It makes sense now to talk about multi-level models. This is definitely an advanced topic, and I'm not going to get into a whole lot of detail here. My objective right now is to introduce the concept of multi-level models to you, and let you understand some of the challenges and how to think about them when you're putting them together. That's it.

The concept of multi-level models is that some effects happen at various levels in the hierarchy. For example, your health. Your health might depend on how healthy your individual cells are, and those cells might be a function of how healthy the organs that they're inside are, and the health of your organs might depend on the health of you as a whole. Your health might depend in part on your family's health and the environment your family gives you. And your family's health in turn might depend on some factors of the city that you live in, how much crime is there, how much stress is there, how much pollution is there. And even beyond that, it might depend on factors in the entire world that we live in. Maybe just the state of medical technology in the world is a factor, right?

Another example: your wealth. How much money do you make? Well, that's a factor of your individual hard work, but it's also a factor of the work that your parents did, how much money were they able to invest into your education and the environment that you grew up in, and in turn, how about your grandparents? What sort of environment were they able to create and what sort of education were they able to offer for your parents, which in turn influenced the resources they have available for your own education and upbringing.

These are all examples of multi-level models where there is a hierarchy of effects that influence each other at larger and larger scales. Now the challenge of multi-level models is to try to figure out, "Well, how do I model these interdependencies? How do I model all these different effects and how they affect each other?"

The challenge here is to identify the factors in each level that actually affect the thing you're trying to predict. If I'm trying to predict overall SAT scores, for example, I know that depends in part on the individual child that's taking the test, but what is it about the child that matters? Well, it might be the genetics, it might be their individual health, the individual brain size that they have. You can think of any number of factors that affect the individual that might affect their SAT score. And then if you go up another level, look at their home environment, look at their family. What is it about their families that might affect their SAT scores? How much education were they able to offer? Are the parents able to actually tutor the children in the topics that are on the SAT? These are all factors at that second level that might be important. What about their neighborhood? The crime rate of the neighborhood might be important. The facilities they have for teenagers and keeping them off the streets, things like that.

The point is you want to keep looking at these higher levels, but at each level identify the factors that impact the thing you're trying to predict. I can keep going up to the quality of the teachers in their school, the funding of the school district, the education policies at the state level. You can see there are different factors at different levels that all feed into this thing you're trying to predict, and some of these factors might exist at more than one level. Crime rate, for example, exists at the local and state levels. You need to figure out how those all interplay with each other as well when you're doing multi-level modeling.

As you can imagine, this gets very hard and very complicated very quickly. It is really way beyond the scope of this book, or any introductory book in data science. This is hard stuff. There are entire thick books about it, you could do an entire book about it that would be a very advanced topic.

So why am I even mentioning multi-level models? It is because I've seen it mentioned on job descriptions, in a couple of cases, as something that they want you to know about in a couple of cases. I've never had to use it in practice, but I think the important thing from the standpoint of getting a career in data science is that you at least are familiar with the concept, and you know what it means and some of the challenges involved in creating a multi-level model. I hope I've given you those concepts. With that, we can move on to the next section.

There you have the concepts of multi-level models. It's a very advanced topic, but you need to understand what the concept is, at least, and the concept itself is pretty simple. You just are looking at the effects at different levels, different hierarchies when you're trying to make a prediction. So maybe there are different layers of effects that have impacts on each other, and those different layers might have factors that interrelate with each other as well. Multi-level modeling tries to take account of all those different hierarchies and factors and how they interplay with each other. Rest assured that's all you need to know for now.