## Reprise: The co-citation network in European Radical Right studies

In the last post, I tried to reconstruct the co-citation network in European Radical Right studies and ended up with this neat graph.

Co-citations within top 20 titles in Extreme / Radical Right studies

The titles are arranged in groups, with the “Extreme Right” camp on the right, the “Radical Right” group in the lower-left corner, and a small number of publications that is committed to neither in the upper-left corner. The width of the lines represents the number of co-citations connecting the titles.

What does the pattern look like? The articles by Knigge (1998) and Bale et al. (2010) are both in the “nothing in particular” group, but are never cited together, at least not in the data that I extracted. One potential reason is that they are twelve years apart and address quite different research questions.

Apart from this gap, the network is complete, i.e. everyone is cited with everyone else in the top 20. This is already rather compelling against the idea of a split into incompatible two incompatible strands. Intriguingly, there are even some strong ties that bridge alleged intellectual cleavages, e.g. between Kitschelt’s monograph and the article by Golder, or between Lubbers, Gijsberts and Scheepers on the one hand and Norris and Kitschelt on the other.

While the use of identical terminology seems to play a minor role, the picture also suggests that co-citations are chiefly driven by the general prominence of the titles involved. However, network graphs can be notoriously misleading.

## Modelling the number of co-citations in European Radical Right studies

Modelling the number of co-citations provides a more formal test for this intuition. There are $\frac{20\times 19}{2}=190$ counts of co-citations amongst the top 20 titles, ranging from 0 to 5476, with a mean count of 695 and a variance of 651,143. Because the variance is so much bigger than the mean, a regression model that assumes a negative binomial distribution, which can accommodate such overdispersion, is more adequate than one built around a Poison distribution. “General prominence” is operationalised as the sum of external co-citations of the two titles involved. Here are the results.

VariableCoefficientS.E.p
external co-citations0.0004.00002<0.05
same terminology0.4240.120<0.05
Constant2.8520.219<0.05

The findings show that controlling for general prominence (operationalised as the sum of co-citations outside the top 20), using the same terminology (coded as “extreme” / “radical” / “unspecific or other” does have a positive effect on the expected number of co-citations. But what do the numbers mean?

The model is additive in the logs. To recover the counts (and transform the model into its multiplicative form), one needs to exponentiate the coefficients. Accordingly, the effect of using the same terminology translates into a factor of exp(0.424) = 1.53.

## What do these numbers mean?

But how relevant is this in practical terms? Because the model is non-linear, it’s best to plot the expected counts for equal/unequal terminology, together with their areas of confidence, against a plausible range of external co-citations.

Effect of external co-citations and use of terminology on predicted number of co-citations within top 20

As it turns out, terminology has only a small effect on the expected number of co-citations for works that have between 6,000 and 8,000 external co-citations. From this point on, the expected number of co-citations grows somewhat more quickly for dyads that share the same terminology. However, over the whole range of 6,000 to 12,000 external co-citations, the confidence intervals overlap and so this difference is not statistically significant.

Unless two titles have a very high number of external co-citations, the probability of them being both cited in a third work does not depend on the terminology they use. Even for the (few) heavily cited works, the evidence is insufficient to reject the null hypothesis that terminology makes no difference.

While the analysis is confined to the relationships between just 20 titles, these titles matter most, because they form the core of ERRS. If we cannot find separation here, that does not necessarily mean that it does not happen elsewhere, but if happens elsewhere, that is much less relevant. So: no two schools. Everyone is citing the same prominent stuff, whether the respective authors prefer “Radical” or “Extreme”. Communication happens, which seems good to me.

Are you surprised?

• Arzheimer, Kai. “Conceptual Confusion is not Always a Bad Thing: The Curious Case of European Radical Right Studies.” Demokratie und Entscheidung. Eds. Marker, Karl, Michael Roseneck, Annette Schmitt, and Jürgen Sirsch. Wiesbaden: Springer, 2018. forthcoming.
@InCollection{arzheimer-2018,
author = {Arzheimer, Kai},
title = {Conceptual Confusion is not Always a Bad Thing: The Curious Case of
booktitle = {Demokratie und Entscheidung},
publisher = {Springer},
pages = {forthcoming},
year = 2018,
url =
html =
editor = {Marker, Karl and Roseneck, Michael and Schmitt, Annette and Sirsch,
Jürgen},
}

Following Friday’s events, the attached image went viral. The figures (if correct) are certainly suggestive, but obviously, the population at risk varies widely between countries. What we need is the gun-related homicide rate for a sample of comparable countries. I headed over to the Brady Campaign, which had created the image, but could not easily find comparative data. Next, I tried the very useful Gun Policy Project. Their website features very detailed country profiles, but unfortunately no ready made tables, and so I spent a lazy hour keying in gun-related and total homicide  numbers as well as possession rates (guns per 100 people) for 34 OECD countries.

