Complexity of Non-Linear Models

Gun Violence and School Outcomes

The discussion is about how if educational outcomes affected by how much we spend on schools as well as gun violence in related to gun ownership.

I appreciate that you edge a bit closer to my view here, but I believe we are still on entirely different planes of existence when it comes to how to analyze these problems. You are still operating with a very linear model in place with some tweaks.

Let me discuss some of the problems of analyzing each situation from a linear perspective in more detail, as I think you are only consider a very limited set of conditions in your reply.

The Complexity of Analyzing School Results Based on Spending

  1. In increase school funding by 30%, by increasing teachers salaries with 30%. Will this improve school results? Highly unlikely. The same teachers are still doing the same job.
  2. Increased funding is used to hire more teachers, to reduce class sizes. Will this improve outcomes? As you pointed out it highly depends on what the reduction is. Going from say 28 to 24 students may not matter much.
  3. Increased funding of facilities. Whether this helps or not depends on whether facilities where adequate or subpar already. If ventilation was so bad that student could not concentrate then this funding can make a difference. But if the funding just makes the school look prettier it may not matter much. If it gives children more nutritious food than before it could also help.
  4. If school is in a immigrant community, then extra spending to hire language training teachers will help outcomes.

Basically the funding needs vary considerably. As I pointed out New York inner city school may have to pay for security, metal detectors etc which a Utah school does not have to pay for.

How Useful is Arithmetic Averages in Comparing Schools?

The poorer schools may not even be obviously underfunded by just looking at the numbers. However that may be masked by the fact that a large amount of resources is just going to dealing with social problems such as having security guards, metal detectors, on site social workers/psychologists or whatever staff you need for students with sever mental or social problems.

The funding you are left with for each normal student may thus be considerably lower than the statistics imply.

Urban, Suburban and Rural Distribution

The same issue exists with schools. More troubled areas may spend more. That will throw a wrench in all your assumptions.

But perhaps the most likely issue is that urban areas are going to have higher living costs. That means salaries to teachers are higher. Property for school is more expensive. Building the school is more expensive etc. Thus in the statistics you are going to see a bunch of urban schools with higher costs and suburban school with lower cost. Yet if you account for difference in costs in each area there may not be much difference in effective spending.

And these graphs are likely quite complex having more of a u-shape. Speaking from my experience in Norway, rural areas have much higher costs because they have too few students on their schools. Population density is too low to achieve any economies of scale. You end in situations with like 10 students per class or something. In many regards living expenses can go up because you spend so much on gasoline, just traveling. Less competition and smaller scale means all sorts of products are sold at higher price.

I have lived in different areas of Norway and seen these differences. In bigger cities. It is the high property prices which are killing you. In very low density areas, it is the cost of travel and too small units and lack of choice which is killing you.

This is not something you have taking into consideration at all. You point out that Wyoming spends twice as much as Utah or Idaho. Well have you look at their city sizes? Cities there are all tiny. Utah and Idaho have much more similar sized cities. And judging by my own intuition they have quite decent sized cities in terms of cost optimization. Not too small to get inefficient, but not too large to get high property prices killing you.

How do you measure living costs?

Local Supply and Demand of Teachers

There are many factors in play here. For instance what are alternative career choices. If the state or city offers much higher paid alternative jobs, then potentially good teachers may end up as say engineers, programmers, lawyers or whatever. However with less opportunities perhaps the cream of the class will become teachers. I see some of this difference when comparing e.g. the US and Norway. In the US a lot of public sector jobs seem to pay less, while professions such as programmers, engineers etc pay somewhat more. It creates a different distribution in talent. Especially the US medical profession is a stark example of this. US medical doctors are typically paid a ton in the US compared to most of Europe. Yet if you analyze it close you also see that they have to be paid more because their student loans are astronomical. This is simple risk/reward assessment. If you need to put on a huge financial burden to become a doctor, well then the payoff has to be bigger as well to make it worthwhile.

