Finding Slope of Linear Regression: Battle-Related Deaths & Year

[Doug Kalagian]

Hello, I’m trying to find the slope of the regression line of the three graphs attached to this post.
For each graph, I want to make a statement similar to: "From 2010-2019, the average number of battle deaths in the region increased by 25 deaths."

Dependent Variable: Number of Battle-Related Deaths
Time Span: 2010-2019
Countries: 10

Countries in graph labeled: "Figure #: Battle-Related Deaths in the Sahel": All 10 Countries
Countries in graph labeled "Figure 2: Battle-Related Deaths in the G5 Sahel Region": Chad, Mali, Niger, Burkina Faso, Mauritania
Countries in graph labeled "Figure #: Battle-Related Deaths in Non-G5S": Algeria, Senegal, Chad, Nigeria, Eritrea


Panel DataSet

country year battledeaths Mali 2010 28 Mali 2011 18 Mali 2012 218 Mali 2013 805 Mali 2014 189 Mali 2015 172 Mali 2016 96 Mali 2017 359 Mali 2018 522 Mali 2019 603 Senegal 2010 Senegal 2011 25 Senegal 2012 Senegal 2013 Senegal 2014 Senegal 2015 Senegal 2016 Senegal 2017 Senegal 2018 Senegal 2019 Sudan 2010 1054 Sudan 2011 1404 Sudan 2012 1411 Sudan 2013 593 Sudan 2014 849 Sudan 2015 1264 Sudan 2016 1309 Sudan 2017 160 Sudan 2018 243 Sudan 2019 Nigeria 2010 Nigeria 2011 324 Nigeria 2012 811 Nigeria 2013 1629 Nigeria 2014 3811 Nigeria 2015 4493 Nigeria 2016 2488 Nigeria 2017 1879 Nigeria 2018 1173 Nigeria 2019 1327 Burkina Faso 2010 Burkina Faso 2011 Burkina Faso 2012 Burkina Faso 2013 Burkina Faso 2014 Burkina Faso 2015 Burkina Faso 2016 Burkina Faso 2017 Burkina Faso 2018 79 Burkina Faso 2019 344 Niger 2010 Niger 2011 Niger 2012 Niger 2013 31 Niger 2014 Niger 2015 368 Niger 2016 274 Niger 2017 229 Niger 2018 74 Niger 2019 298 Mauritania 2010 1 Mauritania 2011 8 Mauritania 2012 Mauritania 2013 Mauritania 2014 Mauritania 2015 Mauritania 2016 Mauritania 2017 Mauritania 2018 Mauritania 2019 Algeria 2010 236 Algeria 2011 267 Algeria 2012 256 Algeria 2013 147 Algeria 2014 107 Algeria 2015 110 Algeria 2016 86 Algeria 2017 60 Algeria 2018 33 Algeria 2019 Chad 2010 4 Chad 2011 Chad 2012 Chad 2013 Chad 2014 Chad 2015 275 Chad 2016 Chad 2017 57 Chad 2018 150 Chad 2019 184 Eritrea 2010 Eritrea 2011 Eritrea 2012 Eritrea 2013 Eritrea 2014 Eritrea 2015 Eritrea 2016 25 Eritrea 2017 Eritrea 2018 Eritrea 2019

For the first graph, can this be accomplished by running a simple "regress battledeaths year"? I'm assuming my "year" variable is a categorical variable, so I'm not sure if the coefficient that STATA provides is biased.

[Clyde Schechter]

First let's be clear what you actually want.

I’m trying to find the slope of the regression line of the three graphs attached to this post.
For each graph, I want to make a statement similar to: "From 2010-2019, the average number of battle deaths in the region increased by 25 deaths."

Those two sentences contradict each other. Which is it?

The first requires fitting the regressions and finding the slopes of the regression lines. It would also require reporting the result as number of deaths per year, not as a number of deaths.

The second requires ascertaining the number of battle deaths in the region in 2010, and again in 2019 and subtracting. That's different and requires no regression at all.

On the assumption that you actually want the regression slopes, what you need to do here is to treat year as a continuous variable, not a discrete one. so -regress battledeaths year- will be fine, and the coefficient in the year row of the regression table Stata creates will be what you are looking for.

