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Mass shootings and availability of gun dealerships

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Some days ago, after the most deadly mass shooting in recent US history in Orlando, a colleague and friend of mine Professor Celso Grebogi sent me an article that compared the availability of gun shops to coffee shops in the US. It presents striking representations that are easy to reproduce in the Wolfram Language as we will see below. I also wanted to go a bit beyond the comparison of coffee and gun shops, and used data of a couple of years of mass shootings in the US for a comparison. The article links to a website of the ATF (Bureau of Alcohol, Tobacco, Firearms and Explosives) that offers data on all (official) gun shops in the US. I downloaded the" latest complete listing" and then imported the file:

data = Import["/Users/thiel/Desktop/0516-ffl-list.txt", "TSV"];

Alternatively, you can import directly from the website:


The data contains


79447 entries, the first two of which are headers. For each entry the dataset contains the following information:

enter image description here

We are only interested in the establishments which have licence types 1 and 2, which leaves us with:

Select[data, (#[[4]] == 1 \[Or] #[[4]] == 2) &] // Length

64483 entries. We will not make heavy use of the Interpreter function. I could have used SemanticImport, but in spite of the relatively slow evaluation of the following line, it is quite straight forward to understand:

citiesguns = (Interpreter["City"][#] & /@ 
DeleteDuplicates[StringJoin[#[[1]], ", ", #[[2]]] & /@ Select[data, (#[[4]] == 1 \[Or] #[[4]] == 2) &][[1 ;;, {10, 11}]]]);

You can safely ignore potential warnings. Not all entries were properly resolved:

citiesguns // Length

gives 16390, whereas

Select[citiesguns, Head[#] == Entity &] // Length

only gives 13313 entries. I will only use the correct entries and save them into a file:

Export["~/Desktop/citiesgunsok.csv", Select[citiesguns, (Head[#] == Entity) &]];
citiesguns = ToExpression /@ Flatten[Import["~/Desktop/citiesgunsok.csv", "TSV"], 1];

Let's plot that:

styling = {GeoBackground ->GeoStyling["StreetMapNoLabels",GeoStylingImageFunction -> (ImageAdjust@
ColorNegate@ColorConvert[#1, "Grayscale"] &)],GeoScaleBar -> Placed[{"Metric", "Imperial"}, {Right, Bottom}],GeoRangePadding -> Full,ImageSize -> Large};
GeoListPlot[Select[citiesguns, Head[#] == Entity &][[1 ;;]], GeoRange -> Entity["Country", "UnitedStates"], ImageSize -> Full, PlotMarkers -> Point, PlotStyle -> PointSize[0.002], styling]

where my thanks as always goes to @Bernat Espigule for the styling.

enter image description here

So these are all the gun dealers. We can now also create a histogram:

coords = EntityValue[citiesguns, "Coordinates"];
shopDensityDistribution = SmoothKernelDistribution[RandomChoice[DeleteCases[coords, {"", ""}], 2000], "SheatherJones"];
cplot = ContourPlot[PDF[shopDensityDistribution, {y, x}], Evaluate@
Flatten[{x, {#[[1, 1, 2]], #[[2, 1, 2]]} &@GeoBoundingBox[Entity["Country", "UnitedStates"]]}], 
Evaluate@Flatten[{y, {#[[1, 1, 1]], #[[2, 1, 1]]} &@GeoBoundingBox[Entity["Country", "UnitedStates"]]}], 
ColorFunction -> "Rainbow", Frame -> False, PlotRange -> All, Contours -> 405, MaxRecursion -> 2, 
ColorFunction -> ColorData["TemperatureMap"], PlotRangePadding -> 0, ContourStyle -> None, ImageSize -> Full];
GeoGraphics[{Opacity[0.5], GeoStyling[{"GeoImage", cplot}], Polygon[Entity["Country", "UnitedStates"]]}, 
 GeoRange -> Entity["Country", "UnitedStates"], ImageSize -> Full]

enter image description here

This we can then combine with our gun dealer plot:

GeoGraphics[{Opacity[0.6], GeoStyling[{"GeoImage", cplot}], Polygon[Entity["Country", "UnitedStates"]], Yellow, Opacity[0.6], 
PointSize[0.002], Point[Select[Reverse /@ coords, 25.1246 < #[[2]] < 49.3845 && -124.733 < #[[1]] < -66.9498 &]]}, 
GeoRange -> Entity["Country", "UnitedStates"], ImageSize -> Full, styling]

enter image description here

This image does not tell the entire story because it only really plots the cities with shops. In many cities there are multiple dealers, of course. We will later produce a plot which represents that. But before we go there we will use the power of the Wolfram Language to combine different data sets from many different sources. There have been several posts for example by @Jofre Espigule for the year 2016 and by @Dan Lou before that. I will here use Dan Lou's data updated for 2016 including the Orlando shooting and the mass shootings that have happened in the couple of days between Orlando and now. You can get all files from this website.

