- - - - - - -
- - +Abstract— The aim of this paper is to provde a summary analysis +of the data regarding the effectiveness of gunrestriction policy in +diminishing the numberof gun-related deaths. We do so by conducting an +analysis of three different datasets, and by combining the data we +gathered from them, constructing a linear regression model. The +constructed linear regression model shows a negative correlation between +the gun-related death rate and the amount of legislation present within +the state. This leads us to believe that it’s possible for legislation +to have a positive effect on gun-related deaths.
+Index terms—Gun regulation, Gun death rate, Violent crime rate
+Introduction
+The topic of gun regulation has been discussed at length in the United +States of America, because of the real and present danger that it poses +to Public Safety. There’s little doubt that policy has potential to do +enourmous amounts of harm, as well as benefit, but it needs direction +from data. The aim of this paper is to conduct a summmary analysis of +the correlation between overall presence of gun restriction and the rate +of deaths caused by guns.
+Paper overview
+In this paper, we analyse data coming from three different datasets: one +[@Lawprovisions] is a collection of all gun restiction laws that have +been put in place by individual states, the second [@Gundeaths] is a +collection of gun deaths by county. The third [@Violentcrimes] trakcs +violent crime rates.
+The scope of the paper is national, and we aim to obtain valuable +information by comparing the performance of different states within the +same country: we expect the cultural differences to be (even if still +present) less impactful than they would be in a inter-country +comparison, and thus hope to be able to eliminate most untraceable +biases that would arise from it.
+To reach our conclusions, we conducted an analysis of the 3 datasets, +using them as follows:
+-
+
-
+
From the first dataset, we extracted an index to answer the question +‘how much regulation around guns is present in this state?’
+
+ -
+
From the second dataset, we extracted aggregated data by year and by +state regarding deaths and death rate by guns
+
+ -
+
From the third dataset, we extracted information about the change in +violent crime rates over time, to be able to set up a multiple +regressor linear regression model
+
+
Overall, we found a negative correlation between the gun provision index +and the gun death rate, even when accounting for the changes in violent +crime.
+Methods
+Preparing the Datasets
+Dataset 1
+The first dataset is comprised of informations regarding deaths by guns +divided by county, but our analysis takes place at the state level. +Therefore, the dataset was grouped by state and we removed superfluous +variables like county code, state code and state initials.
+Additionally all of our datasets contain data compiled at different +points in time so the information was filtered to be in years +overlapping across all three datasets, the nineteen years from 1999 to +2017.
+The preparation was done in the following way:
+gundeaths_cut <- gun_deaths_us_1999_2019[-c(1, 3:5, 7)]
+gundeaths_cut <- subset(gundeaths_cut, !gundeaths_cut$Year > 2017)
+gundeaths_cut <- gundeaths_cut[-c(5:10)]
+gundeaths_cond <- gundeaths_cut %>%
+ group_by(across(where(is.character))) %>%
+ summarise(across(where(is.numeric), sum, na.rm = T), .groups = "drop")
+We then constructed a simple rate, balanced over 100,000 people, to +provide for the different populations between states.
+gundeaths_cond$Rate <- 0
+for (i in 1:nrow(gundeaths_cond)) {
+ r <- ((gundeaths_cond$Deaths[i] / gundeaths_cond$Population[i]) * 100000)
+ gundeaths_cond$Rate[i] <- r
+}
+The the final form of the dataset was:
+| Year | +State | +Deaths | +Population | +Rate | +
|---|---|---|---|---|
| 1999 | +Alabama | +605 | +3047241 | +19.854025 | +
| … | +… | +… | +… | +… | +
Dataset 2
+The second dataset contains all of the laws restricting gun usage for +each US state, represented by 133 binary variables. Aside from filtering +for the correct years a Index (referred to as “Gun Regulation Index” +from here on) was constructed usin min-max normalization.
+law_provision_norm <- subset(law_provision_norm, !law_provision_norm$year < 1999)
+proc_lawprov <- preProcess(as.data.frame
+(law_provision_norm$lawtotal),
+ method = c("range"))
+law_provision_norm$index <- predict(proc_lawprov, as.data.frame(law_provision_norm$lawtotal))
+To account for differences, states were given scores, “Very Low” “Low” +“Medium” “High”, according to their Gun Regulation Index.
+merged$Score <- ifelse(unlist(merged$index) <0.25, "Very Low",ifelse(unlist(merged$index) <0.5, "Low", ifelse(unlist(merged$index) <0.75, "Medium","High")))
+Final product:
+| Year | +State | +Law Total | +Index | +Score | +
|---|---|---|---|---|
| 1999 | +Alabama | +16 | +0.126213592 | +Very Low | +
| … | +… | +… | +… | +… | +
Dataset 3
+The third dataset, mainly added for multiple linear regression purposes +in an attempt to account for Omittted Variable Bias, contains the raw +numbers of different types of crimes committed in each state. To keep +the data as closely related to guns as possible, and to make sure there +was no instance of double counting (it wasn’t made clear what of the +specific crimes listed counted as a ‘Violent Crime’) we just included +“Violent Crimes”.
