Article Text

A new proxy measure for state-level gun ownership in studies of firearm injury prevention
  1. Michael Siegel1,
  2. Craig S Ross2,
  3. Charles King III3,4
  1. 1Department of Community Health Sciences, Boston University School of Public Health, Boston, Massachusetts, USA
  2. 2Virtual Media Resources, Natick, Massachusetts, USA
  3. 3Greylock McKinnon Associates, Cambridge, Massachusetts, USA
  4. 4Pleiades Consulting Group, Inc., Lincoln, Massachusetts, USA
  1. Correspondence to Dr Michael Siegel, Department of Community Health Sciences, Boston University School of Public Health, 801 Massachusetts Avenue, 3rd Floor, Boston, MA 02118, USA; mbsiegel{at}bu.edu

Abstract

Since many states are considering gun control laws, researchers need reliable data on rates of gun ownership at the state level. Survey measures of gun ownership in all 50 states, however, are only available for 3 years, and no state-level data have been collected since 2004. Consequently, the National Research Council has declared the development of a valid proxy that can be constructed from accessible, annual, state-level data to be a priority. While such a proxy does exist (the proportion of suicides in a state committed using a gun (FS/S), its correlation with state estimates of gun ownership in recent years is only 0.80. Using state-level data for the years 2001, 2002 and 2004, we developed an improved proxy for state-level gun ownership that uses FS/S (firearm suicides divided by all suicides) and also the per capita number of hunting licenses. We validated this measure using data from surveys of gun ownership conducted in 48 states during 1996 and 1999, and in 21 states during 1995–1998. Adding per capita hunting licenses to the proxy increased its correlation with survey-measured gun ownership from 0.80 to 0.95. The correlations of the new proxy with gun ownership in the two validation studies were 0.95 and 0.97. We conclude that the combination of FS/S and per capita hunting licenses improves substantially upon FS/S alone. This new proxy is easily computed from data that are available annually by state and may be useful for investigating the effect of gun prevalence on firearm-related morbidity and mortality.

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The Newtown tragedy has rekindled the research agenda on the potential of firearms control to prevent more than 11 000 firearm homicides that occur among US residents each year.1 Understanding the relationship between the prevalence of gun ownership (and therefore the availability of guns) and firearm-related violence is critical to guiding policy decisions regarding firearm violence. Given the many new laws that are being considered to control the availability of guns, researchers need reliable data on rates of gun ownership. Specifically, to investigate changes in firearms violence at the state level that occur in relation to changes in the state-specific prevalence of firearm ownership, researchers need a valid panel of longitudinal data on gun ownership at the state level.

Only two existing national surveys regularly measure gun ownership. The General Social Survey (GSS) measures household gun ownership annually or biannually on a national level.2 Unfortunately, the GSS cannot be used to derive state-specific estimates of gun ownership because its sampling scheme is not designed to generate state-level data.3 ,4

The only source for periodic survey data on state gun ownership levels is the Behavioral Risk Factor Surveillance System (BRFSS) survey.5 However, the BRFSS only measured gun ownership in all 50 states for the years 2001, 2002 and 2004. Gun ownership was assessed sporadically for only 21 states during the period 1992–1998.6 Since 2004, the BRFSS has not measured gun ownership in any state.

We re-examine the performance of the fraction of the total suicides committed with a gun (FS/S) as a proxy for gun ownership at the state level by testing its association with the most recent available data from the BRFSS. We then explore revisions of the proxy measure that improve its correlation with gun ownership levels as measured by the BRFSS during the years 2001, 2002 and 2004. Finally, we validate the new measure by exploring its correlation with (1) gun ownership at the state level from the Harvard Injury Control Research Center (HICRC) surveys in 1996 and 1999 and (2) gun ownership at the state level from the BRFSS surveys during the period 1995–1998.

