Gun Control and Gun Violence, Part 2

After my first go-around looking at the connection between gun control and gun violence, I decided to revisit this question with a more detailed dataset. Before, I was using the FBI's Uniform Crime Report statistics, which cover eight major crimes across almost every police jurisdiction in the United States. This time, I looked at the National Incident-Based Reporting System, which is much more comprehensive; documenting every incident reported by participating jurisdictions and including time, place, crime, weapon used, characteristics of the suspect and victim, and much more information. A problem with the UCR is that data does not include weapon used- I couldn't tell if a criminal in Florida had used a gun or just a banana to rob their victim.

Unlike the much simpler UCR dataset, I had quite a few difficulties getting the NIBRS files to do what I wanted. As you might expect, a comprehensive crime dataset for the United States was big. Really big. I was able to do my first analysis on a puny ARM-powered chromebook. I had to use my desktop to even be able to open the file, which was a tab-delimited ASCII file 6 gigabytes large. I normally use R to do quantitative analysis these days, but I had to load an open-source clone of SPSS to properly load the file and convert it. This isn't even "Big Data" territory, and I still started running into performance issues. I started using dplyr to get its performance benefits, but a query on the entire database would still take me about 10-15 minutes to run, even with a Solid State Drive. This is where you learn about the importance of using a subset of your data as a test, because any typo you make stacks up quickly!

More discouraging was the fact that NIBRS is not universal. Now, UCR is a voluntary system, but still covers 98% of all Americans. The NIBRS only covers 30% (mostly broken up by state), and doesn't include crimes from the seven biggest states. Look at the coverage map below:

(data from a JRSA report)

Fortunately, there is data available on the proportion of crime in and out of the database (the numbers above reflect the percent of crime covered in NIBRS for each state), so it is possible to normalize this data somewhat, but the lack of data for many parts of the country may make a definitive analysis difficult.

Even with a more detailed dataset, I wasn't able to find any connection between gun laws and crime. Even controlling for things like crime rates (is a higher percentage of crime gun-related violent crime?), or a disproportionate effect on victims of color, I saw no impact.

Where I did see a big difference was (oddly) with population size. The bigger the state's population, the more often violent crime tended to involve a gun. The trend was twice as strong for overall population than for just urban population. Population density had no impact.

In order to get good enough quality data, I cut out any state that did not report at least half of its total crime. As you can see in the map, that leaves only a smattering of state agencies, and even fewer cities. The strong correlation between population and crime ratios may be an artifact of two of the largest states (Ohio and Michigan) being home to a number of poor rust belt cities, while many of the smaller states are not in the traditionally poor deep south.

I'd be interested in seeing the impact as more police agencies sign on to NIBRS and open their case data to the public. A larger source of crime data would revolutionize criminology and sociology, and make it easier to understand trends like this. In the meantime, I'm going to have to say the jury's still firmly out on gun control.

How Margarine is Tearing New England Families Apart

(Spoiler: It's not. Despire a very strong correlation)

Source: Spurious Correlations at tylervigen.com

When I was in my Econometrics class at college, my professor drilled into me the "Ten Commandments of Applied Econometrics", from an influential paper of the same name by Peter Kennedy. These rules apply as much to econometrics as they do any statistical modelling exercise:

1. Thou shalt use common sense in economic theory
   The "Common Sense" that Kennedy (and by extension, Professor Khemraj) talks about is truly basic methodology. Things like mixing up stock and flow variables (eg confusing wealth/assets (stock) with income (flow)), or comparing a per capita figure with a total.
2. Thou shalt ask the right questions
   If you walk into an analysis blindfolded, the results might not look too good when you turn the lights back on. Make sure you truly understand the question that you're asking.
3. Thou shalt know the context - do not perform ignorant statistical analysis
   You should always know how your data came to be and how that might influence your results. If you're looking at vacation days across the developed world, remember that Brits count paid holidays in vacation time while Americans do not. If you're analyzing vote totals for municipal candidates across the US, remember that candidates in New York and Minnesota can stand for multiple parties. What was the wording on the survey that you're basing your analysis off of? How did each of your record labels classify their artists' genres?
4. Thou shalt inspect the data
   These days it's incredibly easy to just type summary(lm(dataset, formula = a ~ b)) into an r prompt, see a significant result, copy the coefficient, and declare victory. It's also incredibly easy to take a closer look at your data. At least plot out what your data looks like; humans are visual creatures and it's much easier to see something absurd if you visualize it properly.
5. Thou shalt not worship complexity
   The simpler your model is, the easier it's going to be to tell if you have a bad/misspecified variable, the less demanding it will be on your data, the more likely it is that you will be able to replicate your findings in the future. 
6. Thou shalt look long and hard at thine results
   When you find something, look at your results and make sure that they are sane. Make sure that everything's going the right way (i.e. your coefficients are properly positive or negative); that the right things are significant, and that the overall conclusion is sane. You don't want to produce a report only to find out that you transposed two of your variables!
7. Thou shalt beware of the cost of data mining
   With a firehose of data at our fingertips, it's tempting to just plug 'n' chug, blindly regressing things against each other and seeing what fits. This rarely ends well. Congratulations, you just discovered a random correlation that just happens to only fit your dataset perfectly. Your results are often bunk and evaporate as soon as more data becomes available.
8. Thou shalt be willing to compromise
   Unfortunately for economists, statisticians, and data analysts everywhere, we live in the real world; not a neatly-defined model. Your data will not be perfect, and it is your responsibility to work with what you have; not to cross your arms and hold out for that "perfect special dataset". Like in real life, there is no Mr./Mrs. Right. It is up to you to work with the conditions that you have, and understand the implications, to deliver as good a result as you can.
9. Thou shalt not confuse significance with substance
   Just because a result is significant, does not mean it actually means anything. With enough data points; you'd be surprised at how much can magically become statistically significant. It's as important to look at coefficients and effect sizes to understand if the relationship is worthwhile.
10. Thou shall confess in the presence of sensitivity
    One of Nate Silver of 538's favorite hobbies is to eat up overfitted political models. If your model relies on a small leap of faith in your variable specification, be responsible and make sure that's disclosed. Otherwise you could end up with egg on your face.