+estimatedcrimes_cut <- subset(estimated_crimes, estimated_crimes$year >= 1999)
+estimatedcrimes_cut <- subset(estimatedcrimes_cut, estimatedcrimes_cut$year <= 2017)
+estimatedcrimes_cut <- subset(estimatedcrimes_cut, !estimatedcrimes_cut$state_name == "District of Columbia")
+estimatedcrimes_cut <- subset(estimatedcrimes_cut, !estimatedcrimes_cut$state_name == "")
+estimatedcrimes_cut <- estimatedcrimes_cut[-c(2,4,6:15)]
+A Violent crime rate was then constructed, balanced on thousands of +people.
+estimatedcrimes_cut$VCrime_Rate = 0
+for (i in 1:nrow(expl_merge)) {
+ expl_merge$VCrime_Rate[i]<- ((expl_merge$violent_crime[i] / expl_merge$Population[i]) * 1000)}
+The data obtained was formatted in the following way:
+| Year | +State | +Violent Crimes | +VCrime Rate | +
|---|---|---|---|
| 1999 | +Alabama | +21421 | +7.029638 | +
| … | +… | +… | +… | +
Descriptive Analysis
+Dataset 1
+The Gun Deaths dataset shows the average deaths to be 515.34, with a +standard deviation of 605.09, the death rate instead has an average of +11.90% and a standard deviation of 4.67%, these descriptive statistics, +although weak alone, show a variance of considerabe size.
+
+.png)
The graphs show the variance and its evolution over time.
+To aid visualization we also constructed a histogram representing the
+death count for each state
+
Dataset 2
+For the law provision dataset the mean of the law total is 24.92, with a +standard deviation of 23.60, instead the mean of the Gun Regualtion +Index is 0.21, with a standard deviation of 0.23, again showing a big +variance in our data.
+
As it’s easily interpretable most of the states have a kept a very low +index for the time period analyzed in this study, but there are +instances of some states, for example the state of California, keeping +very high Index values across the whole time period. This wide gap was +not a surprise, as the difference of positions of prominent political +figures in the respective states are pretty representative of their -be +it high or low- index score. +.png)
+In order to understand the importance of the division of the states in +accordance to their scores, it’s important to visualize the position of +the US states, as the differences will become painfully obvious.
+
This bar chart represents the scores of all the US states across our 19 +year time period, and it’s pretty easy to say that seeing these +discrepancies also shaped our future analyisis and prompted us towards +conducting it by keeping track at all times of each state’s score.
+Dataset 3
+The third dataset, the one containing the information about violent +crimes in the us presents itself in an analogous way to the previous +datasets. The mean of the violent crimes is 26976.7, with a standard +deviation of 34431.64, while the mean of the violent crime rate is +6.18%, with a standard deviation of 2.62%
+Once again, a high variance is observable across all of our data, again +suggesting the importance of a criteria of distinction (in our case the +index score) in the state-level analysis to capture efficiently +correlations and statistically useful results.
+
+
Explorative Analysis
+Having established the nature and characteristics of the three datasets,
+we now proceed to conduct an analysis of the combination of their data.
+The aim of this analysis is to establish the impact (or lack there of)
+of legislation on gun death rates. In order to do so, we first seek to
+check for the presence of correlation, and then formulate a linear
+regression model. We then will try to integrate data from possibly
+correlated variables in an attempt to remove omitted variable bias, and
+thus create a multiple regressor linear regression model.
+The explorative analysis began by plotting and calculating the mean gun
+death rate (by 100,000) over time, and comparing it with the mean Gun
+Regulation index over time.
+
At a first glance just by looking at the graphs side to side may lead us +to think that even if the Gun Regulation Index has been rising over time +the Deaths by guns still don’show any signs of decreasing, but a closer +inspection reveals that the Gun Regulation Index over nineteen years has +only increased by a meager 0.04% and to discern a pattern we need to go +deeper and look for substantial causal effects.
+By calulating the Pearson correlation between the Gun Regulation Index +and the gun death rate we’re returned with a value -0.624, suggesting a +non-negligible negative correlation between them
+
By plotting them in the same graph the negative correlation becomes
+obvious, but we can also notice the skewedness of observations towards
+the low values of the Gun Regulation Index, so in accordance to our
+prior suggestion we split the observations in accordance with their own
+Index score bracket and run the same analysis.
+
By splitting the
+observations we get a clearer image: the -0.624 correlation isn’t
+consistent across all states, but the pattern can still be observed.
The correlations for each groups are as follows:
+-
+
-
+
Very low score states = -0.375
+
+ -
+
Low score states = -0.254
+
+ -
+
Medium score states = -0.555
+
+ -
+
High score states = -0.4123633
+
+
Here we also begin to see the signs of a pattern repeating also in the +next steps: Medium score countries tend to have the highest correlation +among all of the groups.
+Now, after setting up a linear model, we obtained the results of an +intercept equal to 14.63 and the index coefficient equal to -12.65.