Our primary purpose in deriving a proxy is not to accurately predict the absolute levels of gun ownership at the state level, but to obtain a proxy that (1) correlates most strongly with survey measures of gun ownership and (2) accurately reflects proportional differences in gun ownership, such that the slope of the relationship between the proxy and gun ownership is close to 1.0. For a slope of 1.0, the regression coefficient on the proxy measure will accurately reflect the regression coefficient that would have been obtained had actual gun ownership been used in the model because proportional changes in both variables are the same.

Methods

Design overview

We examined the validity of the FS/S proxy measure for household gun ownership at the state level in recent years by examining its correlation with BRFSS estimates of gun ownership in the 50 states during the years 2001, 2002 and 2004. To improve the correlation, we examined the effects of adding additional variables to improve the FS/S proxy. The main variable of interest was per capita hunting licenses, which was first suggested as a potential proxy for gun ownership by Krug.7

Data sources

State-level estimates of household gun ownership

We obtained state-level estimates of household gun ownership for each of the 50 states from the BRFSS for the years 2001, 2002 and 2004. 5 Data were missing for 2004 for Hawaii. Thus, there were 149 data points. We obtained state-level estimates of household gun ownership from the HICRC gun ownership surveys (using combined data for the years 1996 and 1999) as reported by Azrael et al.6 There were 48 data points, as the survey was only conducted in the lower 48 states. We also obtained state-level estimates of household gun ownership from the BRFSS surveys conducted in 21 states during the period 1995–1998.5 Because of the sporadic nature of the inclusion of the gun ownership question, there were 29 data points. Although several states independently included a question on firearm ownership prior to 1995 (1992–1994), question wording was not consistent across states, and those data are not publicly available. We limited our analysis to the publicly available data from the 21 states that assessed gun ownership using an identical question during the period 1995–1998.

FS/S proxy measure

State-specific estimates of total and firearm suicides in each year were obtained from the CDC's Web-based Injury Statistics Query and Reporting System (WISQARS) database.1

State level data on hunting licenses

Data on the annual number of hunting license holders in each state were obtained from the US Fish & Wildlife Service.8 These figures were divided by a state's population ages 15+ 1 to derive hunting licenses per capita for each state.

A summary of data sources, including the average gun ownership, average FS/S, average hunting license rates and number of observations per state is included in an online-only data supplement.

State-level demographic data

We obtained data on the following state-level demographic factors: proportion of young adults (ages 15–29 years),1 proportion of young males (ages 15–29 years),1 proportion of AFricanAmericans,1 proportion of Hispanics,9 level of urbanisation, educational attainment, poverty status, unemployment,10 median household income,11 income inequality (the Gini ratio), per capita alcohol consumption12 and divorce rate.13 Where some values of a variable in certain years were missing or unavailable (for 4 of these 12 variables), we linearly interpolated data from surrounding years or linearly extrapolated from the two closest years.

Analysis

Using the BRFSS state-level gun ownership data from 2001, 2002 and 2004, we ran a set of linear regressions with the survey measure of gun ownership as the outcome variable. Beginning with the FS/S proxy, we sequentially added independent variables to the model, one at a time, in order of their descending correlations with gun ownership. We examined the R2 of the subsequent models to determine whether the addition of each variable substantially increased the proportion of variation in gun ownership explained by the model. Once we developed a final model, we used that to derive a formula to create a new gun ownership proxy variable. Because there were three observations per state, we accounted for the state clustering by running individual models for each year (2001, 2002 and 2004) to make sure that the clustering was not biasing the regression coefficients. The results were similar by year. A model that used the average of the coefficients for the 3 years produced a formula that was nearly identical to that derived from a model unadjusted for clustering.

We then validated the proxy by estimating gun ownership rates and comparing them to state-level gun ownership estimates from the HICRC surveys in 1996 and 1999 and state-level gun ownership estimates from the BRFSS surveys during the period 1995–1998. We compared the correlation between FS/S and gun ownership with that between our new proxy measure and gun ownership. We ran regression models with survey-measured gun ownership as the dependent variable and the new proxy measure as the independent variable to determine how close the regression coefficient for the proxy was to 1.0.