[Doug Kalagian]

You are right! My mistake. I meant to say: For each graph, I want to make a statement similar to: "From 2010-2019, the average number of battle deaths in the region increased by 25 deaths per year."

In the case of treating 'year' as a continuous variable, this was my initial intuition, but here is where my confusion arose.

For Graph 2 (Chad, Mali, Niger, Burkina Faso,) my coefficient is 25.16
For Graph 3 (Algeria, Senegal, Chad, Nigeria, Eritrea), my coefficient is 31.32
For Graph 1, when I combine all 10 countries, my coefficient is 6.95

I would expect that by combining all 10 countries, the coefficient would be somewhere between 25-31 battle-related deaths per year. Is my thinking here off?

[Clyde Schechter]

I would expect that by combining all 10 countries, the coefficient would be somewhere between 25-31 battle-related deaths per year. Is my thinking here off?

Yes, your thinking is off here. This is a common fallacy, and it is generally not taught about in statistics courses.

Notice that the vertical axes in figures 2 and 3 are on very different scales.

Try re-doing figure 1, where everything is on the same scale, using a different symbol or color for the two different groups of countries and you will see with your eyes what is going on here.

In any case, you should discard the intuition that if you put two subsets together for a regression that the combined regression slope will be some kind of (possibly weighted) average of the slopes in the separate subsets. It's only true in special circumstances.

[Doug Kalagian]

Ahh!!! Thank you!! This was extremely difficult for me to find the answer to this question. Sending some good Karma your way! ⭐⭐⭐⭐⭐

[Nick Cox]

Note that linear regression may be what is needed (instructed???) here but the application cries out for Poisson regression if a simple trend makes any sense at all. Most crucially a straight line is qualitatively wrong as implying zero deaths at some recent date and resurrection at any point earlier.

[Mead Over]

Another issue that you might want to addess is that you do not seem to be allowing any country to have zero -battledeaths- in a year. You are treating the absence of reported battle deaths as missing data when in fact, for many of these country-years, the absence of data may indicate an absence of battle deaths. Should you convert all the missing value to zero before running your regressions? Or do you have a way of distinguishing which country years are likely to be zero in reality and which are just unknown (and thus should rightfully be coded as missing)?

If in fact many years are truly zero, then you might want to separately model whether a country has a non-zero number of deaths (using a simple regression or logit or probit) and the number of deaths, given that it has some non-zero number of deaths. The first of these two sugggested regresssions might turn out to be most useful, since your slopes could then be interpreted as the increase in the probability of battle deaths per year. You could then distinguish the change in the probability of battledeaths per year between Sahel and non-Sahel countries. More sophisticated "hurdle" models are also possible, but might not add much.

As a fomer Peace Corps Volunteer to Burkina Faso, the subject of your research is of particular interest to me. Best of luck with your analysis.

[Doug Kalagian]

Another issue that you might want to addess is that you do not seem to be allowing any country to have zero -battledeaths- in a year. You are treating the absence of reported battle deaths as missing data when in fact, for many of these country-years, the absence of data may indicate an absence of battle deaths. Should you convert all the missing value to zero before running your regressions? Or do you have a way of distinguishing which country years are likely to be zero in reality and which are just unknown (and thus should rightfully be coded as missing)?

If in fact many years are truly zero, then you might want to separately model whether a country has a non-zero number of deaths (using a simple regression or logit or probit) and the number of deaths, given that it has some non-zero number of deaths. The first of these two suggested regresssions might turn out to be most useful, since your slopes could then be interpreted as the increase in the probability of battle deaths per year. You could then distinguish the change in the probability of battledeaths per year between Sahel and non-Sahel countries. More sophisticated "hurdle" models are also possible, but might not add much.

As a fomer Peace Corps Volunteer to Burkina Faso, the subject of your research is of particular interest to me. Best of luck with your analysis.

Hi Mead, I am a former Peace Corps Volunteer as well! I was placed in China back in 2013. I'm sure you have countless interesting stories from this time of your life

Thank you for your feedback. This particular dependent variable is the best estimate of the number of battle deaths in a given year (as explained in the UCDP codebook). While it may be true that there were no battle deaths in a given year, the data is provided as missing, without a 0, because it would be inaccurate to say there are 0 deaths when more deaths may have occurred and were not reported. This, at least, is my understanding of the situation.