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https://github.com/opencasestudies/old-ocs-bp-right-to-carry


https://github.com/opencasestudies/old-ocs-bp-right-to-carry

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# OpenCaseStudies



[![Build Status](https://travis-ci.org/opencasestudies/ocs-right-to-carry-case-study.svg?branch=master)](https://travis-ci.org/opencasestudies/ocs-right-to-carry-case-study)



### Disclaimer 



The purpose of the [Open Case

Studies](https://opencasestudies.github.io) project is **to demonstrate

the use of various data science methods, tools, and software in the

context of messy, real-world data**. A given case study does not cover

all aspects of the research process, is not claiming to be the most

appropriate way to analyze a given dataset, and should not be used in

the context of making policy decisions without external consultation

from scientific experts.



### License 



This case study is part of the [OpenCaseStudies](https://opencasestudies.github.io) project. 

This work is licensed under the Creative Commons Attribution-NonCommercial 3.0 ([CC BY-NC 3.0](https://creativecommons.org/licenses/by-nc/3.0/us/)) United States License.



### Citation 



To cite this case study:



Wright, Carrie, and Ontiveros, Michael and Jager, Leah and Taub, Margaret and Hicks, Stephanie. (2020). https://github.com/opencasestudies/ocs-right-to-carry-case-study. Examination of Multicollinearity Influence on Inference Using Right-to-Carry Gun Law and Violent Crime Data (Version v1.0.0).



### Acknowledgements



We would like to acknowledge [Daniel Webster](https://www.jhsph.edu/faculty/directory/profile/739/daniel-webster) for assisting in framing the major direction of the case study.



We would also like to acknowledge the [Bloomberg American Health Initiative](https://americanhealth.jhu.edu/) for funding this work. 



### Title 



Examination of Multicollinearity Influence on Inference Using Right-to-Carry Gun Law and Violent Crime Data



### Motivation 



The influence of the implementation of less restrictive right-to-carry gun laws on violent crime is a historically controversial topic. One reason for the contriversy, is concern that some earlier reports examing this topic may have used methods that were inappropriate. 



One of the major concerns is that an earlier report included multiple demographic variables that were collinear with one another. This resulted in different a very coefficient estimate for right-to-carry gun law adoption than other reports that did not include colinear varaibles. This phenomenon is called [multicollinearity](https://en.wikipedia.org/wiki/Multicollinearity), and it can result in abberant findings for particular explanatory variables, despite not altering the overall predictive power of a model.



In this case study we use data peform simplified analyses similar to those of reports on this topic to explore the influence of multicolinearity on coeffcient estimate stability. We however, do not recreate the previous analyses. The reports that we use as a guide for our analysis are:



1. John J. Donohue et al., Right‐to‐Carry Laws and Violent Crime: A Comprehensive Assessment Using Panel Data and a State‐Level Synthetic Control Analysis. *Journal of Empirical Legal Studies*, 16,2 (2019).



2. David B. Mustard & John Lott. Crime, Deterrence, and Right-to-Carry Concealed Handguns. *Coase-Sandor Institute for Law & Economics* Working Paper No. 41, (1996).



### Motivating question



1) How does the inclusion of different numbers of age groups influence the results of an analysis of right to carry laws and violence rates?



### Data   



In this case study, we perform analyses similar to those in [Donohue, et al.](https://www.nber.org/papers/w23510.pdf){target="_blank"} article and the [Lott and Mustard](https://chicagounbound.uchicago.edu/cgi/viewcontent.cgi?article=1150&context=law_and_economics){target="_blank"} article, however **we do not try to recreate them**, instead we perform simplified analyses to allow us to focus on multicolinearity.