shootings2016 = Import["~/Desktop/2016CURRENT.csv"];
shootings2015 = Import["~/Desktop/2015CURRENT.csv"];
shootings2014 = Import["~/Desktop/2014MASTER.csv"];
shootings2013 = Import["~/Desktop/2013MASTER.csv"];
shootings = Join[shootings2013[[2 ;;]], shootings2014[[2 ;;]], shootings2015[[2 ;;]], shootings2016[[2 ;;]]];

We now need to find out where the shootings happened; we will do this in two steps to save time:

shootingcoords = CityData[Entity["City", {#[[3]], #[[2]], "UnitedStates"}], "Coordinates"] & /@ shootings;
shootingcoordscorr = (If[Head[#[[1]]] == Missing, (Interpreter["City"][StringJoin[Riffle[#[[2, {3, 2}]], ", "]]])["Coordinates"], , #[[1]]]) & /@ 
Transpose[{shootingcoords, shootings}];

Not very clean code but it does the trick. There are 1002 shootings for the last years (nearly one shooting every day!) in the database

Select[shootingcoordscorr, Head[#] == List &] // Length

922 of which we can use. We next create a list of coordinates and info on how many people were killed and injured.

coordskilled = Flatten /@ Transpose[{shootingcoordscorr, shootings[[;; , {6, 7}]]}];

When we plot this

GeoGraphics[GeoDisk[#[[{1, 2}]], Quantity[10. #[[-2]], "Kilometers"]] & /@ (Select[coordskilled, Length[#] == 4 \[And] NumberQ[#[[-2]]] &]), 
GeoRange -> Entity["Country", "UnitedStates"]]

we obtain the following tragic result:

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The largest circle in Florida corresponds to the Orlando shooting. Note that the radius of the discs is proportional to the people killed - it might have been better to make the area proportional to the people killed. It is obvious that there is a correlation between shop density and locations of shootings, but that could be because of the very heterogeneous population density in the United States. The curated data in the Wolfram Language can help us to build a graphic on population and population density for the US.

subdivisions = #["Subdivisions"] & /@ Entity["Country", "UnitedStates"]["AdministrativeDivisions"];
countyData = {#, #["Population"], #[EntityProperty["AdministrativeDivision", "PerCapitaIncome"]], #[EntityProperty["AdministrativeDivision","BorderingCounties"]]} & /@ Flatten[subdivisions];
GeoRegionValuePlot[Rule @@@ Transpose[{countyData[[All, 1]], countyData[[All, 2]]}], ImageSize -> 1000, ColorFunction -> (ColorData["Rainbow"][#^.2] &), GeoRange -> Entity["Country", "UnitedStates"]]

enter image description here

which shows the absolute number of people living in the counties and

countypopdensityData = {#, #["Population"], #["PopulationDensity"]} & /@ Flatten[subdivisions];
GeoRegionValuePlot[Rule @@@ Transpose[{countyData[[All, 1]], countypopdensityData[[All, 3]]}], ImageSize -> 1000, 
ColorFunction -> (ColorData["Rainbow"][#^.2] &), GeoRange -> Entity["Country", "UnitedStates"]]

enter image description here

for the population density. So there is an obvious correlation between many people and many shootings. The question is: Can we find anything beyond that in the data?

Let's first try to get some insight into the number of gun dealers in the United States:

rules = (# -> Interpreter["City"][#] & /@ DeleteDuplicates[StringJoin[#[[1]], ", ", #[[2]]] & /@ 
Select[data, (#[[4]] == 1 \[Or] #[[4]] == 2) &][[1 ;;, {10, 11}]]]);
tallyshops = Reverse@SortBy[Tally[Select[rules[[1 ;;, 2]], Head[#] == Entity &]],Last];
dispatchrules = Dispatch[rules];
citiesmultiplestores = (StringJoin[#[[1]], ", ", #[[2]]] & /@ Select[data, (#[[4]] == 1 \[Or] #[[4]] == 2) &][[All, {10, 11}]]) /. dispatch rules;

which gives something like:

