Friday, September 01, 2006
Predicting Self-inflicted Deaths of Active United States Military Personel
Abdul Karim Bangura
American University
Washington, DC 20016
bangura@american.edu
Walter W. Hill, Jr.
St. Mary’s College of Maryland
St. Mary’s, Maryland
wwhill@smcm.edu
Introduction
While combat related deaths of active United States military personnel resulting from accidents, hostile actions, homicides, illnesses, and terrorist attacks are relatively expected, self-inflicted deaths are a bit difficult to expect. Consequently, it behooves us to investigate and understand the trend in such deaths (i.e. self-inflicted). Scholars of International Relations, especially those studying protracted conflicts, employ a series of mathematical models that are potentially highly useful and, at the least, interestingly suggestive, in predicting trends in protracted phenomena [ 1 ]. From this methodological approach, we believe that self-inflicted deaths of active American military personnel increase over time. This is due in part to the fact that the United States seems to be involved in protracted conflict situations.
The goal of this paper is to forecast self-inflicted deaths among active American military personnel. We consider a battery of models to fit the available data. We also choose univariate time series models, as they permit forecasting [ 2 ]. We discover that these models say that self-inflicted deaths of active United States military personnel will continue to increase.
The data
We take as our objective to predict the level of the self-inflicted deaths over the next few years. We therefore use models in the next section which have potential for modeling dynamic processes. The data are the number of self-inflicted deaths from 1980 through 2004 reported by the Congressional Research Service [ 3 ].
We first want to know if these data roughly track the level on conflict as indicated by non-quantitative observers of the situation. There is more or less a consensus from the narrative literature on the outline of the trajectory of events in our time span. This pattern is replicated well in our data as shown in Figure 1. The number of the self-inflicted deaths rose in 1996 as we predicted. The expected plateau and slow decline also appear. We are well satisfied that the data meet this initial test.
Figure 1 Number of self-inflicted deaths
The models
We now turn to formal models to see if we can better understand the system which we are studying. Most of the estimated models we examine in the following pages are dynamic. We take advantage of this feature by making predictions about the likely trajectory of the trend. Our a priori expectation is that the trend is unstable. In the following discussion, we look at to what extent, if any, that this projection is supported by the data. We first turn briefly to a check on the validity of the data.
One potential problem in the method of analysis here is that, given that we simply count the number of self-inflicted deaths, it may be the case that we severely underweight the importance of high intensity events. Given that the data correctly track the explosion in 1996, we are not immediately fearful that this presents a problem, at least on first cut. Nevertheless, it would be more persuasive if we are able to test to see if we have excluded an important feature of the system.
We have data from 1980 through 2004. If we take data from these years exclusively, we will have 25 observations. We are able to write a program to perform Fourier Analysis. We make the usual transformation that the observations are over a time period of 2*pi [ 4 ]. On the data on self-inflicted deaths, we used the following model:
deaths = a0 + a1*sin(t) + b1*cos(t) + a2*sin(2t) + b2*cos(2t) + ... (1)
a0 = 211.68
a1 = 482.71 b1 = 482.17
a2 = 1.51 b2 = 77.67
a3 = 287.08 b2 = 144.77
a4 = 101.29 b3= 113.40
We think the data set is too short. We believe that anything more that the first few parameters are not meaningful. We run the program on data in a text book using 1,000 observations and we got reasonable results. So the program passes the little test we give it.
We do a test to see if there is a significant difference in self inflicted deaths in years with a war than in years without a war. The operational definition of a year with a war was more than one battle death. There was no significant difference.
We then look at a bar chart of the data to see if the distribution looked Poisson. The variance of the data is a bit high for a Poisson distribution. We did a quick square test in which we would accept the null hypothesis that the data are from Poisson distribution, but there is not a lot of observations. Also, the distribution is bimodal. This implies that there are in fact two underlining processes. We then notice that deaths after 1995 are much less than those before that year. That seems like the break point we earlier intuited is there?
The Muncaster-Zines model [ 5 ] is not appropriate as one needs to believe that their model will work here. Hibbs-like models [ 6 ] comes out of a Box Jenkins tradition.
A plot of the data across time presented in Figure 1 shows two different regions. First, the self inflicted deaths for 1980 1995 look random. Second, the self-inflicted deaths from 1996 show a consistent trend downwards except for the first war year.
