Hi, this video is on paths and associations. We have two main objectives. One is to understand the various types of paths between nodes. And the other is to understand which types of paths induce association between nodes. So we'll begin by looking at different types of paths. First, we'll look at a fork. This is an example of a fork. So we have E sort of sitting in the middle here, which is affecting two variables, D and F. You could basically think of it as getting the name. Because you could re-write it like this where it, basically, looks a bit like a fork. So we have E affecting D and F and when you have the arrows there, it kind of looks like a fork. At this point, we just trying to learn the terminology. So this is a particular path, right? There's a path between D and F, and we'll call it a fork because this middle part E affects the two outer parts D and F. And that sort of looks like a fork. Then there's something called the chain, and a chain you could think of as essentially like a chain reaction. So here we see that D effects E which effects F. So everything is sort of flowing in one direction. So we have a fork and a chain and those are just two different kinds of paths. Finally there's something called an inverted fork. So that looks just like the fork did except the arrows are flipped around. Next we'll think about when paths induce associations between nodes. So imagine that A and B are on the ends of a path, and we want to know when are they associated with each other through this path. So what we'll need to happen is it they'll have to have some information flowing between them. And so information from one could also make it to the other. So here's an example where information would flow to both of them. So again, we're interested in whether A and B are associated with each other. Here we are looking at a folk and we'll see that information as flowing to both of them from E. So E is affecting A and is affecting B. So we can see that there where we saw that E affects A and B. So information is flowing to both of them. So that implies A and B are not independent. So, they have E in common. E affected both of them, so A and B are dependent because E affected both of them. So information from E flowed into both of them. You could also consider a more complex kind of path. And again, we're still thinking about A and B. So here we'll see that information is still going to flow from E, to both A and B. So this is a type of fork, a kind of longish fork. And we'll see that we're able to sort of draw in a way where it becomes clear that E is really the thing that is triggering the chain reaction that ends up effecting both B and A. So information from E eventually reaches it's way to both A and B. Therefore A and B are going to be dependent on each other through this path. So we could also write this path in this way. So it was easier to see when we sort of had E at the top and we showed information flowing down, but equivalently we could write it this way and on this path, A and B are associated with each other. Next we could consider a chain, and again we're still thinking about the relationship between A and B, and are they associated with each other via this path? So here, information is going to flow from A to B. So this is a chain, a chain reaction, and we see that A ultimately effects B through its effect on G. You could also consider a longer chain. So here A effects G which effects D which effects F which affects B. So A is getting information to B through G and through D and through F. But information is getting there and so A and B are associated with each other. Here is an example of a path that is not induce association. So, consider this inverted fork. So both A and B affect G. So information from A and B basically collide at G. So this is why G is known as a collider. So when you have two arrows going in to the same node, we'll consider that a collider. You can think of these arrows that are flowing into G as some kind of force, and they collided at G. So A and B both affect G. But there's no information flow from G to either A or B. So you could think of A and B as things, they start off as independent pieces of information. They transfer some of their information to G but there's nothing that flows between A and B. So A and B are actually independent here on this path. So there might be other paths between A and B, but on this particular path, there's no association between A and B. So A and B essentially start off as random nodes, they share information with G, they affect G, but nothing is flowing back to A and B. So we see that there, there's a collision right at G. So here's another example of a path that does not induce association. So this is a slightly more complicated path than on the previous slide. But it also involves a collision. So here, again, G is a collider. So information flows from A and B to G, but everything stops at G. So, these forces that began at A and B, collide at G. So, there's no free flow of information between A and B, nothing is able to sort of reach B from A or vice versa. So, if there is a collider anywhere on the path from A to B, then we have independence between A and B on this particular path. So what we've seen is that when we're thinking about whether or not two nodes are associated we feel each other on a path, we need to look at what kind of path it is. And most importantly, is there a collision somewhere, is there a collider on that path that would prevent information from getting from one node to another? We're going to end up using this kind of knowledge to help us identify what variables we need to control for when it comes to causal inference.