Results

The correlation between FS/S and state-level estimates of gun ownership from the BRFSS conducted in 50 states in 2001, 2002 and 2004 was 0.80. Per capita hunting licenses was also strongly correlated with gun ownership (r=0.80). In a linear regression model with gun ownership as the outcome and FS/S as the sole predictor variable, the R2 was 0.64. Adding per capita hunting licenses to the model increased the R2 to 0.89. There were no other variables that, when added to the model along with FS/S and per capita hunting licenses, increased the R2 above 0.91. Thus, we chose the model with FS/S and per capita hunting licenses as our final model.

The final model was: gun ownership (%)=(0.62 * FS/S)+(0.88 * per capita hunting licenses)—4.48. The correlation between this new proxy measure and gun ownership in the 2001, 2002, 2004 BRFSS surveys was 0.95 (table 1).

Table 1

Correlations between FS/S versus new proxy measure and survey measures of household gun ownership

The correlation between FS/S and household gun ownership measured in the HICRC surveys in 1996 and 1999 was 0.80. The correlation between the new proxy measure and gun ownership was 0.95 (table 1, figure 1). A regression of gun ownership on the proxy measure using the HICRC data yielded a slope of 1.22 (table 2).

Table 2

Results of regression models* of relationship between new proxy measure and survey measures of household gun ownership

Figure 1

Survey-based state-level household gun ownership (Harvard Injury Control Research Center survey—1996–1999) versus new proxy measure.

The correlation between FS/S and household gun ownership measured in the BRFSS surveys between 1995 and 1998 was 0.91. The correlation between the new proxy measure and gun ownership was 0.97 (table 1, figure 2). A regression of gun ownership on the proxy measure using the BRFSS data yielded a slope of 1.09 (table 2).

Figure 2

Survey-based state-level household gun ownership (Behavioral Risk Factor Surveillance System survey—1995–1998) versus new proxy measure.

We used the newly derived proxy measure to estimate household gun ownership using all the available state-level data combined (226 data points). The correlation between FS/S and gun ownership was 0.81, while the correlation between the new proxy measure and gun ownership was 0.94 (table 1). A regression of gun ownership on the proxy measure using all available state data yielded a slope of 1.07 (table 2).

Discussion

We derive a new proxy for state-level gun ownership that increases the correlation between the proxy and recent survey-measured, household gun ownership to 0.95 compared with 0.80 for the previous proxy (FS/S). The new proxy is proportional to gun ownership, making it useful for monitoring differences in state-level gun ownership, and for modelling the effects of gun ownership on outcomes, such as homicide or suicide. This new proxy incorporates per capita hunting licenses in addition to FS/S. Both variables are readily available annually by state. The proposed proxy is both readily computed and has increased validity.

Why does the addition of per capita hunting licenses improve the proxy? One possibility is that guns used for hunting are not often used in suicides and that their ownership is therefore not reflected in the FS/S measure. If true, then the FS/S measure would perform least well in states with high per capita hunting licenses. An examination of our combined database revealed that for the 10 states with the highest rates of hunting licenses (Idaho, Wyoming, Montana, South Dakota, Vermont, North Dakota, Maine, Alaska, Utah and West Virginia), the correlation between gun ownership and the old proxy was only 0.48 (improved to 0.74 with the new proxy), but in the remaining states, the correlation between gun ownership and the old proxy was 0.86 (improved to 0.94 with the new proxy). Thus, the new proxy appears to be most valuable in improving the previous proxy in states with high hunting license rates. Data from the CDC's National Violent Death Reporting System for 16 states in 2010 show that only 5.2% of suicides were committed using a rifle, while 49.3% of suicides were committed with another type of gun.14 It is therefore possible that hunting gun ownership is largely not reflected in the FS/S measure.