Hence it would be interesting to say look at differences in costs for people to become teachers in Utah vs New York. As well as differences in opportunities. New York offers quite a lot of high paid opportunities for academically talented people.

I remember talking to a biology teacher in Washington DC, who drove a cab. He hated his teaching job so much he became a cab driver instead. That may be the reality for a lot of inner city schools. What kind of talent do you attract if people rather be cab drivers than teach? I know this is just one story, but it is not exactly unknown that being an inner city teacher isn’t easy.

Contrast this with Utah. I am pretty sure that is a lot more rewarding experience, hence attracting more talented teachers.

Long Term vs Short Term Funding

Hence when comparing school outcomes, it may be just as important to look at funding over several years and not just presently as that would have affected recruitment to the profession.

A spending cut today e.g. by freezing salaries or making them stagnate, may not have much immediate consequence but could cause fall in school results over time as lower skilled teachers will get recruited.

So with this in mind, let me address some of the claims you made.

Increased school spending? Doesn’t seem to help.

As outlined above, you have no way of knowing that based on simple linear regression. Secondly it is about how you spend not just dumping money on the school. The point is that you should listen to the needs of individual schools. If a school has need of hiring special language trainers, you should give them that, rather than go “Oh but you already spend more than the average and our study shows that increasing spending more will not help you.”

This line of argument always go against schools needing help but never against the affluent schools overspending on privileged students.

Parental wealth and education? Doesn’t seem to help.

A surprising claim, that seems to run counter to everything I have heard over the years. Just some random google searches seems to suggest that plenty of studies think it makes a difference.

No, I haven’t checked these studies or assessed their quality. It is just an example of the stuff I could get from a quick googling.

Preschool? Doesn’t seem to help with test scores, though there appear to be other benefits.

That is not necessarily how I read the study. I only glanced at it but there seems to be a common issue of fading effects over time. Unless that is understood it is premature to draw too sweeping conclusions. I think of intellectual development much like physical training.

If you get a good training regime 1 year, then that will not matter much if you do very little exercise in the coming years.

Richard Nisbett wrote a book Intelligence and How to Get It, which points to a lot of studies showing how early involvement with children is important in intelligence. You kind of simplify this to pre-school here, but it is broader than that. It is also about parent involvement.

Busing was tried in places, it didn’t eliminate the gaps.

That is too simplistic. Bussing may not have helped but changing neighborhood does. The Stanford economist Raj Chetty has studied this among others. And the results seem pretty clear. They talk about on this Freakonomics episode:

CHETTY: And, quite remarkably, and I still vividly remember seeing this when we were studying this at the IRS, looking at the data — when you look at children who moved when they were young, you see extremely clearly that they are doing dramatically better today as adults. They are earning 30 percent more, they are 27 percent more likely to go to college, they’re 30 percent less likely to become single parents.

This was based on re-examining the Moving to Opportunity Program. What had not been understood initially, was that to have an effect you need to change environment while you are below 9 years old or so. The older get the less the effect.

And kids still stratify by race within mixed race schools.

The important thing is to understand this issue. There is nothing deterministic about this. I live in a highly diverse neighborhood myself. I observe this stuff myself and have actually spent some time trying to understand it.

What both me and my wife as concluded is that it is not really a skin color or race thing. Rather it is a cultural thing. Minority kids from families which acted more Norwegian where more likely to play with my kids. First generation immigrant kids in contrast was far less likely to play with my kids.

My kids where unlikely to play with other white kids if they where culturally very different. E.g. there are many Polish first generation immigrants here. They look very similar to Norwegians but really live in a separate bubble. That is cultural. Lack of language skills etc.

The US is no different. I have read accounts from black kids who experienced bussing. Blacks and whites have lived so separate in the US, that it is as if they are from different countries. There is a major cultural barrier. You cannot change that for kids who are older. As Chetty pointed out, change has to happen early.