Reverse[SortBy[Tally[Select[citiesmultiplestores, Head[#] == Entity &]], Last]]

enter image description here

We now calculate some additional lists with data:

citiesshootings = Select[{Entity["City", StringDelete[#, " "] & /@ {#[[3]], #[[2]], "UnitedStates"}], #[[6]]} & /@ shootings, Head[#[[1]]] == Entity &];
dispatchrules2 = Rule @@@ Reverse[SortBy[Tally[Select[citiesmultiplestores, Head[#] == Entity &]], Last]];
totaldeathspercity = {#[[1, 1]], Total[#[[All, 2]]]} & /@ GatherBy[citiesshootings, First];
gunshopsvsdeatsh = Cases[totaldeathspercity /. dispatchrules2, {_Integer, _Integer}];

We see for example that there is no convincing correlation between gun shops and deaths:


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We can now rank the cities with respect to the number of gun dealerships:

ListLogLogPlot[Reverse[SortBy[Tally[Select[citiesmultiplestores, Head[#] == Entity &]], Last]][[;; , 2]], PlotRange -> All, Filling -> Bottom, 
 AxesLabel -> {"Rank", "Stores"}, LabelStyle -> Directive[Bold, Medium]]

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We see that some cities have massive numbers of stores. The following representation tries to show that:

shopsincity = Reverse[SortBy[Tally[Select[citiesmultiplestores, Head[#] == Entity &]], Last]];
GeoGraphics[{Red, GeoDisk[#[[1]], Quantity[10. Sqrt[#[[2]]], "Kilometers"]] & /@ shopsincity}, GeoRange -> Entity["Country", "UnitedStates"], 
ImageSize -> Full, styling]

enter image description here

In what is about to be discussed we will need the following two auxiliary lists:

gunshopspercity = Rule @@@ shopsincity[[;; , {1, 2}]];
citieskilled = citiesshootings[[All, 1]];

We now ask the following question: How many gun shops are close to the location of the shootings. We choose neighbouring cities at a distance less than 40km.

Dynamic[ProgressIndicator[1. k/Length[coordskilled]]]

Monitor[shopsclose = 
Table[If[Length[coordskilled[[k]]] < 4, "NA", Total[Select[Select[GeoNearest["City", 
GeoPosition[coordskilled[[k, {1, 2}]]], 5], GeoDistance[GeoPosition[coordskilled[[k, {1, 2}]]], #] < Quantity[40, "Kilometers"] &] /. gunshopspercity, 
NumberQ[#] &]]], {k, 1, Length[coordskilled]}], k]

Some of the data took a while to generate so we better save it:

alldata = Flatten /@ Transpose[{citieskilled[[All, 1]], coordskilled, shopsclose}];
Export["~/Desktop/allshootingdata.csv", alldata];

We can now plot a histogram of how many shops were close to the shootings.

Histogram[{DeleteCases[shopsclose, "NA"]}, 120, "PDF", AxesLabel -> {"close shops", "prob."}, LabelStyle -> Directive[Bold, Medium]]

enter image description here

The problem is that this does not tell us much. Let's see whether there is a higher gun availability close to the locations of the shootings than on average. We will proceed as follows: we will estimate the gun dealer availability for an "average American citizen". This estimate won't be perfect, but hopefully suffices for our purpose. Our algorithm is as follows: we will generate a list of all cities that are in the curated database of Wolfram. Then we will use their populations to "draw a random American citizen" - we obviously ignore some parts of the population here.

Here are the cities and their populations:

citiespopulationUS = {#, CityData[#, "Population"]} & /@ CityData[{All, "UnitedStates"}];

We then "draw" 1002 random citizens (actually their cities) from this list according to the respective population sizes:

randomcities = RandomChoice[(QuantityMagnitude[citiespopulationUS[[;; , 2]]] /. {QuantityMagnitude[Missing["NotAvailable"]] -> 0.} ) -> citiespopulationUS[[;; , 1]], 1002];

We next calculate how many gun dealerships there are close to these imaginary people:

Monitor[shopscloserandom = Table[Total[Select[Select[GeoNearest["City", randomcities[[k]], 5], 
GeoDistance[randomcities[[k]], #] < Quantity[40, "Kilometers"] &] /. gunshopspercity, NumberQ[#] &]], {k, 1, Length[coordskilled]}], k]

So this is the average number of gun dealerships close to shooting locations:

Mean[DeleteCases[shopsclose, "NA"]] // N

which gives 35.7354; and this is the average number for an "average citizen":

Mean[shopscloserandom] // N

which gives 24.4112. So there appear to be many fewer shops close to the average person. We can plot the histograms:

Histogram[{shopscloserandom, DeleteCases[shopsclose, "NA"]}, 120, "PDF", 
AxesLabel -> {"close shops", "prob."}, LabelStyle -> Directive[Bold, Medium]]

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where the orange bars are for our average citizen (control) and the blue ones for the shooting locations. It is relatively obvious that this is statistically significant.

