Suicide and Male Violence: Plausibility Model
Note: this is part of the Youth Suicide Rise project.
Note: the context is presumed to be ages 15-19 from 1981 to 2018 -- so below 'male suicide' means male youth suicide 1981-2018, unless stated otherwise. This post is a follow-up to the the Suicide and Homicide Rates and Homicide and M/F Suicide Ratio posts.
Factor V
Let us postulate a 'violence' factor V that is responsible for male homicide rates.
This imaginary factor V is really an encapsulation of a family of causes behind homicide, which may include innate aggressiveness, social dysfunction, poverty, parental abuse, lead poisoning, access to guns, and so on.
Factor V and Causation
We measure factor V by one of its results, homicide rates, but we do not identify V with homicides.
The reason we differentiate between factor V and homicides is to keep in mind that a relationship between suicide and homicide could be due to underlying causes (factor V), rather than due to the influence of one on the other.
Consider these two possibilities:
A) When homicide increases, so does suicide because boys become desensitized to death and because of the trauma of witnessing homicides, or losing a relative or friend to homicide, or being victimized by violence.
B) When homicide increases, it is due to causes (factor V) that also increase suicide; for example, innate aggressiveness, social dysfunction, poverty, parental abuse, lead poisoning, access to guns, and so on.
In symbolic form, these two possibilities are A) V --> Hom --> Sui and B) V --> Sui + Hom.
If type A causation was the only possibility, we could identify V with Homicide, but in reality the type B causation mechanism is likely to be true as well.
The Goal
We will attempt to show that even when measurement of the underlying causes is simplified down to a single yearly value (homicide rates), it can help predict how male suicide rates differ from female suicide rates.
The influence of factor V on male suicide should be strong enough to explain much of the male-to-female suicide ratio fluctuations in the past (1981-2018).
At the same time, this influence on male suicide would have to be weak enough to be over-shadowed by other forces at times.
For example, between 2007 and 2014, male youth homicide rates decreased greatly (-35%) but male suicide rates increased considerably (+21%).
Is existence of such a factor V compatible with our suicide data?
Minimal Plausibility Model
Let us try to create a model of suicide rates that is as simple as possible while fulfilling the above requirements.
So let us postulate that there is only one other factor besides V, and that this factor Z affects female and male suicide rates proportionally the same.
Therefore when factor V is stable, male and female suicide rates should move in tandem, doubling or halving according to factor Z only. On the other hand, fluctuations in the male-to-female suicide ratio should be entirely due to fluctuations in factor V.
Let us measure V by male homicide rates (MH) and Z by female suicide rates (FS), and require that male suicide (MS) is predicted to be zero if both V and Z are zero:
The question now is this: how well can this linear model improve predictions of male suicide and the male-to-female suicide ratio over using a linear model based ONLY on female suicide rate?
Female Suicide Rates Model of Suicide
Female suicide rates alone do not suffice for very good modelling of male suicide rates: the linear correlation has r = 0.56, with an average prediction error of 1.6 points (11% off the mean rate).
Furthermore, such a linear model has male suicide only halved if female suicide is null. Forcing the intercept to be zero -- that is requiring a more realistic model if the female rates are to truly explain the male rates -- leads to a much greater prediction error of 2.1 points (14%).
Male Violence plus Female Suicide Rates Model of Suicide
Now let us return to the Predicted_MS = 2.6 * FS + 0.29 * MH model.
The predicted rates versus the actual rates:
We see that this is a considerable improvement: the average error is 1 point (instead of 2.1 points).
We also have a decent prediction of male suicide, since the mean error is only 7% off the average suicide rate(14.4).
Similarly with the male-to-female suicide ratio:
Here the mean error is 0.3 and -- quite good given that the M/F suicide ratio is a bit volatile.
Significance
We have previously noticed that the female share of child and youth suicides has been increasing during much of The Rise (especially 2010-2015), but it also turns out that this trend has been present long before The Rise.
We have now also shown that homicide rates can help predict much of the year-to-year fluctuations in the M/F suicide ratio since at least 1981.
This adds yet another reason not to jump to the conclusion that the causes primarily responsible for The Rise must be affecting girls much more than boys.
Violence and Suicide and Gender
As to the underlying relationship between violence and suicide and gender, we can only speculate.
It may be that high levels of violent crime desensitize youth to death; it may also be that inclination to violence is equally a risk factor in suicide as it is in homicide. Such inclination may be due to not only social developments, but also due to biological factors such as lead poisoning.
Finally, since severe violence -- especially homicide -- is behavior an order of magnitude more common among males, it would be no surprise that fluctuations in levels of violence would not be linked to female suicide anywhere close to as much as to male suicide.
Discussion
We must keep in mind that this was a plausibility demonstration, not a probability analysis. We did not estimate how likely it is that homicide is linked to suicide, nor did we calculate some related measure, such as how unlikely it would be to have our data if no link was present.
Notice also that we demonstrated plausibility despite simplifications, not due to simplifications. Our modelling criterion has been actually made harder to achieve by decisions such as limiting the factors to two, stipulating that factor V affects suicide only among males, or forcing the intercepts to be zero (e.g. requiring MS to be 0 if FS and MH are both 0). What we did not simplify was the test of the model: how well we can approximate fluctuations of male suicide and the male-to-female suicide ratio by using a male violence indicator on top of knowledge of female suicide rates.
Notes:
Our model used only concurrent homicide rates, so trauma several years old was not included, but this too could be additional factor. Note, however, that trauma due to homicide is likely to be psychologically different from trauma due to 'abandonment' deaths like parental suicide or drugs overdose.
