Chapter 18 Regression methods

18.1 R

John Fox and Sanford Weisberg, An R Companion to Applied Regression, Second Edition, Sage (2011)

Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani, An Introduction to Statistical Learning: With Applications in R, Springer (2013) (Gareth James 2014)

Paul Roback and Julie Legler, Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R, CRC Press, 2021 (Paul Roback 2021)

Jeremy Anglin, “Using R to replicate common SPSS multiple regression output” (2013-12-04)

Selva Prabhakaran, Linear Regression (part of the r-statistics.co R tutorials)

18.2 Logistic Regression (Generalized Linear Models, GLM)

18.2.0.1 text books

Michael Friendly and David Meyer, Discrete Data Analysis with R: Visualization and Modeling Techniques for Categorical and Count Data (Friendly and Meyer 2016)

  • see Chapter 7, “Logistic Regression Models”

Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani, An Introduction to Statistical Learning: With Applications in R (Gareth James 2014)

  • Chapter 4, “Classification”, includes a section on Logistic Regression

18.3 Packages

18.3.0.2 {brms}

brms: Bayesian Regression Models using Stan

“…an interface to fit Bayesian generalized (non-)linear multivariate multilevel models using Stan”

github page

18.3.0.2.1 {brmstools}

18.3.0.3 {modelr}

github page

18.4 Quantile regression

Quantile regression](https://en.wikipedia.org/wiki/Quantile_regression) at Wikipedia

18.4.1 Theory and methods

Despa, Simon. (2007/2012) “Quantile Regression”, Cornell University, StatNews #70.

Dade, Brian S. and Barry R. Noon (2003) “A gentle introduction to quantile regression for ecologists”, Front Ecol Environ; 1(8): 412– 420.

Koenker, Roger and Kevin F. Hallock (2001) “Quantile Regression”, Journal of Economic Perspectives—Volume 15, Number 4 —Fall 2001—Pages 143–156.

Marzban, Caren. “Quantile Regression” Invited paper presented at the joint session between AI and Prob & Stats Conference. 88th American Meteorological Society Annual Meeting, New Orleans, Jan. 20-24, 2008. (More of Marzban’s papers can be found on his University of Washington faculty page.

University of Virginia Library Research Data Services, “Getting Started with Quantile Regression”.

18.4.2 R

18.4.2.1 {quantreg}

package

CRAN page: quantreg: Quantile Regression

articles

Koenker, Roger. (?) “Quantile Regression in R: A Vignette”.

18.5 Dominance Analysis

Armando B. Mendes, “Dominance Analysis”, Chapter 28 in The SAGE Dictionary of Quantitative Management Research, eds. Luiz Moutinho & Graeme Hutcheson, 2011. (paywalled)

Dominance Analysis: Overview, Research Methodology Center, 2018.

S. Yasaman Amirkiae (2016) Dominance Analysis: A Necessity of Paying Attention to Relative Importance of Predictors in Decision Making Issues

Paywalled articles:

  • Budescu, D. V. (1993). Dominance analysis: A new approach to the problem of relative importance of predictors in multiple regression. Psychological Bulletin, 114(3), 542-551. https://doi.org/10.1037/0033-2909.114.3.542

  • Azen, R., & Budescu, D. V. (2003). The dominance analysis approach for comparing predictors in multiple regression. Psychological Methods, 8(2), 129-148. https://doi.org/10.1037/1082-989X.8.2.129

  • Azen, R., & Budescu, D. V. (2006). Comparing Predictors in Multivariate Regression Models: An Extension of Dominance Analysis. Journal of Educational and Behavioral Statistics, 31(2), 157-180. https://doi.org/10.3102/10769986031002157

  • Azen, R., & Traxel, N. (2009). Using Dominance Analysis to Determine Predictor Importance in Logistic Regression. Journal of Educational and Behavioral Statistics, 34(3), 319-347. https://doi.org/10.3102/1076998609332754

  • Luo, W., & Azen, R. (2013). Determining Predictor Importance in Hierarchical Linear Models Using Dominance Analysis. Journal of Educational and Behavioral Statistics, 38(1), 3-31. https://doi.org/10.3102/1076998612458319

18.5.1 R

18.5.1.1 {dominanceanalysis}

CRAN page: dominanceanalysis: Dominance Analysis

GitHub page:

  • Dominance Analysis (Azen and Bodescu), for multiple regression models: OLS (univariate, multivariate), GLM and HLM

18.5.1.3 {yhat}

CRAN page: yhat: Interpreting Regression Effects

-30-

References

Friendly, Michael, and David Meyer. 2016. Discrete Data Analysis with r: Visualization and Modeling Techniques for Categorical and Count Data. CRC Press.
Gareth James, Trevor Hastie, Daniela Witten. 2014. An Introduction to Statistical Learning. Springer. https://www.statlearning.com/.
Paul Roback, Julie Legler. 2021. Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in r. Chapman; Hall/CRC Press. https://www.routledge.com/Beyond-Multiple-Linear-Regression-Applied-Generalized-Linear-Models-And/Roback-Legler/p/book/9781439885383.