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53_regression.Rmd
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# Regression methods {#regression}
## R
John Fox and Sanford Weisberg, [_An R Companion to Applied Regression, Second Edition_](http://socserv.socsci.mcmaster.ca/jfox/Books/Companion/), Sage (2011)
Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani, _An Introduction to Statistical Learning: With Applications in R_, Springer (2013) [@James_Witten_Hastie_Tibshirani_2014]
Paul Roback and Julie Legler, _Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R_, CRC Press, 2021 [@Roback_Legler_2021]
Jeremy Anglin, ["Using R to replicate common SPSS multiple regression output"](http://jeromyanglim.blogspot.ca/2013/12/using-r-to-replicate-common-spss.html) (2013-12-04)
Selva Prabhakaran, [Linear Regression](http://r-statistics.co/Linear-Regression.html) (part of the [r-statistics.co](http://r-statistics.co/) R tutorials)
***
## Logistic Regression (Generalized Linear Models, GLM)
<blockquote class="twitter-tweet" data-lang="en"><p lang="en" dir="ltr">It's only called a Neural Network if it comes from the Neuralè region of France. Otherwise you have to call it a logistic regression.</p>— Vicki Boykis (/@/vboykis) <a href="https://twitter.com/vboykis/status/1077024069126668289?ref_src=twsrc%5Etfw">December 24, 2018</a></blockquote>
<script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
#### text books
Michael Friendly and David Meyer, _Discrete Data Analysis with R: Visualization and Modeling Techniques for Categorical and Count Data_ [@Friendly_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_ [@James_Witten_Hastie_Tibshirani_2014]
* Chapter 4, "Classification", includes a section on Logistic Regression
#### online resources
Tavish Srivastava, [Building a Logistic Regression model from scratch](https://www.analyticsvidhya.com/blog/2015/10/basics-logistic-regression/) (2015-10-04)
Michy Alice, [How to perform a Logistic Regression in R](https://www.r-bloggers.com/how-to-perform-a-logistic-regression-in-r/) (2015-09-13)
Data Flair, [Generalized Linear Models in R](https://data-flair.training/blogs/generalized-linear-models-in-r/), 2018-01-17 in R by Data Flair
stackoverflow: ["Confidence intervals for predictions from logistic regression"](https://stackoverflow.com/questions/14423325/confidence-intervals-for-predictions-from-logistic-regression)
http://andrewgelman.com/2017/03/04/interpret-confidence-intervals/
***
## Packages
#### `{broom}`
CRAN: [broom: Convert Statistical Analysis Objects into Tidy Tibbles](https://cran.r-project.org/package=broom)
[github page](https://github.com/tidymodels/broom)
[Introduction to broom](https://cran.r-project.org/package=broom/vignettes/broom.html)
David Robinson (2015-03-19) [broom: a package for tidying statistical models into data frames](http://varianceexplained.org/r/broom-intro/)
#### `{brms}`
[brms: Bayesian Regression Models using Stan](https://cran.r-project.org/package=brms)
"...an interface to fit Bayesian generalized (non-)linear multivariate multilevel models using Stan"
[github page](https://github.com/paul-buerkner/brms)
##### `{brmstools}`
* [tools and helpers for `brms`](https://mvuorre.github.io/brmstools/)
#### `{modelr}`
[github page](https://github.com/tidyverse/modelr)
***
## Quantile regression
Quantile regression](https://en.wikipedia.org/wiki/Quantile_regression) at Wikipedia
### Theory and methods
Despa, Simon. (2007/2012) ["Quantile Regression"](https://www.cscu.cornell.edu/news/statnews/stnews70.pdf), Cornell University, StatNews #70.
Dade, Brian S. and Barry R. Noon (2003) ["A gentle introduction to quantile regression for ecologists"](http://www.econ.uiuc.edu/~roger/research/rq/QReco.pdf), _Front Ecol Environ_; 1(8): 412– 420.
Koenker, Roger and Kevin F. Hallock (2001) ["Quantile Regression"](http://www.econ.uiuc.edu/~roger/research/rq/QRJEP.pdf), Journal of Economic Perspectives—Volume 15, Number 4 —Fall 2001—Pages 143–156.
Marzban, Caren. ["Quantile Regression"](http://faculty.washington.edu/marzban/quantile.pdf) 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](http://faculty.washington.edu/marzban/).
University of Virginia Library Research Data Services, ["Getting Started with Quantile Regression"](http://data.library.virginia.edu/getting-started-with-quantile-regression/).
### R
#### `{quantreg}`
**package**
CRAN page: [quantreg: Quantile Regression](https://cran.r-project.org/package=quantreg/)
**articles**
Koenker, Roger. (?) ["Quantile Regression in R: A Vignette"](https://cran.r-project.org/package=quantreg/vignettes/rq.pdf).
***
## Dominance Analysis
Armando B. Mendes, ["Dominance Analysis"](http://sk.sagepub.com/books/the-sage-dictionary-of-quantitative-management-research/n28.xml), Chapter 28 in _The SAGE Dictionary of Quantitative Management Research_, eds. Luiz Moutinho & Graeme Hutcheson, 2011. (paywalled)
[Dominance Analysis: Overview](https://rmc.ehe.osu.edu/files/2018/08/DominanceAnalysisFeb2018.pdf), Research Methodology Center, 2018.
S. Yasaman Amirkiae (2016) [Dominance Analysis: A Necessity of Paying Attention to Relative Importance of Predictors in Decision Making Issues](http://www.swdsi.org/proceedings/2016/Papers/Papers/PA027.pdf)
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
### R
#### `{dominanceanalysis}`
CRAN page: [dominanceanalysis: Dominance Analysis](https://cran.r-project.org/package=dominanceanalysis/)
[GitHub page: ](https://github.com/clbustos/dominanceAnalysis)
* Dominance Analysis (Azen and Bodescu), for multiple regression models: OLS (univariate, multivariate), GLM and HLM
#### `{relaimpo}`
CRAN page: [relaimpo: Relative Importance of Regressors in Linear Models](https://cran.r-project.org/package=relaimpo/)
#### `{yhat}`
CRAN page: [yhat: Interpreting Regression Effects](https://cran.r-project.org/package=yhat/)
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