Linear regression models: applications in R
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, London, New York
CRC Press, Taylor & Francis Group
2022
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| Series: | Statistics in the social and behavioral sciences
A Chapman & Hall book |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xv, 420 Seiten Illustrationen, Diagramme |
| ISBN: | 9780367753689 9780367753665 |
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Contents Preface. ix Acknowledgments.xiii Author Biography. xv 1 Introduction. 1 Our Doubts are Traitors and Make Us Lose the Good We Oft Might Win. 2 Best Statistical Practices. 3 Statistical Software. 4 2 Review of Elementary Statistical Concepts.7 Measures of Central Tendency. 9 Measures of Dispersion.14 Samples and Populations. . 16 Sampling Error and Standard Errors. 17 Significance Tests. 19 Unbiasedness and Efficiency. 25 The Standard Normal Distribution and
Z-Scores. 26 Covariance and Correlation.28 Comparing Means from Two Groups.30 Examples Using R. 33 Chapter Summary. 35 Chapter Exercises. 35 3 Simple Linear Regression Models.37 Assumptions of Simple LRMs. 42 An Example of an LRM Using R. 44 Formulas for the Slope Coefficient and Intercept.51 Hypothesis Tests for the Slope Coefficient. 53 Chapter Summary. 61 Chapter Exercises. 62 4 Multiple Linear Regression Models.65 An Example of a Multiple LRM. 66 Comparing Slope Coefficients.74 Assumptions of Multiple LRMs. 80 Some Important
Characteristics of Multiple LRMs. 84 Chapter Summary. 85 Chapter Exercises. 86 v
Contents VI 5 The ANOVA Table and Goodness-of-Fit Statistics.89 Another Example of a Multiple LRM. 98 Chapter Summary. 101 Chapter Exercises.102 6 Comparing Linear Regression Models.105 The Partial F-Test and Multiple Partial F-Test. 106 Evaluating Model Fit with Information Criterion Measures.Ill Confounding Variables.112 Chapter Summary. 113 Chapter Exercises. 114 * * 7 Indicator Variables in Linear Regression Models.115 Indicator Variables in Multiple LRMs.121 LRMs with Indicator and Continuous Explanatory Variables. 124 Chapter Summary. 133 Chapter Exercises. 133 8 Independence.137 Determining
Dependence.139 Example of Adjustment for Clustering.141 LRM with No Adjustment for Clustering. 142 LRM That Adjusts for Clustering.143 Serial Correlation. 144 Linear Regression Model. 146 Solutions for Serial Correlation. 149 Linear Regression Model (OLS). 150 Prais-Winsten Regression Model.151 Generalized Estimating Equations for Longitudinal Data. 152 Linear Regression Model (OLS). 153 General Estimating Equation (GEE) Model with AR(1) Pattern.154 General Estimating Equation (GEE) Model with Unstructured Pattern. 155 Spatial Autocorrelation.158 Chapter Summary.161 Chapter Exercises. 162 9
Homoscedasticity. 165 Assessing Homoscedasticity in Multiple LRMs.169 What to Do About Heteroscedasticity.176 Chapter Summary. 183 Chapter Exercises. 184
Contents vii 10 Collinearity and Multicollinearity. 187 Multicollinearity. 192 How to Detect Collinearity and Multicollinearity. 193 What to Do About Collinearity and Multicollinearity.196 Chapter Summary.198 Chapter Exercises. 199 11 Normality, Linearity, and Interaction Effects. 201 Are the Errors of Prediction Normally Distributed?.202 Nonlinearities.209 Testing for Nonlinearities in LRMs.212 Incorporating Nonlinear Associations in LRMs. 215 Interaction Effects. 220 Interaction Effects with Continuous Explanatory Variables.228 Classification and Regression Trees (CART).233 A Cautionary Note about Interaction Effects.236 Chapter Summary. 237 Chapter
Exercises.,. 238 12 Model Specification.241 Variable Selection. 242 Overfitting—or the Case of Irrelevant Variables. 243 Underfitting—or the Case of the Absent Variables. 244 Endogeneity Bias. 250 Selection Bias.252 How Do We Assess Specification Error and What Do We Do about It?. 254 What to Do about Selection Bias?. 257 Cross-Validation. 262 Variable Selection Procedures. 269 Chapter Summary. 272 Chapter Exercises. 273 13 Measurement Errors.275 The Outcome Variable Is Measured with Error. 277 The Explanatory Variables Are Measured with
Error.279 What Should We Do about Measurement Error?. 280 Latent Variables as a Solution to Measurement Error.281 Chapter Summary. 290 Chapter Exercises.291 14 Influential Observations: Leverage Points and Outliers. 293 Detecting Influential Observations. 295 An Example of Using Diagnostic Methods to Identify Influential 298 Observations.