Although our new proxy correlates very highly with state-level gun ownership as measured by surveys, it is not intended as a predictor of absolute levels of gun ownership. The negative intercept terms in table 2 demonstrate that the new proxy tends to overestimate gun ownership by several percentage points. The utility of the proxy is not in predicting levels of gun ownership but in accurately reflecting proportional differences in gun ownership between states. The proxy allows for studies to validly examine the effect of differences in state-level gun ownership on violent injury or death at the state level.

A second important limitation is that the proxy has only been validated for short cross-sectional time periods during which reported gun ownership was stable, it is not clear that this proxy can be used to measure changes in gun ownership over time.

The survey measures used as the benchmark for state-level household gun ownership are relatively old. Thus, it is also not clear how well the new proxy performs in more recent years. While the proxy is not intended to be used for national gun ownership estimates (as GSS data are available), we examined the correlation between the new and old proxies and GSS estimates of national household gun ownership during the period 1982–2010.15 This analysis revealed that although the new proxy was more closely correlated with national estimates (r=0.88) than the old proxy (r=0.81) during the entire period of 29 years, the two measures were almost equally correlated with national estimates for the most recent two decades (r=0.89 for new proxy, r=0.86 for old proxy). Thus, it appears that the new proxy may be most useful in improving upon the old proxy for older data. Per capita hunting licenses have declined over time, with national rates falling from 9.3/100 in 1982 to 5.6/100 in 2010.8 To the extent that the old proxy was underperforming because it failed to account for guns used for hunting, this bias is declining over time, which may explain why the correction for hunting licenses included in the new proxy is less important in more recent years.

Another limitation of this study is that survey measures of gun ownership may themselves be inaccurate because of small sample sizes in some states, non-response bias and reporting bias.6 Thus, it is not clear to what extent observed differences between the new proxy and survey measures of gun ownership are attributable to limited predictive value of the proxy compared with errors in the survey measures themselves.

Despite these limitations, we conclude that the combination of FS/S and per capita hunting licenses provides the best available proxy for state-level gun ownership, improving substantially upon FS/S alone. This new proxy is easily computed from readily accessible data that are available annually by state, correlates highly with survey measures of household gun ownership, and is almost directly proportional to gun ownership. This new proxy may be useful for studying the effect of state-level gun control laws on gun ownership and for investigating the effect of gun prevalence on firearm-related morbidity and mortality.

What is already known on this subject

  • In response to the tragic shooting in Newtown, Connecticut in December 2012, many states are considering, or have enacted, gun control legislation.

  • To evaluate the impact of new state gun control laws, researchers need reliable data on rates of gun ownership at the state level.

  • Since there is no source for state-specific gun ownership data, a proxy for gun ownership—the proportion of suicides committed with a firearm (FS/S)—has been used.

  • In recent years, the FS/S proxy has not performed as well as in the past. Consequently, the National Research Council has called for more research into the use of proxies for gun ownership.

What this study adds

  • We derive a new proxy for state-level gun ownership that increases the correlation between the proxy and recent survey-measured, household gun ownership to 0.95 compared with 0.80 for the previous proxy (FS/S). The new proxy is proportional to gun ownership, making it useful for modelling the effects of gun ownership on outcomes, such as homicide or suicide.

  • The new proxy incorporates per capita hunting licenses in addition to FS/S. Both variables are readily available annually by state. The proposed proxy is both readily computed and has increased validity.

  • This new proxy may be useful for studying the effect of state-level gun control laws on gun ownership, and for investigating the effect of gun prevalence on firearm-related morbidity and mortality.

References

Supplementary materials

  • Supplementary Data

    This web only file has been produced by the BMJ Publishing Group from an electronic file supplied by the author(s) and has not been edited for content.

    Files in this Data Supplement:

Footnotes

  • Contributors All authors contributed to the conception and design, analysis and interpretation of data, and revising the article critically for important intellectual content, and approved the final version. Dr MS acquired the data and drafted the manuscript.

  • Competing interests None.

  • Provenance and peer review Not commissioned; externally peer reviewed.

  • Data sharing statement The study analyses data from publicly available secondary databases.