So far, you have offered one revised adoption study suggesting that black kids will do better if given white parents. Even if that’s replicable and true

That is to my knowledge true across all adoption studies. What was relevant from the one I pointed to is that this was (1) the last one I could find, (2) it showed that black-white IQ gap was pretty much removed. Earlier examinations of the same data has shown a more clear black-white gap but they still show a clear advantage of having white parents.

I don’t see how giving white parents to all black children is a scalable solution to racial inequality.

Come on this is a silly counter-argument, unless you truely believe the color of the skin is the factor here. Clearly the issue is that these white parents will on average have more human capital, which make them better at raising children. It is not that they are white. The point is to raise the human capital of the black population. By giving people better opportunities. Better neighborhoods, better pay etc you will get a knock on effect, where African-American parents will become better parents who will raise more successful children, which will then become better parents to their children. It is all about creating a positive circle.

Should We Just Give Up Because it is Too Complex?

Suggesting that the situation is just so complex and non-linear that no model can work seems like a lazy way to avoid the question.

No, my point is to quit this obsessive speculation that race plays a role. I am in line with Eric Turkheimer here:

Despite what you seem to suggest about him, he does not deny that racial differences does not exist or that one cannot check it. What he is against is the constant racist speculation. And this is what I oppose as well. We have the flimsiest of reasons to believe there are racial differences, and we have significant reasons to believe culture and environment plays the key role. Yet people will still prefer to obsess about race rather than to study environmental factors.

The complexity of the world, also suggest you should be more humble about what you can grasp about cause and effect by simply doing a linear regression. Don’t be so brazen as to think that has settled the issue for you.

And I don’t rule out studying the models. But as I have repeated again and again. I think you need to formulate some kind of model before looking at data. You need to have an idea of what you should be finding. You seem to just grab the easiest available data and hack away. Not very scientific IMHO.

I am not claiming that I am doing science. Rather I am humble enough to realize that this is a too large undertaking for a lay person like me. I would have to study too many variable. And adjust for a ton of different variables. Real science is a big job. It isn’t just some simple linear regression you can do in an afternoon.

Gun Control Modeling Complexity

But there might not be much difference in homicide rates between 20% gun ownership and 60% gun ownership. And, no gun control program I’ve heard suggested in the US will get us below 20% gun ownership.

I have never suggested that this is a simple question of number of guns. It is also about regulation, accessibility etc. And to judge this one could look at a variety of different countries with different gun ownership. My point is that you are better off looking at different countries than different states within one country.

The suggestions are usually things like “ban magazines with more than 10 bullets” or “ban assault rifles”. When most of the killings are done with handguns anyways.

It does matter in particular for things like mass-shootings. Anders Behring Breivik was close to giving up on his mass killing when America came to his rescue. The expiration of the Assault Rifle Ban in the US, meant he could order a high capacity magazine from the US. It was a glitch in our security checks in Norway that we had not taken into account people ordering high capacity magazines from the US.

He tried initially to get high capacity assault rifles in the Eastern European black market. He failed. His “solution” was to get a low capacity rifle in Norway through the low boring process we have for guns in Norway. It took him about a year. But with the help from the US, he didn’t need Eastern European black market gun dealers. Point is, this only worked in Norway because Breivik was extremely dedicated and willing to spend considerable time to get his mass murder carried out. This would easily have deterred a lot of other potentiall mass murdereres.

I would conclude that any gun control I’ve heard suggested in the US will not have a large effect on the murder rate.

Probably not, but a reduction in mass shooting would have a major positive impact on US society. Yes gang shootouts in the hood may still happen. But I think parents would be happy to know that school shootings become a rarity. Or that black churches or gay bars don’t have to worry about a mad man busting in the doors and massacring everybody.

The New York article does show a correlation between mass shootings and number of guns. And as far as I remember mass shootings went down in Australia after stricter gun laws even if regular shootings may not have changed.