Looking at the data, I decided to remove Mexico from the sample: The civil war like situation in the North means that relatively few guns are enough to kill about 11,000 people each year in a population of just over 112 million people. Put differently, about one in 10,000 Mexicans is shot dead each year. Thankfully, no other OECD member is in a comparable predicament.

Next, I created boxplots for the distribution of possession rates, gun-related and total homicide rates.

Possession, total homicide and gun-related homicide rates for OECD members

The US of A is clearly an outlier in every respect. I was somewhat surprised by Estonia’s high homicide rate. While the country’s population is small at 1.3 million people so that random fluctuation could have an impact,  a rate that is roughly six times the median seems excessively high.

Next, I specified a Negative-Binomial model of gun homicide counts as a function of the gun possession rate, controlling for the population at risk of being shot dead. Yes, I know this is dodgy with a small, non-random sample:

Negative binomial regression                      Number of obs   =         33
LR chi2(1)      =       8.17
Dispersion     = mean                             Prob > chi2     =     0.0043
Log likelihood = -162.78208                       Pseudo R2       =     0.0245

------------------------------------------------------------------------------
gunhomicides |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
possrate |   .0209951   .0083522     2.51   0.012      .004625    .0373652
_cons |  -12.85624   .2292694   -56.07   0.000    -13.30559   -12.40688
ln(popula~n) |          1  (exposure)
-------------+----------------------------------------------------------------
/lnalpha |  -.1823302    .228441                     -.6300664     .265406
-------------+----------------------------------------------------------------
alpha |   .8333261   .1903659                      .5325565     1.30396
------------------------------------------------------------------------------
Likelihood-ratio test of alpha=0:  chibar2(01) = 2361.65 Prob>=chibar2 = 0.000

As expected, gun possession raises the risk of being shot dead significantly. According to the model, each additional gun per 100 citizens increases the relative risk by exp(0.021) = two per cent (careful: If the initial risk is very low, that means that you are still quite safe).

These findings are, however, largely driven by the US with their very high possession and homicide rates. If they are excluded from the sample, the effect of gun possession is much less pronounced:

Negative binomial regression                      Number of obs   =         32
LR chi2(1)      =       0.09
Dispersion     = mean                             Prob > chi2     =     0.7660
Log likelihood = -151.9413                        Pseudo R2       =     0.0003

------------------------------------------------------------------------------
gunhomicides |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
possrate |   .0043764   .0148325     0.30   0.768    -.0246948    .0334475
_cons |  -12.61879    .298236   -42.31   0.000    -13.20332   -12.03426
ln(popula~n) |          1  (exposure)
-------------+----------------------------------------------------------------
/lnalpha |  -.1926419   .2319586                     -.6472725    .2619886
-------------+----------------------------------------------------------------
alpha |   .8247772   .1913142                      .5234716    1.299512
------------------------------------------------------------------------------
Likelihood-ratio test of alpha=0:  chibar2(01) = 2318.53 Prob>=chibar2 = 0.000

And yet, given the countries the number of gun homicides in the US is massively underestimated
by the model:

Negative binomial models for gun possession/gun homicides w and w/o US

Gun possession is easily comparable across countries but a less than perfect measure of the underlying regime. As a ratio, it does not capture the actual distribution/accessibility of guns, nor does it pick up differences in licensing laws or the availability of automatic weapons. As can be seen from the dashed line, outside the US more guns still mean more killings, but there is a lot of noise in that relationship. There are, however, three countries with very low possession rates of less than 1.5. Unsurprisingly, they also have extremely low gun homicide rates. A final, nonparametric plot picks up this relationship:

Nonparametric model for gun possession / gun homicide

So what’s the implication for the US? If the model was true and the US would bring down its possession ratio to the OECD median of 13.5 per 100 citizens, the model predicts 1071 gun homicides, as opposed to 9,146 actual cases (2009). That would be 8,075 lives saved.

But the model does not fit very well, and we might be better off with a very naive, non-parametric estimate. If the US  became less like the US and more like the rest of the OECD, its gun homicide rate might come down to the OECD median. That would amount to 846 people murdered using a gun, less than 10 per cent of the current figure. Of course, some of those people who would be spared the bullet might be killed by other means, but that is arguably more difficult. And this is just homicides. If you add manslaughter, suicides and accidents, it seems safe to assume that the NRA/Second Amendment culture costs at least 8,000 lives a year.