We perform an OLS regression (Box Jenkins style but not their estimation routine) for the period 1980 1995 with various lags. Nothing significant appears:
self(t) = 0.190*self(t 2) + 293 (2)
The first order lag even drops out when we perform a backwards regression.
For the period after that, we have the following:
self(t) = 79.5 + 0.39*self(t 1) + 66.5*Dummy, (3)
where Dummy = 1 if year = 2003, otherwise Dummy = 0.
We have p=0.028 so this is significant at the 5% level.
Note also that something dramatic happened in 2003. It was the beginning of the second war with Iraq.
Conclusion: A Stable System
We have taken self-inflicted deaths of active United States military personnel data from 1980 through 2004, and we have estimated parameters of the phenomenon after positing several different models. We have consistently found that the models predict that the trend is endemic, and that the level of these self-inflicted deaths is expected to be stable over time. This means that we would expect the level of violence to change over time, perhaps to shocks exogenous to our model. Those shocks, however, are not expected to increase to such an extent as to result in a change in the system.
REFERENCES
1. See, for example, E. E. Azar and J. D. Ben Dak, eds., Theory and Practice of
Events Research, Gordon and Breach, New York, 1975; E. E. Azar and N. Farah, The structure of inequalities and protracted social conflict: a theoretical framework, International Interactions, 7:4 (1981); E. E. Azar, Protracted social conflict in Lebanon (unpublished working paper, University of Maryland College Park Department of Government and Politics, n.d.); P. Allan, Diplomatic time and climate: a formal model, Journal of Peace Science. 3 (April 1980).
2. C. Chatfield, The Analysis of Time Series: An Introduction, Chapman and Hall,
London (1980).
3. Congressional Research Service, American War and Military Operations
Casualties: Lists and Statistics, CRS Library of Congress, Washington, DC
(2005).
4. R. M. Werner, Spectral Analysis of Time Series Data, Guilford Press, New
York, 1998.
5. R. G. Muncaster and D. A. Zines, 1982/1983. A model of inter nation hostility
dynamics and war, Conflict Management and Peace Science, 6:2 (Spring, 1982/1983).
6. D. Hibbs, D. Political parties and macroeconomic policy, American Political
Science Review, 71:4 (1977).
American University
Washington, DC 20016
bangura@american.edu
Walter W. Hill, Jr.
St. Mary’s College of Maryland
St. Mary’s, Maryland
wwhill@smcm.edu
Introduction
While combat related deaths of active United States military personnel resulting from accidents, hostile actions, homicides, illnesses, and terrorist attacks are relatively expected, self-inflicted deaths are a bit difficult to expect. Consequently, it behooves us to investigate and understand the trend in such deaths (i.e. self-inflicted). Scholars of International Relations, especially those studying protracted conflicts, employ a series of mathematical models that are potentially highly useful and, at the least, interestingly suggestive, in predicting trends in protracted phenomena [ 1 ]. From this methodological approach, we believe that self-inflicted deaths of active American military personnel increase over time. This is due in part to the fact that the United States seems to be involved in protracted conflict situations.
The goal of this paper is to forecast self-inflicted deaths among active American military personnel. We consider a battery of models to fit the available data. We also choose univariate time series models, as they permit forecasting [ 2 ]. We discover that these models say that self-inflicted deaths of active United States military personnel will continue to increase.
The data
We take as our objective to predict the level of the self-inflicted deaths over the next few years. We therefore use models in the next section which have potential for modeling dynamic processes. The data are the number of self-inflicted deaths from 1980 through 2004 reported by the Congressional Research Service [ 3 ].
We first want to know if these data roughly track the level on conflict as indicated by non-quantitative observers of the situation. There is more or less a consensus from the narrative literature on the outline of the trajectory of events in our time span. This pattern is replicated well in our data as shown in Figure 1. The number of the self-inflicted deaths rose in 1996 as we predicted. The expected plateau and slow decline also appear. We are well satisfied that the data meet this initial test.
Figure 1 Number of self-inflicted deaths
The models
We now turn to formal models to see if we can better understand the system which we are studying. Most of the estimated models we examine in the following pages are dynamic. We take advantage of this feature by making predictions about the likely trajectory of the trend. Our a priori expectation is that the trend is unstable. In the following discussion, we look at to what extent, if any, that this projection is supported by the data. We first turn briefly to a check on the validity of the data.
