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Gun Violence and Gun Ownership – further refinement and response to reader comments

By Joshua Tewksbury

Facebook is a powerful thing.  Before I wrote the previous post on Gun Violence and Gun Ownership rates I simply posted the second graph from that post to my Facebook wall.  48 hours later, is has been sent all over the world, shared over 1000 times that I know of, and it has gathered a number of very interesting critiques.  I should start by saying I am an environmental biologist and a father of young children.  There are social scientists who have studied the links I am exploring here quite seriously, and if you want to go deeper into this literature, or you don’t like my analysis or interpretation, you should look through a few of the reviews in this field.  Papers such as Helpburn and Hemenway’s 2004 Review of gun access and gun violence (including homicide) or Richardson et al.’s 2011 examination of homicide rates in the US compared to a group of 23 populous high-income OECD countries are good places to start.  Or, for a look within the US at household gun ownership rates and homicide rates, look over Miller et al’s paper in 2003.  For all of you without academic associations, it will cost you $120 to view these papers (products of research funded largely through public funds, written and reviewed through volunteer efforts of academics). If you think that is odd, or wrong, and if you think this potentially contributes the amount of mis-information in the world,  here is the tip of the iceberg on that subject.

Below I  update the analysis and clarify my approach and address some of the critiques that came from some of the more statistically-minded readers.

I gave some thought to the right way to create comparables between countries, and I think the use of the Inequality-Adjusted Human Development Index (IHDI) may be preferable to the use of the newer HDI that does not adjust for inequality of human welfare distribution among citizens in a country.   There are a lot of reasons why differences in the distribution of welfare among citizens could be important, and the goal in using one of these indices is to create a set of comparables among countries.  In the following two graphs, I first plot the same relationship as before (now with Great Brittan Included – thanks Cooper), and I then plot the same relationship using IHDI (> 0.75). They show similar trends, with IHDI showing a stronger fit (correlation going from 0.7 to 0.8) as I expected it might.

Perhaps the most interesting critique of these data comes from the idea that suicide rates should be removed from the data.  I can see both sides of this.  If we include suicide, as I do here, we are focused on all violent gun deaths, and the relationship between gun deaths and gun access appears relatively clear (a bit on leverage below).   When we remove suicide from gun violence, and keep the same restrictions as above (using HDI or IHDI) the relationship weakens considerably, and we get extremely large leverage values for the US.  (I have included the data I used at the end of this post for people to play with, and an example graphic is here). As Richardson et al (2011) point out – the US had a homicide rate that was 6.9 times higher than other high-income countries in 2003 (the year used in their analysis).  The disparity in the data I am using is slightly less, but the massive outlier status of the US  – both in terms of gun availability and in terms of homicides and gun violence in general, makes me think this discussion is worth the ink.  Bottom line,  we have a bunch of countries with relatively low firearm deaths and relatively low firearm availability, and we have the US, at the other extreme. When we remove suicide from the mix,  tts pretty hard to use this data to make strong conclusions.  Is this a scale dependent relationship that is obscured by other differences between countries until  we get out past 50 or so firearms per person?  Is there something very different going on in the US that has nothing to do witb gun availability?  We are  not going to answer these questions with the data at hand, and we are probably better served by looking at other datasets – particularly data comparing gun availability and gun violence among states in the US, where we start to develop stronger control groups.  For those interested in digging deeper, Miller’s 2003 paper is a good place to start, or the review by Helpburn and Hemenway.  My quick read of the data suggests a significant link between these variables.

One more point here – as a matter of public policy, it may also be a bit questionable to remove gun-related suicides from the debate over the relationship between gun violence and gun availability, but that depends a lot on your perspective, and I will let others hammer that out.