LocationTest[{shopscloserandom, DeleteCases[shopsclose, "NA"]}, Automatic, "TestConclusion"]

which evaluates to:

enter image description here

There is, in fact, a very small p-value

LocationTest[{shopscloserandom, DeleteCases[shopsclose, "NA"]}] 

enter image description here

There are some pitfalls here, such as that we only look at correlation, which - as we know- does not imply causality. There are many potential confounding factors. It could be that shootings and larger number of gun dealerships are consequences of some common cause such as gang crime etc. Also, some of the smaller cities have not been recognised by Interpreter. We also have ignored the fact that there are often non-fatal injuries:

Histogram[{shootings[[All, 5]], shootings[[All, 6]]}, PlotRange -> {{0, 16}, All}, PlotTheme -> "Detailed"]

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where orange is for deaths and blue for injured. Having said all of this the data suggests a strong correlation between dealerships and shootings.

Also note that the code is not quite clean and optimised. I recalculate many things lots of times and basically post code that I just wrote down without any attempt at optimising it. The CPU time for the entire code is nearly half a day, but could be more on slower machines.

I am planning to run a GLM on this data and see what else we can learn from it.



PS: @Vitaliy Kaurov, I know that the code is quite inefficient. There is much more WL curated data that could be used. At the Wolfram Technology Tour Europe I have heard some really exciting stuff about future machine learning in Mathematica, which might offer great potential for this type of analysis.

POSTED BY: Marco Thiel
7 Replies

Nice work Marco!

But keep in mind correlation does not imply causation.

Posted 4 years ago

Will be willing to share the notebook script for this?

POSTED BY: Peter Amedzake
Anonymous User
Anonymous User
Posted 4 years ago


but if WR Inc adds "democrat party functions" political data to the subscription fee i'll start saying "hey i'm not paying for those modules - don't include them - give an appropriate discount"

where the money is

POSTED BY: Anonymous User
Posted 4 years ago

The original post is quite misleading. The implication of the title (Mass shootings and availability of gun dealerships) and the subsequent analysis is that there are vast numbers gun "shops"/"dealerships" across the U.S. The author apparently failed look at the requirements for being identified as such. In actual fact, what the author did was analyze the number of "Federal Firearms License" holders (aka FFL's). Anyone interested should take a look at Who is eligible for a firearms license. These licenses are not handed out like candy. The application is quite involved and requires photos and fingerprints. They are not all used in specifically as a means to sell firearms to the general public. Many FFL holders were required to obtain a license because they:

  • work for a manufacturer and have sales responsibilities,
  • are one of many employees who work for a retail gun shop ("dealership" if you prefer) and have sales responsibilities,
  • buy and sell collectable firearms for a small or as a side business related to their primary business,
  • do not currently buy/sell firearms, but would like to be legally prepared to so in the future,

I can give you a real world example. My wife works for a small firearms parts/accessories manufacturer. She and all other employees that would ever be in a situation where they might be involved in the actual sales transaction were required to obtain FFL's when the business owner began plans for the simply possibility of selling lower receivers in the future. To be clear, this is ONE business with MULTIPLE FFL holders. I'm relatively certain there are countless other similar examples. While the wonderful power of Wolfram Language was showcased, it is clear that such data was overlooked by the author.

I remember seeing the post 3 years ago, but I didn't open it to read at the time because of the heightened emotional context that surrounds a mass shooting. I regret that now.

I can only hope that someone finds it worthwhile to expend the same energy analyzing the nearly 685 deaths per day that occur due to medical errors in the U.S.


Beautiful post. Just an FYI if you do Interpreter[type] /@ list it's much slower than Interpreter[type][list], because the latter parallelizes the calls to alpha.

Also if all you're interested in are the coordinates you can use Interpreter["Location"].

POSTED BY: Carlo Barbieri

enter image description here - another post of yours has been selected for the Staff Picks group, congratulations !

We are happy to see you at the top of the "Featured Contributor" board. Thank you for your wonderful contributions, and please keep them coming!

POSTED BY: Moderation Team

Beautifully crafted, @Marco, outstanding as usual. Our geo-team always speaks highly of your posts, thank you!

POSTED BY: Vitaliy Kaurov
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