+This number may seem absurdly big, but during the interpretation it is +useful to remember that our index is normalized, so states will benefit +from the full value only if they have a high enough index.
+Due to the general unreliability and susceptibility to outliers of +linear regression it was at this point that we decided to aid our +analysis with the inclusion of the third dataset, with the aim of +constructing some additional linear models and useful plots.
+
Before cimenting
+ourselves into the actual model building, we included the evolution of
+the mean violent crime rate over time and, once again an immediate
+analysis may lead us to think that as the Gun Regulation Index increased
+the violent crime rate decreased, and this is also supported by the
+corrlation between them (-0.293), and their plot.
+
But we
+very quickly found out that this plot is actually very misleading. It
+simply takes a division of states by score and we can analyze much more
+interesting data.
+
Now that
+the plots are much clearer, while our pattern in the sheer size of the
+negative correlation between our values in medium score states is
+visible to the naked eye, we can also observe some instances of positive
+correlations in some of the following cases:
-
+
-
+
Very low score states = -0.0596
+
+ -
+
Low score states = 0.403
+
+ -
+
Medium score states = -0.654
+
+ -
+
High score states = 0.229
+
+
While the social interpretation of these findings is out of the scope of +this study without claiming anythin we can still infer that the data +shows that increasing the Gun Regulation Index has some dubious effects +in relation with the Violent Crime Rate, we can still interpret that +Violent Crime is not a simple enough issue that can be fixed just by +increasing Gun Control.
+Building a linear model emphasizes this finding since it returned us a
+value of 6.896 for the intercept and of -3.335 for our Gun Regulation
+Index.
+
+Now, we may also be interested in the relationship between gun deaths
+and the violent crime rate, so we calculated once again the correlation
+between them and obtained a value of 0.471, showing that indeed they are
+correlated.
+
Now,to understand relationships on a deeper level, we once again divided
+the states in accordance to their score.
+
In this case we can observe that all of our brackets contain some level +of positive correlation, in particular:
+-
+
-
+
Very low score states = 0.371
+
+ -
+
Low score states = 0.285
+
+ -
+
Medium score states = 0.685
+
+ -
+
High score states = 0.239
+
+
As anticipated before, medium score states continue to stand out in +their correlations in our analysis this has been a constant so far +[think of a possible explanation][criminals don’t steal from the +middle class!][no but srs help needed]
+By building a linear model we’re met with the following results: a value
+of 3.029 for the intercept and 0.264 for the Death Rate coefficient,
+showing a surprisingly low coefficient, but understandable, since the
+Death Rate is balanced over 100.000 people.
+
+For the final passage of our study we culminated the research by trying
+to draw some conclusions making use of multiple linear regression in an
+attempt to fix eventual mistakes made with the usage of linear
+regression, in other words by adding the Violent Crime rate we try to
+solve some of the omitted variable bias that could have tampered with
+our data.
+
+With the construction of the Multiple linear regression model we
+obtained the values of: 10.755 for the intercept, -10.775 for the
+coefficient of our Gun Regulation Index and 0.563 for the coefficient of
+the violent crime rate.
Even if the coefficient of the violent crime rate returned pretty small +values, since also the intercept and the coefficient for Gun Regulation +got smaller means that we achieved our aim of covering some of the +unexplained variance.
+We then plot these results in a 3d interactive plot (available for
+download in the GitHub repository for this study and
+here),
+that due to the limitations of pdfs can be relayed here only in the form
+of an image. 
Conclusions
+The relationship that emerges from the data is clear, even if not
+perfectly consistent: there’s a negative correlation between our gun
+provision index and the gun death rate. This correlation gets weaker
+with the introduction of violent crime rates as a regressor in the
+linear regression model, but it remains negative on the whole (although
+it becomes positive in the case of low and high score states. It’s worth
+noting that they’re a much smaller sample than the very low score
+states, which remains negative. This is visible by the total remaining
+overall negative).
+While the policy analysis is complicated, this would seem to suggest
+that it’s possible, although obviously not guaranteed, to write
+legislation that aims and achieves and improvement in the number of
+gun-related deaths.
Future work
+The work could benefit with an expansion in a few areas:
+-
+
-
+
Integration of more variables that might be correlated with the gun +death rate in order to escapoe possibleomitted variable bias
+
+ -
+
analysis of the effectiveness in relation to the intentionality +behind gun deaths: what kind of deaths does gun control prevent?
+
+
Appendix
+The full script and project contents are freely available here under the GPL_v3 license.
+Contributions
+Francesco Prem Solidoro
+Contributed to the writing of the code, to the search and reformatting +of the datasets, to the writing of the document (in particular: +abstract, conclusions) and management of the tooling used for the +project (github, git, typst.app, firebase)
+Michele Salvi
+Contributed to the writing of the code, to the search and reformatting +of the datasets, and to the writing of the document (in particular: +methodology, sections A, B and C)
+Juan Calani
+Contributed to the ideation of the project, and provided a reiview of +the work
+Elena Rocco
+Contributed provided a review of the work