A guide to the implementation and interpretation of Quantile Regression models
This book explores the theory and numerous applications of quantile regression, offering empirical data analysis as well as the software tools to implement the methods.
The main focus of this book is to provide the reader with a comprehensive description of the main issues concerning quantile regression; these include basic modeling, geometrical interpretation, estimation and inference for quantile regression, as well as issues on validity of the model, diagnostic tools. Each methodological aspect is explored and followed by applications using real data.
- Presents a complete treatment of quantile regression methods, including, estimation, inference issues and application of methods.
- Delivers a balance between methodolgy and application
- Offers an overview of the recent developments in the quantile regression framework and why to use quantile regression in a variety of areas such as economics, finance and computing.
- Features a supporting website (www.wiley.com/go/quantile_regression) hosting datasets along with R, Stata and SAS software code.
Researchers and PhD students in the field of statistics, economics, econometrics, social and environmental science and chemistry will benefit from this book.
About the Author
Cristina Davino is the author of Quantile Regression: Theory and Applications, published by Wiley.
Marilena Furno, Department of Agriculture, University of Naples Federico II, Italy.
Domenico Vistocco, Department of Economics and Law, University of Cassino, Italy.
Table of Contents
1 A visual introduction to quantile regression 1
1.1 The essential toolkit 1
1.2 The simplest QR model: The case of the dummy regressor 8
1.3 A slightly more complex QR model: The case of a nominal regressor 13
1.4 A typical QR model: The case of a quantitative regressor 15
1.5 Summary of key points 20
2 Quantile regression: Understanding how and why 22
2.1 How and why quantile regression works 22
2.2 A set of illustrative artificial data 33
2.3 How and why to work with QR 38
2.4 Summary of key points 60
3 Estimated coefficients and inference 64
3.1 Empirical distribution of the quantile regression estimator 64
3.2 Inference in QR, the i.i.d. case 76
3.3 Wald, Lagrange multiplier, and likelihood ratio tests 84
3.4 Summary of key points 92
4 Additional tools for the interpretation and evaluation of the quantile regression model 94
4.1 Data pre-processing 95
4.2 Response conditional density estimations 107
4.3 Validation of the model 117
4.4 Summary of key points 128
5 Models with dependent and with non-identically distributed data 131
5.1 A closer look at the scale parameter, the independent and identically distributed case 131
5.2 The non-identically distributed case 137
5.3 The dependent data model 152
5.4 Summary of key points 158
Appendix 5.A Heteroskedasticity tests and weighted quantile regression, Stata and R codes 159
5.A.1 Koenker and Basset test for heteroskedasticity comparing two quantile regressions 159
5.A.2 Koenker and Basset test for heteroskedasticity comparing all quantile regressions 159
5.A.3 Quick tests for heteroskedasticity comparing quantile regressions 160
5.A.4 Compute the individual role of each explanatory variable to the dependent variable 161
5.A.5 R-codes for the Koenker and Basset test for heteroskedasticity 161
Appendix 5.B Dependent data 162
6 Additional models 163
6.1 Nonparametric quantile regression 163
6.2 Nonlinear quantile regression 172
6.3 Censored quantile regression 175
6.4 Quantile regression with longitudinal data 183
6.5 Group effects through quantile regression 187
6.6 Binary quantile regression 195
6.7 Summary of key points 197
Appendix A Quantile regression and surroundings using R 201
A.1 Loading data 202
A.2 Exploring data 205
A.3 Modeling data 211
A.4 Exporting figures and tables 217
Appendix B Quantile regression and surroundings using SAS 220
B.1 Loading data 221
B.2 Exploring data 223
B.3 Modeling data 229
B.4 Exporting figures and tables 239
Appendix C Quantile regression and surroundings using Stata 242
C.1 Loading data 243
C.2 Exploring data 245
C.3 Modeling data 249
C.4 Exporting figures and tables 255