A final point on leverage values and the US – A number of readers on the blog and in facebook took issue with my fit line, and suggested that the US was a significant outlier, artificially increasing the fit of the relationship.  To some extent, that is exactly the point.  I was careful in the previous post not to stake to strong a claim on the linear fit, but it is worth pointing out a couple of things here.  The US is an outlier, both in terms of gun ownership and in terms of gun violence, but if we take the US out of the analysis (which sort of misses the point, but is interesting from a statistical perspective), we still get a significant positive correlation between gun ownership rates and gun-related violence, regardless of whether we restrict the data using HDI or IHDI, though it is stronger using IHDI. This is true for gun violence, but not when we remove suicides (see previous paragraph).

I got a few comments on the blog focused on alternative modeling approaches, and I like where they are heading, so I am posting the data here both as a CSV called guns, and in the original excel format, called gunsdata.  This way, Tarj, SKG, Alex and  others can build on this late night obsession of mine.

Back to Environmental issues for me!

 

UPDATE  Dec 20h, 5:51 AM:  The data I have posted  are taken from the following websites:

 

 

1,028 Comments:

  1. Daniel Nikolić

    I don’t know if illegal guns are taken into the account. When a line is inserted e.g. Croatia (country I live in) is above the line. However, there are a lot of illegal guns in Croatia, left over from the war that ended 17 years ago. But there’s definitely something odd with the USA, it would be interesting to insert individual states into the graph. — Daniel

    Reply to this comment ↓

      • Andrew G.

        The murder rate in Texas is about 4 times that of England (source: FBI UCR 2011), and about 2/3rds of Texas murders are with firearms (whereas only a tiny fraction of English murders are). In fact, the murder-with-firearm rate in Texas is over 60 times higher than England. The non-firearm murder rate in Texas is also about 1.5 times the English rate.

  2. Andrew Ducker

    Probably not easy to do – but I wonder if some States in the USA are particularly bad for this – i.e. they end up being much more like Guatemala or Colombia, while other states are more like Canada.

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  4. Alan Hurd

    Joshua,
    Funny, I plotted the same data–including suicides–with the same kind of filtering (I used GDP per capita both above $20K and below) last fall to settle a dispute with my sister who maintained that Switzerland has as many guns but much lower crime than the US owing to deterrence. I was not able to convince her that Switzerland, with half the gun concentration, has half the homicide-suicide crime due to ready availability in the inevitable times of blind rage and deep despair. She sees deterrence; I see availability. We got nowhere. But at least the correlation is established.

    After Newtown, I sent my Senator an argument for a buy-back program based on the linear fit for the developed countries. The slope of your regression line and mine is 1/8: annually 1 death in 10,000 per 8 guns owned among 100 people. Inverted, this proportionality implies that for every 800 guns taken out of society 1 life is saved per year. If the useful life of a gun is 10 yr, then a one-time buyback reducing gun concentration in the US by 50%–bringing the US down to Switzerland’s neighborhood–would save 1.9 MILLION lives per decade.

    True, this reasoning skips cause-and-effect, but the linearity of the correlation is pretty good. In this set of developed countries, a person is less likely by half to be killed by a gun when living in half the concentration of guns.
    alan hurd

    Reply to this comment ↓

    • Jack

      In 2011, in the US, there were not quite 15,000 homicides deaths buy gun. Even if there were zero homicide deaths by gun for the next ten years, the amount of lives saved based upon the 2011 homicide number would be less than 150,000. How do you get 1.9 million? Sometimes you have to look past the computer models and look at the real world.

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  5. Joshua Tewksbury

    Nice work Alan. As you say, there are lots of reasons we might be a bit worried about the direct link, and lots of other sttistical tricks we might do to dig a little deeper, but the strong logic you present surrounding the potential effectiveness of a buyback program is really nice. I would be really excited if we got half the effect the regression suggests. Nice work. Time for me to put together a similar letter

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  6. jacob

    I wonder if you can find data for say # of households or individuals who own at least 1. Many people in the US are gun enthusiasts and keep a large collection. I dont know that having 10 guns in your house makes you 10x as deadly..

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