One potential problem in the method of analysis here is that, given that we simply count the number of self-inflicted deaths, it may be the case that we severely underweight the importance of high intensity events. Given that the data correctly track the explosion in 1996, we are not immediately fearful that this presents a problem, at least on first cut. Nevertheless, it would be more persuasive if we are able to test to see if we have excluded an important feature of the system.
We have data from 1980 through 2004. If we take data from these years exclusively, we will have 25 observations. We are able to write a program to perform Fourier Analysis. We make the usual transformation that the observations are over a time period of 2*pi [ 4 ]. On the data on self-inflicted deaths, we used the following model:
deaths = a0 + a1*sin(t) + b1*cos(t) + a2*sin(2t) + b2*cos(2t) + ... (1)
a0 = 211.68
a1 = 482.71 b1 = 482.17
a2 = 1.51 b2 = 77.67
a3 = 287.08 b2 = 144.77
a4 = 101.29 b3= 113.40
We think the data set is too short. We believe that anything more that the first few parameters are not meaningful. We run the program on data in a text book using 1,000 observations and we got reasonable results. So the program passes the little test we give it.
We do a test to see if there is a significant difference in self inflicted deaths in years with a war than in years without a war. The operational definition of a year with a war was more than one battle death. There was no significant difference.
We then look at a bar chart of the data to see if the distribution looked Poisson. The variance of the data is a bit high for a Poisson distribution. We did a quick square test in which we would accept the null hypothesis that the data are from Poisson distribution, but there is not a lot of observations. Also, the distribution is bimodal. This implies that there are in fact two underlining processes. We then notice that deaths after 1995 are much less than those before that year. That seems like the break point we earlier intuited is there?
The Muncaster-Zines model [ 5 ] is not appropriate as one needs to believe that their model will work here. Hibbs-like models [ 6 ] comes out of a Box Jenkins tradition.
A plot of the data across time presented in Figure 1 shows two different regions. First, the self inflicted deaths for 1980 1995 look random. Second, the self-inflicted deaths from 1996 show a consistent trend downwards except for the first war year.
We perform an OLS regression (Box Jenkins style but not their estimation routine) for the period 1980 1995 with various lags. Nothing significant appears:
self(t) = 0.190*self(t 2) + 293 (2)
The first order lag even drops out when we perform a backwards regression.
For the period after that, we have the following:
self(t) = 79.5 + 0.39*self(t 1) + 66.5*Dummy, (3)
where Dummy = 1 if year = 2003, otherwise Dummy = 0.
We have p=0.028 so this is significant at the 5% level.
Note also that something dramatic happened in 2003. It was the beginning of the second war with Iraq.
Conclusion: A Stable System
We have taken self-inflicted deaths of active United States military personnel data from 1980 through 2004, and we have estimated parameters of the phenomenon after positing several different models. We have consistently found that the models predict that the trend is endemic, and that the level of these self-inflicted deaths is expected to be stable over time. This means that we would expect the level of violence to change over time, perhaps to shocks exogenous to our model. Those shocks, however, are not expected to increase to such an extent as to result in a change in the system.
REFERENCES
1. See, for example, E. E. Azar and J. D. Ben Dak, eds., Theory and Practice of
Events Research, Gordon and Breach, New York, 1975; E. E. Azar and N. Farah, The structure of inequalities and protracted social conflict: a theoretical framework, International Interactions, 7:4 (1981); E. E. Azar, Protracted social conflict in Lebanon (unpublished working paper, University of Maryland College Park Department of Government and Politics, n.d.); P. Allan, Diplomatic time and climate: a formal model, Journal of Peace Science. 3 (April 1980).
2. C. Chatfield, The Analysis of Time Series: An Introduction, Chapman and Hall,
London (1980).
3. Congressional Research Service, American War and Military Operations
Casualties: Lists and Statistics, CRS Library of Congress, Washington, DC
(2005).
4. R. M. Werner, Spectral Analysis of Time Series Data, Guilford Press, New
York, 1998.
5. R. G. Muncaster and D. A. Zines, 1982/1983. A model of inter nation hostility
dynamics and war, Conflict Management and Peace Science, 6:2 (Spring, 1982/1983).
6. D. Hibbs, D. Political parties and macroeconomic policy, American Political
Science Review, 71:4 (1977).
# posted by Abdul Karim Bangura @ 11:31 AM 