Therefore we use a subset of the **explanatory variables** used by each article including:   



1. Data about state demographics in terms of population compositions for age, sex, race, as well as overall population values from the US Census Bureau:



Data   | Link                                                                        

---------- |-------------

**years 1977 to 1979**  | [link](https://www2.census.gov/programs-surveys/popest/tables/1900-1980/state/asrh/)  

**years 1980 to 1989**  | [link](https://www2.census.gov/programs-surveys/popest/tables/1980-1990/counties/asrh/) * county data was used for this decade which also has state information

**years 1990 to 1999**  | [link](https://www2.census.gov/programs-surveys/popest/tables/1990-2000/state/asrh/)

**years 2000 to 2010**  | [link](https://www.census.gov/data/datasets/time-series/demo/popest/intercensal-2000-2010-state.html) 
 [technical documentation](https://www2.census.gov/programs-surveys/popest/technical-documentation/file-layouts/2000-2010/intercensal/state/st-est00int-alldata.pdf){target="_blank"}



Six demographic variables are created for the [Donohue, et al.](https://www.nber.org/papers/w23510.pdf){target="_blank"}-like analysis and 36 were created for the [Lott and Mustard](https://chicagounbound.uchicago.edu/cgi/viewcontent.cgi?article=1150&context=law_and_economics){target="_blank"}-like analysis.



To use this data, we also need [Federal Information Processing Standard (FIPS) state codes](https://en.wikipedia.org/wiki/Federal_Information_Processing_Standard_state_code){target="_blank", to identify what demographic data corresponds to what state. This is also available from the [US Census Bureau](https://www.census.gov/geographies/reference-files/2014/demo/popest/2014-geocodes-state.html){target="_blank"}.



2. Police staffing data, which was downloaded from the [Federal Bureau of Investigation](https://crime-data-explorer.fr.cloud.gov/downloads-and-docs){target="_blank"}



3. Unemployment data, which was downloaded from the [U.S. Bureau of Labor Statistics](https://data.bls.gov/cgi-bin/dsrv?la){target="_blank"}. 



4. Poverty data, extracted from Table 21 from this [US Census Bureau Poverty Data ](https://www.census.gov/data/tables/time-series/demo/income-poverty/historical-poverty-people.html){target="_blank"}



5. Right-to-carry law data, which is available in a table in the [Donohue paper](https://www.nber.org/papers/w23510.pdf){target="_blank"}



Finally our outcome of interest is violent crime rates. The violent crime data was downloaded from the [FBI uniform crime reporting system](https://www.ucrdatatool.gov/Search/Crime/State/StatebyState.cfm){target="_blank"}



#### Learning Objectives



The skills, methods, and concepts that students will be familiar with by the end of this case study are:



**Statistical Learning Objectives:** 



1) what multicollinearity is and how it can influence linear regression coefficients  

2) how to look for the presence of multicollinarity and determine the severity

3) the difference between multicollinearity and correlation 

4) implementation of panel regression analysis (`plm`)

5) calcuation of VIF (`car`)



**Data science Learning Objectives:**



1) data import of many different file types with special cases (`readr`, `readxl`, `pdftools`)

2) joining data from multiple sources (`dplyr`)  

3) working with character strings (`stringr`)

4) data comparisons (`dplyr` and `janitor`)

5) reshaping data into different formats (`tidyr`)  

6) visualizations (`ggplot2`) 

7) perform iterative simulations (`rsample`)



#### Data import 



In this case study particularly covers many different types of data import. We cover data import using the Tidyverse `readr` package to import the various types of text files, the Tidyverse `readxl` package to import excel files, and the Tidyverse `pdftools` package to import a PDF file. We demonstrate special cases where header rows need to be skipped, or colum data types need to be specified. We also use the the `list.files()` base function together with the `map()` function of the Tidyverse `purrr` package to efficiently perform data importation of multiple files with one command.



#### Data wrangling



This case study is covers many details about wrangling data from excel files with unusual header structures and with similar data in multiple tables within the same file. This involves using the `stringr` package to split, subset, detect, extract, and modify patterns of text. This also involves using the `tidyr` package to change data shape and using the `dplyr` package to summarise, select, filter, modify, and join data. They case study also covers using various `map_*()` functions of the `purrr` package to perform functions across tibbles within lists and the `across()` function of the `dplyr` package to perform functions across columns of an individual tibble. This case study provides especially diverse material about data wrangling.



#### Data Visualization



This case study demonstrates how to make correaltion plots and scatter plots with error bars. We also show how to add formulas and arrows to plots. The instruction about data visualization assumes that students have some familiarity with `ggplot2`.



### Analysis



This case study covers balanced panel regression model data analysis with fixed effects. In doing so we provide an introduction to longitudinal analysis in general, as well as use of the `plm` package. We also show how to calculate [Variance inflation factor (VIF)](https://en.wikipedia.org/wiki/Variance_inflation_factor) values  using the `car` package to quantify the severity of multicollinearity. As another assesment of multicollinearity, we demonstrate how to perform simulations to evaluate the stability of coefficient estimates.



