visualising the Estimated Regression Line From a Poisson
Model 158 Negative Binomial Regression 159
REGRESSION MODELS FOR CATEGORICAL AND COUNT DATA viii Zero-Truncation: When No Zeroes Are Observed 164 Too Many Zeroes: Zero-Inflation and Hurdle Models 165 Zero-Inflated Count Distributions Count Distributions With Hurdles 166 167 Models for Outcomes With Excess Zeroes 168 Model Comparison and Inference Investigating Overdispersion: Poisson or Negative Binomial Model? 177 Information Criteria 180 Inference for Individual Parameters and Nested Models Within the Same Model Type 184 On Standard Errors in Count Models 186 Model Evaluation Deviance Residuals for Poisson and Negative Binomial Regression Offsets: Accounting for Population Size, Time of Exposure, or Area What Is an Offset, and Why Might We Need One? Research Example: Socio-Economic Differences in the Uptake Rate ofFree Eye Tests 6 176 186 187 190 190 191 The Practice of Modelling 197 Decision-Making in Statistical Modelling 198 Match Between the Statistical Model and the Aims of the Research 199 Most Rules Are Just Guidelines 201 Usually You Can't Be Sure That You Have Found the 'Best' Model 201 The Importance of the Analysts' Judgement 203 Some General Principles That Apply Most of the Time What If We're Not Sure About Model Assumptions: Sensitivity Analysis 205 206 How to Test a Finding: Replication and Out-of-Sample Prediction Statistical Models and Uncertainty 207 209 Two Ways of Getting It Wrong: Overfitting and Underfitting 210 Is Science in a Statistical Crisis? On p-Values and Hypothesis Tests 214 Critique of Current Practice Around Statistical Hypothesis Tests 215 What Is a Statistical Hypothesis Test
Again? 215 Misuses and Misunderstandings ofp-Values 218 Exclusive Focus on Hypothesis Tests Distracts From Other Useful Purposes of Models Beyond This Book: Other Types of Models Glossary ■ 222 224 227 References 237 Index 243 |
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| spelling | Martin, Peter Verfasser (DE-588)1046973851 aut Regression models for categorical and count data Peter Martin Los Angeles ; London ; New Delhi ; Singapore ; Washington DC ; Melbourne Sage [2021] xiv, 247 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier The Sage quantitative research kit 8th volume Enthält Literaturverzeichnis Seite 237-242 und Index Zähldaten (DE-588)4588029-3 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 gnd rswk-swf Kategoriale Daten (DE-588)4327512-6 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 s Kategoriale Daten (DE-588)4327512-6 s Zähldaten (DE-588)4588029-3 s DE-604 The Sage quantitative research kit 8th volume (DE-604)BV047607953 8 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032995503&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title_short | Regression models for categorical and count data |
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