The lack of a correlation between guns and murder is true, internationally, as well. Gun ownership vs. murder in developed countries is more or less a random scatter plot

Again it is not a simple linear relationship which you seem to always assume. And I even covered this in my article about gun violence, which I linked to earlier. Let me quote myself quote:

Rather, they found, in data that has since been repeatedly confirmed, that American crime is simply more lethal. A New Yorker is just as likely to be robbed as a Londoner, for instance, but the New Yorker is 54 times more likely to be killed in the process.

In other words you need to correlate with other crimes. You are not going to find a lot of dead people due to guns in a society that has little crime to start with.

Ireland is more violent than Germany or Iceland or Norway, despite lower gun ownership.

Uh… yeah, higher levels of inequality, delinquency and many other issues. My brother has lived there so he could talk at length about that.

You assume things are not linked because you don’t see a correlation. But my question is, why would you?

I repeat what I said about schools. You need to stop and formulate a model first about what you are likely to see in the world. Just like places with high crime are likely to hire more police, places with a lot of gun violence or homicide are likely to enact stricter gun laws. Hence there is a high risk of even getting the correlation opposite: seeing a correlation suggesting fewer guns give more violence.

You have to sit down and think about what causes a person to shoot somebody in the first place. You need social problems, inequalities. You need an ample supply of troubled individuals. That is the starting requirement. Once you got that, the question is: “How easy is it to get hold of a gun?”

In this case it will not be a linear relation. If I want to wack somebody and have to wait 1 or 3 days, it may not matter much. But if it will take me a year to get a gun, I may give up on it.

BJ Campbell’s whole series on guns is worth reading, maybe start here:

He makes exactly the same mistakes as you. He only looks at very simple linear relationships with few variables. Let me comment on his graph over Europe to point out how silly this comparison is.

Image for post
Image for post

So he got countries such as Bulgaria, Moldova with serious problems in the graph. Are we surprised they have higher firearm homicide rates than Iceland? Come on! This is a joke!

The statistics here isn’t even right. Many surveys will show that both Switzerland and Finland have more guns than Norway and Sweden e.g. Finland is quite well known to have among the least strict gun regulation among Nordic and they have most fire arm deaths despite otherwise being a fairly similar country. You need to make apples to apples comparisons.

You cannot do apples and oranges comparisons where you are comparing troubled countries like Croatia to countries running like a Swiss clock like Switzerland.

Given how many guns Switzerland has and how well run that country is, it is highly surprising that it has more gun related deaths than say the United Kingdom which has more serious crimes and social problems, in addition to having larger cities.

As far as I can tell, sources like Vox and the NYT are just manipulating the data to fit their ideology. Usually they do it by conflating homicides and suicides, because firearm suicides do correlate with gun ownership.

I think that depends on the articles or studies you look at in respective papers. And they will usually point that out. I agree that conflating the two is generally not a good idea.

It is easy to point fingers, when I would say your own analysis is also rather selective and manipulative. You throw together countries which are completely different and say “look now correlation!” Well who expected to see a correlation in that mess?

But there are a number of other tricks used in misrepresenting the data, like selectively omitting countries to produce a better correlation plot.

That is not necessarily an issue. Quite the contrary, often a good study will require eliminating outliers. The point is that you need to be able to give a rational explanation for why you eliminate a country.

Incidentally, gun bans in the UK, Ireland, and Australia didn’t have immediate or significant consequences on murder rates:

As far as I know it did cause a marked drop in mass shootings. Again you need to think of models of how these things work. We cannot just hack around. Who is the typical mass shooter? They are loners diconnected from any criminal underworld. Stricter gun laws will easily hit these kinds of people.

Meanwhile criminals don’t usually engage in that many mass shootings. But guns are already circulating in their networks and they are likely not giving those guns up right away. It will take a a long time before they start having a shortage of guns to kill people.