With those in mind, let's go back to the connection between margarine consumption and divorce rates in Maine. This is from "Spurious Correlations", an excellent demonstration of the dangers of blindly trusting your preferred statistic above common sense. The website pulls a number of data feeds from public and private-sector data sources from a ten-year period ('00-'09), and picks out the strongest correlations between them. Thus you dig up alarming "conclusions" about Nicholas Cage's film appearances, Oil imports from Norway, or American sour cream consumption. Of course, all of these connections are absurd, merely drawn from finding the biggest coincidences in a suitably large time series dataset.

In conclusion, be responsible when using statistics, or you could end up a sworn enemy to the American margarine industry from your faulty analysis on American marriages.

Diversity and Inequality

Last weekend, a post on Reddit's linguistics subforum showing a map of worldwide language diversity was a big hit. This map used a metric called Greenberg's Linguistic Diversity Index, which is the percent chance that two random inhabitants of a given country have two different mother tongues. States like largely-homogeneous South Korea and Haiti have low scores (0.003 and 0.000, respectively), while places like Tanzania and Papua New Guinea, where every village might speak a different language, have LDIs of 0.95 or higher.

Source: Reddit User Whiplashoo21

In the ensuing discussion, one user was interested in seeing how linguistic diversity compared with development. As you can see on the map above, many of the most linguistically diverse countries are in impoverished sub-Saharan Africa. In fact, this is a popular topic in political science and economics, studying whether cultural diversity makes a country better off, or whether it leaves a state susceptible to Balkanization and ethnic conflict.

To test this out, I started by looking at exactly what the commenter was asking about; LDI against inequality-adjusted HDI. For those who don't know, the Human Development Index is an attempt at a more holistic measure of development, which looks at three basic indicators (life expectancy, educational attainment, and per capita GDP) to come up with a single number. Since 2010, the UNDP has also published a second index, adjusted for inequality. Most states provide the UN with enough data to compute both indices, although there are a number of notable exceptions.

Source: Wikipedia image, Data from UNDP.

For my data, I used UNESCO's 2009 report on linguistic diversity for the LDI, and the UNDP's 2014 figures for HDI. This data is slightly different than the reddit post's source, but there aren't very substantial variations between the two LDIs.

IHDI = -0.308LDI + 0.691, R² = 0.246***, p < 0.00001

Unfortunately, diversity does not appear to be a positive at first glance. As the graph shows, there's a strong, but small, negative correlation. This model estimates that linguistic diversity accounts for about 25% of the variation in HDI scores. While this isn't a very large impact, it is a very interesting effect to see. Of course, it's a cardinal error in statistics to equate correlation with causation, and in this case there are two things to look out for: First, it's very likely that linguistic diversity isn't endogenous; it doesn't happen by itself. Second, there's very likely some third variable acting on both a country's diversity and development. To showcase this better, I grouped countries by continent.

Notice how much more diverse and poorer Africa is than the rest of the world. Both of these are a product of colonialism; the former a product of the Scramble for Africa which prioritized natural resources or landmarks over pre-existing ethnic groups in forming colonial borders.

Looking at greater cultural diversity comes up with similar results. I used a measure from a paper by Erkan Gören at the University of Oldenburg. Gören came up with a new index that takes into account religious, ethnic, and linguistic differences, and then adjusts them for how similar the languages actually are. This cultural diversity map (made for a blog post by Pew research) looks mostly similar to the original linguistic diversity map.

And similarly, looking at his figures come up with similar trendlines.

IHDI = -0.404GI + 0.697, R² = 0.282***, P < 0.00001

Going back to the scramble for Africa, I decided to try something new and adjusted HDI scores by continent. Since there's a lot of similar history for many countries on the same continent (Much of the Americas are monolingual ex-colonies with a very small indigenous population remaining, Africa has boundaries not drawn to ethnic lines, Asia has more-or-less well-drawn ethnic lines), maybe much of this relationship is just a product of colonial history.

IHDI_z = -0.529LDI + 0.242, R² = 0.028, p = 0.0508

And sure enough, the relationship breaks down.

One more thing I noticed is that more linguistically-diverse countries are more unequal.

% Loss = 15.614 LDI + 14.063, R² = 0.200***, p < 0.00001

Then again, that's just because poor countries tend to be more unequal anyway.

% Loss = -58.027HDI + 60.576, R² = 0.7607***, P < 0.00001

Until next time.