viii Contents What to Do about Influential Observations.303 Chapter Summary. 310 Chapter Exercises.311 15 Multilevel Linear Regression Models.313 The Basics of Multilevel Regression Models. 315 The Multilevel LRM.320 Examining Assumptions of the Model. 325 Group-Level Variables and Cross-Level Interactions.329 Chapter Summary. 334 Chapter Exercises. 334 16 A Brief Introduction to Logistic Regression.337 An Alternative to the LRM: Logistic Regression. 340 Extending the Logistic Regression Model.348 Chapter Summary.352 Chapter Exercises.353 17 Conclusions. 355 Sampling Weights.356 Establishing Causal
Associations. 357 Final Words. 360 Linear Regression Modeling: A Summary.360 Appendix A: Data Management.365 Appendix B: Using Simulations to Examine Assumptions of Linear Regression Models. 381 Appendix C: Selected Formulas.389 Appendix D: User-Written R Packages Employed in the Examples.397 References.399 Index.411 |
| adam_txt |
Contents Preface. ix Acknowledgments.xiii Author Biography. xv 1 Introduction. 1 Our Doubts are Traitors and Make Us Lose the Good We Oft Might Win. 2 Best Statistical Practices. 3 Statistical Software. 4 2 Review of Elementary Statistical Concepts.7 Measures of Central Tendency. 9 Measures of Dispersion.14 Samples and Populations. . 16 Sampling Error and Standard Errors. 17 Significance Tests. 19 Unbiasedness and Efficiency. 25 The Standard Normal Distribution and
Z-Scores. 26 Covariance and Correlation.28 Comparing Means from Two Groups.30 Examples Using R. 33 Chapter Summary. 35 Chapter Exercises. 35 3 Simple Linear Regression Models.37 Assumptions of Simple LRMs. 42 An Example of an LRM Using R. 44 Formulas for the Slope Coefficient and Intercept.51 Hypothesis Tests for the Slope Coefficient. 53 Chapter Summary. 61 Chapter Exercises. 62 4 Multiple Linear Regression Models.65 An Example of a Multiple LRM. 66 Comparing Slope Coefficients.74 Assumptions of Multiple LRMs. 80 Some Important
Characteristics of Multiple LRMs. 84 Chapter Summary. 85 Chapter Exercises. 86 v
Contents VI 5 The ANOVA Table and Goodness-of-Fit Statistics.89 Another Example of a Multiple LRM. 98 Chapter Summary. 101 Chapter Exercises.102 6 Comparing Linear Regression Models.105 The Partial F-Test and Multiple Partial F-Test. 106 Evaluating Model Fit with Information Criterion Measures.Ill Confounding Variables.112 Chapter Summary. 113 Chapter Exercises. 114 * * 7 Indicator Variables in Linear Regression Models.115 Indicator Variables in Multiple LRMs.121 LRMs with Indicator and Continuous Explanatory Variables. 124 Chapter Summary. 133 Chapter Exercises. 133 8 Independence.137 Determining
Dependence.139 Example of Adjustment for Clustering.141 LRM with No Adjustment for Clustering. 142 LRM That Adjusts for Clustering.143 Serial Correlation. 144 Linear Regression Model. 146 Solutions for Serial Correlation. 149 Linear Regression Model (OLS). 150 Prais-Winsten Regression Model.151 Generalized Estimating Equations for Longitudinal Data. 152 Linear Regression Model (OLS). 153 General Estimating Equation (GEE) Model with AR(1) Pattern.154 General Estimating Equation (GEE) Model with Unstructured Pattern. 155 Spatial Autocorrelation.158 Chapter Summary.161 Chapter Exercises. 162 9
Homoscedasticity. 165 Assessing Homoscedasticity in Multiple LRMs.169 What to Do About Heteroscedasticity.176 Chapter Summary. 183 Chapter Exercises. 184
Contents vii 10 Collinearity and Multicollinearity. 187 Multicollinearity. 192 How to Detect Collinearity and Multicollinearity. 193 What to Do About Collinearity and Multicollinearity.196 Chapter Summary.198 Chapter Exercises. 199 11 Normality, Linearity, and Interaction Effects. 201 Are the Errors of Prediction Normally Distributed?.202 Nonlinearities.209 Testing for Nonlinearities in LRMs.212 Incorporating Nonlinear Associations in LRMs. 215 Interaction Effects. 220 Interaction Effects with Continuous Explanatory Variables.228 Classification and Regression Trees (CART).233 A Cautionary Note about Interaction Effects.236 Chapter Summary. 237 Chapter
Exercises.,. 238 12 Model Specification.241 Variable Selection. 242 Overfitting—or the Case of Irrelevant Variables. 243 Underfitting—or the Case of the Absent Variables. 244 Endogeneity Bias. 250 Selection Bias.252 How Do We Assess Specification Error and What Do We Do about It?. 254 What to Do about Selection Bias?. 257 Cross-Validation. 262 Variable Selection Procedures. 269 Chapter Summary. 272 Chapter Exercises. 273 13 Measurement Errors.275 The Outcome Variable Is Measured with Error. 277 The Explanatory Variables Are Measured with
Error.279 What Should We Do about Measurement Error?. 280 Latent Variables as a Solution to Measurement Error.281 Chapter Summary. 290 Chapter Exercises.291 14 Influential Observations: Leverage Points and Outliers. 293 Detecting Influential Observations. 295 An Example of Using Diagnostic Methods to Identify Influential 298 Observations.
