Women and murder: is there a relationship here? [part 1 of 2]

UPD Added R code ( gist ) to reproduce all the results

A study recently published in the prestigious scientific journal Human Nature found that the prevalence of women is associated with higher crime. The conclusion strongly contradicts the everyday notion that where men are, there are crimes. However, he finds support in relatively young theories of marital market formation.

Despite the slenderness of the methods used in the study, it seems to me that an important variable was missed in it, perhaps the key variable. It would be great to check on the same data, but the authors do not publish them as an appendix to the article, and collecting them yourself is quite a lot of work. So far I have decided to go another way - to eliminate the problem variable from the study design.

I checked whether there is a similar pattern in Europe at the country level. Interested please under the cat.

So, what confused me?

Despite the beauty of analyzing small areas (other things being equal, it is always more pleasant to analyze more fractional data), there are big doubts about the possible missing variable in the study - the division of American counties on the principle of centrality / peripherality (urban / rural).

The fact is that women are more active than men in internal migration. This is one of the laws of Ravenstein-Lee migration.

Due to this pattern in cities, the sex ratio is usually warped towards women. For illustration, here is a map of Russia from my master’s work (Fig. 1).

Figure 1. Sex ratio between the ages of 16-29 years in municipalities and cities of Russia according to the 2010 All-Russian Population Census. (clickable)

As we see, there are more women in cities (there are regional centers, where there are more men, but, as a rule, this is explained by military units — a separate topic). And this is despite the fact that there are always more boys born than girls, and at a young age there are more boys in general. But more on that later. So, thanks to internal migration, women are concentrated in cities.

And in the cities, crime is higher. There are a lot of reasons (mostly different sociological theories about isolation from the environment), but there is no need to prove this thesis.

So, in my opinion, in the study of Mine, Tharp and Smith, the key difference between the city and the periphery is probably missing. In cities, there is more crime because it is a city, and not because there are more women and less men. It is possible that the inclusion of the variable urban / rural in the explanatory model neutralizes the observed effect.

But in order to check whether this is so, one must have the same data that the researchers used. Probably do it sometime later. In the meantime, in the discussion we came to the conclusion that it would be interesting to check the revealed dependence on the data of European countries. The transition to the level of countries should largely solve the effects of migration.

Check on European data

So, the idea is to check the identified relationship on the data on population and crime of European countries. The transition to a higher level of data aggregation is intended to solve the issue of the classification of territories into central and peripheral.

Data

• population age structure - Human Mortality Database (we are interested in the Exposure-to-risk indicator);
• data on the number of murders in European countries - Eurostat (dataset of interest to us is called "crim_gen", it is easier to download here ).

Data from the two bases intersected in 28 countries (in fact, 26, just Scotland and Northern Ireland are present in the statistics separately). Not bad. There is data, then everything is simple. We calculate the ASR, adult sex ratio, the ratio of men to women aged 15-49 years (the authors of the Human Nature article use the age range 15-49 years; deviation from their methodology is dictated by the characteristics of Eurostat data) and HR, Homicide Rate, homicide rate per 100 Thousands of people of the local population.

Next is linear regression. I know that the authors use a more sophisticated statistical model, but for the beginning we will go in a simple way.

But first look at the cards.

Here is the sex ratio between the ages of 15-49 years in European countries (hereinafter, Britain is given as a weighted average of the constituent parts - I was too lazy to look for spatial data and mess with it).

Figure 2 . Sex ratio between the ages of 15-49 in Europe

As you can see, the spread is quite large (just in case, there is data in Estonia and the UK, just the values ​​are very close to 1). And this suggests the need for additional verification (but this is at the end of the article).

The prevalence of homicides in Europe varies greatly between East and West (Fig. 3). In the Baltic countries, the indicator is so much higher than in the rest of Europe (Fig. 3-A) that we have to exclude them (Fig. 3-B) from the regression analysis as outright emissions.

Figure 3 . Homicide rates, incidents per 100K population per year.

Finally, another variable included in the analysis by the authors of the original study is the proportion of the population below the poverty line. The map of European countries looks like this (Fig. 4).

Figure 4 . The proportion of the population below the poverty line.

Eliminating the Baltic countries, let's start, finally, the modeling.