Also it depends on what sort of homicides already exist. Just plotting homicides doesn’t tell me much. Incidents where husband kills his wife due to jealousy or something similar is unlikely to drop due to a gun ban.

I can see a potential change conflicts between gangs, robberies etc. You need to plot against these sorts of things. You need to see e.g. how many people get killed in robberies before and after bans. And you need to take into account intertia. Guns will not disappear over night after a ban.

I was very much a pro-education spending, pro-gun control liberal until about 4 years ago, when I started examining the data for myself and realized that much of my world view was factually wrong.

No, offense, but you did some simple linear regressions and jumped to conclusions.

But let me be a bit more fair to your conclusions. I think we can both agree that school results and homicide is not simple a question of how much you spend on students and on how many guns are in circulation.

Your linear regressions do show one thing very clearly: There are many more variables involved. If you want to reduce homicide rate you have to do more things than simply reduce the number of guns. But what I find so profoundly dishonest about pro-gun advocates in the US is that they are against pretty much every single thing that would reduce homicides:

  1. They don’t want stricter gun regulation.
  2. Not fewer guns.
  3. Nor do they suggest more spending on mental health care.
  4. Where are the proposals for reducing inequality, and reducing social problems?

Quite the contrary gun-advocates tend to advocate for the full cocktail of things which increase gun violence.

As for schools. Yes you cannot simply double the funding in an inner city school and expect magic. Perhaps more important is to reduce ghetto formation. Spread people out more. We know Raj Chetty, that where you live matters.

But you know when a school struggles in a difficult neighborhood with overcrowded class rooms, struggle with attracting good teachers etc, then more funding may be a necessary stop gap measure.

Consequences of Race Science

You know, I follow some people that are diehard believers in genetic differences. I don’t think I’ve seen anyone calling for genocide or apartheid or an ethnostate.

If you read interviews of Hitler or other Nazis in serious newspapers they also never said all Jews should be murdered. They where pretty good at toning down their rhetoric. You see the same today. The elite Neo-Nazis act very professional and polite. They say most of the PC stuff. A lot of dog whistles.

In short I don’t think you can judge what will happen based on what these people explicitly say. Nobody in their right mind will publicly state they want to engage in mass murder. They are not that stupid.

You got to read between the lines. I have discussed this with racists many times. They claim they can easily kick people out of the country. That is EXACTLY what the Nazis thought too. Except in the course of 8 years of terror against German Jews they failed getting all that many out. In large part because the UK, the US and many other countries refused to accept very many Jewish refugees. When they Nazis failed to deliver on their promise of making Jews free of Jews, that is when the mass murder began.

The same will happen today if the racists gain power. They will claim they can just kick out the black, muslims or whoever they don’t like. But they will fail and in their desperation to get rid of undesirables they will begin to murder people.

You’re already under the impression that most of Americans are racists that are holding back minorities from success.

Depends on what you mean by racism. I think there are a lot of Americans who are nice to people of other races on an individual level. But I think a lot of Americans are like you, in that they think differences observed in society are primarily caused by racial differences in intellectual capability.

That means when you see worse test score, worse income, overrepresentation on crime, police violence etc, people similar to you are more likely to shrug and say “well, it is all natural. All genetic. Not much we can do about that.”

Such attitudes makes it very hard to move forward. I see this constantly. Whenever there are stories of police brutality against blacks. People line up ot make excuses. You cannot start holding the police accountable and get reforms when such attitudes are so prevalent.

Let us not forget FOX News is the largest cable news channel in the US. With their popularity you cannot say racism is not a significant problem in the US. A population strongly against racism would likely have boycotted such a channel.

The US public elected a clearly racist president, Donald Trump. And it is not the first time. Ronald Reagan was also clearly racist and one of the most popular American presidents of all time.