Technical notes:
It is important to examine the models themselves, not just look at some number like r or R squared, because even models with a high r can predict nonsense. For example, an eagles population growth data can have a linear model with a high r that predicts negative population in the recent past -- see this lecture.
Factor V
Let us postulate a 'violence' factor V that is responsible for male homicide rates.
This imaginary factor V is really an encapsulation of a family of causes behind homicide, which may include innate aggressiveness, social dysfunction, poverty, parental abuse, lead poisoning, access to guns, and so on.
Factor V and Causation
We measure factor V by one of its results, homicide rates, but we do not identify V with homicides.
The reason we differentiate between factor V and homicides is to keep in mind that a relationship between suicide and homicide could be due to underlying causes (factor V), rather than due to the influence of one on the other.
Consider these two possibilities:
A) When homicide increases, so does suicide because boys become desensitized to death and because of the trauma of witnessing homicides, or losing a relative or friend to homicide, or being victimized by violence.
B) When homicide increases, it is due to causes (factor V) that also increase suicide; for example, innate aggressiveness, social dysfunction, poverty, parental abuse, lead poisoning, access to guns, and so on.
In symbolic form, these two possibilities are A) V --> Hom --> Sui and B) V --> Sui + Hom.
If type A causation was the only possibility, we could identify V with Homicide, but in reality the type B causation mechanism is likely to be true as well.
The Goal
We will attempt to show that even when measurement of the underlying causes is simplified down to a single yearly value (homicide rates), it can help predict how male suicide rates differ from female suicide rates.
The influence of factor V on male suicide should be strong enough to explain much of the male-to-female suicide ratio fluctuations in the past (1981-2018).
At the same time, this influence on male suicide would have to be weak enough to be over-shadowed by other forces at times.
For example, between 2007 and 2014, male youth homicide rates decreased greatly (-35%) but male suicide rates increased considerably (+21%).
Is existence of such a factor V compatible with our suicide data?
Minimal Plausibility Model
Let us try to create a model of suicide rates that is as simple as possible while fulfilling the above requirements.
So let us postulate that there is only one other factor besides V, and that this factor Z affects female and male suicide rates proportionally the same.
Therefore when factor V is stable, male and female suicide rates should move in tandem, doubling or halving according to factor Z only. On the other hand, fluctuations in the male-to-female suicide ratio should be entirely due to fluctuations in factor V.
Let us measure V by male homicide rates (MH) and Z by female suicide rates (FS), and require that male suicide (MS) is predicted to be zero if both V and Z are zero:
Predicted_MS = k * FS + l * MHThis linear regression is optimized when k = 2.6 and l = 0.29.
The question now is this: how well can this linear model improve predictions of male suicide and the male-to-female suicide ratio over using a linear model based ONLY on female suicide rate?
Female Suicide Rates Model of Suicide
Female suicide rates alone do not suffice for very good modelling of male suicide rates: the linear correlation has r = 0.56, with an average prediction error of 1.6 points (11% off the mean rate).
Furthermore, such a linear model has male suicide only halved if female suicide is null. Forcing the intercept to be zero -- that is requiring a more realistic model if the female rates are to truly explain the male rates -- leads to a much greater prediction error of 2.1 points (14%).
Male Violence plus Female Suicide Rates Model of Suicide
Now let us return to the Predicted_MS = 2.6 * FS + 0.29 * MH model.
The predicted rates versus the actual rates:
We see that this is a considerable improvement: the average error is 1 point (instead of 2.1 points).
We also have a decent prediction of male suicide, since the mean error is only 7% off the average suicide rate(14.4).
Similarly with the male-to-female suicide ratio:
Here the mean error is 0.3 and -- quite good given that the M/F suicide ratio is a bit volatile.
Significance
We have previously noticed that the female share of child and youth suicides has been increasing during much of The Rise (especially 2010-2015), but it also turns out that this trend has been present long before The Rise.
We have now also shown that homicide rates can help predict much of the year-to-year fluctuations in the M/F suicide ratio since at least 1981.
This adds yet another reason not to jump to the conclusion that the causes primarily responsible for The Rise must be affecting girls much more than boys.
Violence and Suicide and Gender
As to the underlying relationship between violence and suicide and gender, we can only speculate.
It may be that high levels of violent crime desensitize youth to death; it may also be that inclination to violence is equally a risk factor in suicide as it is in homicide. Such inclination may be due to not only social developments, but also due to biological factors such as lead poisoning.
Finally, since severe violence -- especially homicide -- is behavior an order of magnitude more common among males, it would be no surprise that fluctuations in levels of violence would not be linked to female suicide anywhere close to as much as to male suicide.
Discussion
We must keep in mind that this was a plausibility demonstration, not a probability analysis. We did not estimate how likely it is that homicide is linked to suicide, nor did we calculate some related measure, such as how unlikely it would be to have our data if no link was present.
Notice also that we demonstrated plausibility despite simplifications, not due to simplifications. Our modelling criterion has been actually made harder to achieve by decisions such as limiting the factors to two, stipulating that factor V affects suicide only among males, or forcing the intercepts to be zero (e.g. requiring MS to be 0 if FS and MH are both 0). What we did not simplify was the test of the model: how well we can approximate fluctuations of male suicide and the male-to-female suicide ratio by using a male violence indicator on top of knowledge of female suicide rates.
Notes:
Our model used only concurrent homicide rates, so trauma several years old was not included, but this too could be additional factor. Note, however, that trauma due to homicide is likely to be psychologically different from trauma due to 'abandonment' deaths like parental suicide or drugs overdose.
Technical notes:
It is important to examine the models themselves, not just look at some number like r or R squared, because even models with a high r can predict nonsense. For example, an eagles population growth data can have a linear model with a high r that predicts negative population in the recent past -- see this lecture.
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