Regression analysis

We simulate the homicide rate (hr) using data on the sex ratio at the age of 15-49 (asr), dummy variables for years and, in the second model, the proportion of people below the poverty line (pov). We get the following result (Table 2).

Table 2. Simulation results.

Statistical models

	Model 1	Model 2
(Intercept)	98.94 (24.46) ***	97.38 (04/20) ***
asr	-0.80 (0.24) ***	-0.89 (0.20) ***
year2001	-0.73 (1.91)	-0.72 (1.57)
year2002	-0.75 (1.91)	-0.74 (1.57)
year2003	-2.26 (1.91)	-2.26 (1.57)
year2004	-1.69 (1.91)	-1.68 (1.57)
year2005	-3.47 (1.92)	-3.45 (1.57) *
year2006	-4.32 (1.92) *	-4.28 (1.57) **
year2007	-3.51 (1.92)	-3.46 (1.57) *
pov		0.43 (0.04) ***
R 2	0.10	0.40
Adj. R 2	0.07	0.37
Num. obs.	200	200
RMSE	6.77	5.55
*** p <0.001, ** p <0.01, * p <0.05

It turns out, indeed, a lower sex ratio correlates with higher crime rates. And the poverty variable, while explaining a significant amount of variation in the data, does not neutralize the relationship between sex ratio and crime.

Figure 5. Correlation between the level of crime (murder) and the sex ratio in adulthood.

However, let us note that the sex ratio is significantly lower in Eastern Europe (Fig. 2) than in Western. Here we are likely to encounter once again the manifestation of the influence of migration, but this time migration is international. Another of the laws of migration Ravenstein-Lee argues that in international migration, by contrast, men are more active. It is possible that the results of my small verification were distorted from international migration. Verify by eliminating the effect of international migration.

Analysis by age structure from mortality tables

In order to eliminate the impact of international migration, we will resort to calculating the sex ratio from mortality tables, which can also be downloaded from the Human Mortality Database.

We calculate the sex ratio in adulthood as the ratio of the number of men and women according to the mortality table multiplied by the initial sex ratio at birth.

Thus, we have obtained the sex ratio in adulthood, as it would have been if only mortality had influenced the number of generations. That is, migration is excluded from consideration. This is how our indicator looks on the map (Fig. 7).

Figure 7 . Sex ratio in adulthood based on estimates from mortality tables.

Finally, we calculate models with a new sex ratio in adulthood. With a similar analysis, we obtain the following models.

Table 3. Simulation results, sex ratio based on total mortality rates.

Statistical models

	Model 1	Model 2
(Intercept)	503.99 (78.42) ***	466.81 (63.99) ***
asr_lt	-4.68 (0.75) ***	-4.41 (0.61) ***
year2001	-0.76 (1.80)	-0.76 (1.46)
year2002	-0.80 (1.80)	-0.80 (1.46)
year2003	-2.32 (1.80)	-2.32 (1.46)
year2004	-1.78 (1.80)	-1.78 (1.46)
year2005	-3.65 (1.80) *	-3.65 (1.46) *
year2006	-4.65 (1.80) *	-4.65 (1.46) **
year2007	-3.96 (1.80) *	-3.96 (1.46) **
pov		0.40 (0.04) ***
R 2	0.21	0.48
Adj. R 2	0.18	0.45
Num. obs.	200	200
RMSE	6.35	5.17
*** p <0.001, ** p <0.01, * p <0.05

We see that the coefficients with a variable sex ratio remained negative and increased significantly (pay attention to the scale on the X axis, Fig. 8).

Figure 8. Correlation between the level of crime (homicide) and the sex ratio in adulthood, calculated from mortality tables.

Intermediate output

The result did not meet my expectations. Neither the transition to the level of countries (to eliminate the effect of internal migration), nor the use of the sex ratio in the mortality tables (to eliminate the effect of international migration) did not change the nature of the relationship between homicide rates and sex ratio in adulthood.

In the second part there will be a test of the hypothesis on the American data.

I would appreciate comments - probably missed something.

UPD 2016-10-12 18:45 Promised R code laid out on the gith link (gist) by reference

https://goo.gl/bhOmxp

(comments on the code are welcome)

UPD 2018 : all materials on github .