Racism in America today isn’t so much about “I don’t like you because you are black.” Racism in America today is more like “stop complaining about being a victim. Work harder! Get your shit together!” Or the prevalence of white self-victimization. This idea that blacks have all the advantages with affirmative action etc. This idea that they are in fact the real victims. This idea that liberal PC culture only cares about blacks and minorities.

One saw the same thing in Germany during the Nazi period. The way a lot of Nazis framed the problem wasn’t that they hated Jews per say, rather they framed it as the liberal German state didn’t show enough love for real Germans. The chant was always about how the real Germans had been stabbed in the back and betrayed.

I’m not sure how having a scientific proof of inequality would change that situation, us racist Americans would act about the same.

America is not a monlith. There is a fight over what direction America should take. With scientific proof, the far right will be strengthened and progressives will be weakened.

Let us not forget America is doing a lot of progress. A scientific proof of racial inequality could stall that progress or even throw it in reverse. Of course it could potentially also be used as an argument for why African-Americans would need more support. But in the political climate America is currently in, that seem implausible.

Having accurate polygenic scores for intelligence could be used to augment the next generation by 5–10 IQ points, which could have profound impacts on society.

Maybe, I am not so sure about your strong faith in intelligence. The Nazi leadership of Germany was full of unusually intelligent people. That did not stop them from creating a reign of terror and wreck havoc across the world.

It is not that intelligence is a bad thing. More will usually be better. My worry is that a society obsessing about intelligence is a worse society than one which takes a more holistic view and which values more things than just intelligence. We see dramatic differences in prosperity and outcomes all across the world, even between countries of the same average IQ score. Hence there are far more important factors at play than average intelligence.

One of the most intelligent people who have ever lived John von Neumann had some astonishingly terrible and immoral ideas. E.g. he advocated that the US should as soon as possible nuke all of the USSR. Destroy the whole thing with nuclear weapons in a first strike. His rational for this was that he deemed that the USSR would with absolute certainty, sooner or later attack the US. Whoever responded to a nuclear attack was worse off than those doing the first strike. Hence by his rational America should strike first.

I should probably not get too much into all the stupid things a brilliant man like Elon Musk has said and done the last months.

European countries might become more restrictive with immigration, if more knowledge of genetics makes people more racist.

Maybe, or people will simply say IQ does not define you as a person. There are many other important traits.

I feel like immigration is going to get restricted, either way, given the rates of population growth in the world right now

You are not by any chance using a plot from this Steve Sailor are you?

Image for post
Image for post

Immigration will likely fall also due to the simple reason that many countries are getting richer and more peaceful.

Africa in particular is becoming far more stable. You plot sub-saharan Africa here which in many ways doesn’t make all that much sense from a European perspective. That is not where we are getting most immigrants from.

A lot of refugees come from the middle East in response to various destabilizing American wars and invasions, triggering civil wars and chaos.

Who are the refugees mainly in Norway today? Syrian, Iraqis and Afghans. In other words mostly the result of American wars. Syria was a complex case, but a lot of the reasons for that spinning out of control was ISIS which was formed by former members of the Iraqi military that had spent time in American prisons together.

Before that we got refugees from Vietnam. Another American war. It seem from my perspective like growing world population is not really what determines whether we get immigrants or not, but whether America starts yet another war.

I am crossing my fingers that we are not going to get another flood of Iranian refugees because Trump decides to invade Iran.

Other than that, these kinds of graphs are rather pointless. By 2100 we will be hit like a sledge hammer by global warming. There is no way they are going to get 4 billion people in Africa with major drought and extreme climate problems.

Too many things can change in this time perspective. We also see the beginning of a new space age today. Who can tell where that will lead us the coming decades. Long before 2100 we may have a breakthrough in AI, and human intelligence will be of little significance. Whatever IQ points we can squeeze out by playing eugenicists will be dwarfed by AI super intelligence.

Written by

Geek dad, living in Oslo, Norway with passion for UX, Julia programming, science, teaching, reading and writing.

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store