viii Contents What to Do about Influential Observations.303 Chapter Summary. 310 Chapter Exercises.311 15 Multilevel Linear Regression Models.313 The Basics of Multilevel Regression Models. 315 The Multilevel LRM.320 Examining Assumptions of the Model. 325 Group-Level Variables and Cross-Level Interactions.329 Chapter Summary. 334 Chapter Exercises. 334 16 A Brief Introduction to Logistic Regression.337 An Alternative to the LRM: Logistic Regression. 340 Extending the Logistic Regression Model.348 Chapter Summary.352 Chapter Exercises.353 17 Conclusions. 355 Sampling Weights.356 Establishing Causal
Associations. 357 Final Words. 360 Linear Regression Modeling: A Summary.360 Appendix A: Data Management.365 Appendix B: Using Simulations to Examine Assumptions of Linear Regression Models. 381 Appendix C: Selected Formulas.389 Appendix D: User-Written R Packages Employed in the Examples.397 References.399 Index.411 |
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| isbn | 9780367753689 9780367753665 |
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| series2 | Statistics in the social and behavioral sciences A Chapman & Hall book |
| spelling | Hoffmann, John P. 1962- Verfasser (DE-588)1033144061 aut Linear regression models applications in R John P. Hoffmann Boca Raton, London, New York CRC Press, Taylor & Francis Group 2022 xv, 420 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Statistics in the social and behavioral sciences A Chapman & Hall book R Programm (DE-588)4705956-4 gnd rswk-swf Annahme (DE-588)4240000-4 gnd rswk-swf Koeffizient (DE-588)4385197-6 gnd rswk-swf Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Lineare Regression (DE-588)4167709-2 gnd rswk-swf Lineare Regression (DE-588)4167709-2 s Statistisches Modell (DE-588)4121722-6 s Koeffizient (DE-588)4385197-6 s Annahme (DE-588)4240000-4 s R Programm (DE-588)4705956-4 s b DE-604 Erscheint auch als Online-Ausgabe 978-1-00-316223-0 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=032909801&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hoffmann, John P. 1962- Linear regression models applications in R R Programm (DE-588)4705956-4 gnd Annahme (DE-588)4240000-4 gnd Koeffizient (DE-588)4385197-6 gnd Statistisches Modell (DE-588)4121722-6 gnd Lineare Regression (DE-588)4167709-2 gnd |
| subject_GND | (DE-588)4705956-4 (DE-588)4240000-4 (DE-588)4385197-6 (DE-588)4121722-6 (DE-588)4167709-2 |
| title | Linear regression models applications in R |
| title_auth | Linear regression models applications in R |
| title_exact_search | Linear regression models applications in R |
| title_exact_search_txtP | Linear regression models applications in R |
| title_full | Linear regression models applications in R John P. Hoffmann |
| title_fullStr | Linear regression models applications in R John P. Hoffmann |
| title_full_unstemmed | Linear regression models applications in R John P. Hoffmann |
| title_short | Linear regression models |
| title_sort | linear regression models applications in r |
| title_sub | applications in R |
| topic | R Programm (DE-588)4705956-4 gnd Annahme (DE-588)4240000-4 gnd Koeffizient (DE-588)4385197-6 gnd Statistisches Modell (DE-588)4121722-6 gnd Lineare Regression (DE-588)4167709-2 gnd |
| topic_facet | R Programm Annahme Koeffizient Statistisches Modell Lineare Regression |
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