### Other notes and resources 



[Tidyverse](https://www.tidyverse.org/){target="_blank"}  

[Writing functions](https://r4ds.had.co.nz/functions.html){target="_blank"}   

Also see [this case study](https://opencasestudies.github.io/ocs-bloomberg-vaping-case-study/){target="_blank"} for more information on writing functions      

Please see [this case study](https://opencasestudies.github.io/ocs-bp-co2-emissions/){target="_blank"}  for more details on using `ggplot2`     

[Longitudinal studies](https://www.bmj.com/about-bmj/resources-readers/publications/epidemiology-uninitiated/7-longitudinal-studies){target="_blank"}   

[Panel data](https://en.wikipedia.org/wiki/Panel_data){target="_blank"}    

[Confidence intervals](https://en.wikipedia.org/wiki/Confidence_interval){target="_blank"}   

[Linear regression](https://en.wikipedia.org/wiki/Linear_regression){target="_blank"}  

[panel regression analysis](https://en.wikipedia.org/wiki/Panel_analysis){target="_blank"}   

[Hausmen test](https://en.wikipedia.org/wiki/Durbin%E2%80%93Wu%E2%80%93Hausman_test){target="_blank"} 

[Resampling](https://en.wikipedia.org/wiki/Resampling_(statistics)){target="_blank"}   

[Variance inflation factor (VIF)](https://en.wikipedia.org/wiki/Variance_inflation_factor){target="_blank"}   

[$R^2$ coefficient of determination](https://en.wikipedia.org/wiki/Coefficient_of_determination){target="_blank"}   

[Ridge regression](https://en.wikipedia.org/wiki/Tikhonov_regularization){target="_blank"}  

[LaTeX mathematical notation](https://www.calvin.edu/~rpruim/courses/s341/S17/from-class/MathinRmd.html)target="_blank"}   



For more information on linear regression see this [book](https://rafalab.github.io/dsbook/linear-models.html#linear-regression-in-the-tidyverse){target="_blank"} and this [case study](https://opencasestudies.github.io/ocs-bp-diet/){target="_blank"}.



For more information on the different types of panel regression models see this [book](https://bookdown.org/ccolonescu/RPoE4/panel-data-models.html),  [here](https://www.bauer.uh.edu/rsusmel/phd/ec1-15.pdf), and [here](https://sites.google.com/site/econometricsacademy/econometrics-models/panel-data-models).



For more information on implementing panel regession in R using the `plm` package, see [here](https://cran.r-project.org/web/packages/plm/vignettes/plmPackage.html){target="_blank"}  and [here](http://www.princeton.edu/~otorres/Panel101R.pdf){target="_blank"}.



For more information on multioclinearity and VIF, see this [article](https://link.springer.com/content/pdf/10.1007/s11135-006-9018-6.pdf){target="_blank"}.DOI 10.1007/s11135-006-9018-6



The articles used to motivate this case study are:   

[Lott and Mustard](https://chicagounbound.uchicago.edu/cgi/viewcontent.cgi?article=1150&context=law_and_economics){target="_blank"}  

[Donohue, et al.](https://www.nber.org/papers/w23510.pdf){target="_blank"}     

[See here for a list of studies on this topic ](https://en.wikipedia.org/wiki/More_Guns,_Less_Crime){target="_blank"}  



#### For users 



There is a [`Makefile`](Makefile) in this folder that allows you to type `make` to knit the case study contained in the `index.Rmd` to `index.html` and it will also knit the [`README.Rmd`](README.Rmd) to a markdown file (`README.md`). 



#### For instructors  



Instructors can skip the data wrangling and start at the Data Exploration section, which gives a brief introduction of the data before the Data Analysis section. 



#### Target audience 



For individuals or classes with some familiarity with regression. See this [case study](https://opencasestudies.github.io/ocs-bp-diet/){target="_blank"} for an introduction to regression. 



#### Suggested homework



Ask students to remove one or more of the demographic variables with high VIF values from the Lott-like panel data and perform the panel linear regression analysis again, as well as cacluate the VIF values. 



Ask the students to discuss how this possibly changed the results.