WEBVTT 1 00:00:00.005 --> 00:00:01.007 - [Narrator] And now for something 2 00:00:01.007 --> 00:00:05.006 seemingly completely different, guinea pigs. 3 00:00:05.006 --> 00:00:08.007 Sewall Wright is one of the heroes that emerges 4 00:00:08.007 --> 00:00:09.009 from the "Book of Why". 5 00:00:09.009 --> 00:00:14.003 He innovated path analysis 100 years ago. 6 00:00:14.003 --> 00:00:16.009 He was working in animal heredity 7 00:00:16.009 --> 00:00:20.004 and his animal subjects were guinea pigs. 8 00:00:20.004 --> 00:00:24.000 His contributions to path analysis alone 9 00:00:24.000 --> 00:00:26.007 would deserve mention in the course. 10 00:00:26.007 --> 00:00:30.004 But he also confidently fought back criticism 11 00:00:30.004 --> 00:00:35.006 that he was conflating correlation with causation. 12 00:00:35.006 --> 00:00:39.000 Path analysis and structural equation modeling, 13 00:00:39.000 --> 00:00:42.001 as we shall see, under the right conditions 14 00:00:42.001 --> 00:00:46.004 can shed light on causal relationships. 15 00:00:46.004 --> 00:00:47.008 First, I want to take a look 16 00:00:47.008 --> 00:00:49.009 at one of Wright's original papers 17 00:00:49.009 --> 00:00:52.002 'cause I just think it's so interesting to look 18 00:00:52.002 --> 00:00:55.000 at a 100 year old path diagram. 19 00:00:55.000 --> 00:00:55.008 So here we go. 20 00:00:55.008 --> 00:00:57.002 And I love the title, 21 00:00:57.002 --> 00:01:00.009 "Correlation and causation" by Sewall Wright. 22 00:01:00.009 --> 00:01:02.001 And you can see here 23 00:01:02.001 --> 00:01:05.001 that his title was Senior Animal Husbandman 24 00:01:05.001 --> 00:01:08.008 in Animal Genetics, Bureau Of Animal Industry, 25 00:01:08.008 --> 00:01:11.000 United States Department of Agriculture. 26 00:01:11.000 --> 00:01:12.002 Also very interesting. 27 00:01:12.002 --> 00:01:16.001 And as we said, doing his research with guinea pigs. 28 00:01:16.001 --> 00:01:19.006 So let's scroll down. 29 00:01:19.006 --> 00:01:22.006 Think it's wonderful that you can find these old papers. 30 00:01:22.006 --> 00:01:27.009 So here it is, diagram illustrating the interrelations 31 00:01:27.009 --> 00:01:29.008 among the factors which determine 32 00:01:29.008 --> 00:01:34.002 the weight of guinea pigs at birth and at weaning, 33 00:01:34.002 --> 00:01:37.003 which is apparently at 33 days, I did not know that. 34 00:01:37.003 --> 00:01:40.007 So you can see heredity, the size of the litter, 35 00:01:40.007 --> 00:01:42.008 the condition of the dam, 36 00:01:42.008 --> 00:01:45.004 the dam is the female guinea pig, 37 00:01:45.004 --> 00:01:48.008 and so on, really fascinating stuff. 38 00:01:48.008 --> 00:01:52.007 And what we do today is not wildly different 39 00:01:52.007 --> 00:01:54.000 from what you see. 40 00:01:54.000 --> 00:01:56.005 Note that these are all rectangles. 41 00:01:56.005 --> 00:01:58.000 So this is path analysis. 42 00:01:58.000 --> 00:02:00.002 We're going to have more to say about that later on 43 00:02:00.002 --> 00:02:04.000 in the course, the shapes are relevant here. 44 00:02:04.000 --> 00:02:08.005 I love this quote describing Wright's path diagrams 45 00:02:08.005 --> 00:02:09.009 in the "Book of Why". 46 00:02:09.009 --> 00:02:12.003 "I want to emphasize that path diagrams 47 00:02:12.003 --> 00:02:14.003 are not just a pretty picture. 48 00:02:14.003 --> 00:02:18.000 It is a powerful computational device 49 00:02:18.000 --> 00:02:20.008 because the rule for calculating correlations 50 00:02:20.008 --> 00:02:24.001 involves tracing the paths. 51 00:02:24.001 --> 00:02:29.000 Also notice the omitted arrows actually convey 52 00:02:29.000 --> 00:02:31.002 more significant assumptions 53 00:02:31.002 --> 00:02:34.000 than those that are present." 54 00:02:34.000 --> 00:02:37.001 Goes on to explain why, "An omitted arrow 55 00:02:37.001 --> 00:02:40.002 restricts the causal effect to zero." 56 00:02:40.002 --> 00:02:44.005 So when an arrow is present, unless you tell the model 57 00:02:44.005 --> 00:02:47.009 that you need that to be a particular value, 58 00:02:47.009 --> 00:02:51.006 normally it calculates that coefficient for you. 59 00:02:51.006 --> 00:02:54.001 But when an arrow is absent 60 00:02:54.001 --> 00:02:58.000 it forces that effect to be zero. 61 00:02:58.000 --> 00:02:59.009 So where the arrows are present 62 00:02:59.009 --> 00:03:02.003 and where they're absent is terribly important. 63 00:03:02.003 --> 00:03:06.006 And that's how the researcher is communicating their theory 64 00:03:06.006 --> 00:03:09.003 in the form of the diagram. 65 00:03:09.003 --> 00:03:12.000 Now this was all 100 years ago. 66 00:03:12.000 --> 00:03:14.003 When some of the folks that we talked about 67 00:03:14.003 --> 00:03:17.009 in the companion course like Carl Pearson 68 00:03:17.009 --> 00:03:22.003 were even more influential than they continue to be today. 69 00:03:22.003 --> 00:03:26.004 So there was no talk of causation at the time. 70 00:03:26.004 --> 00:03:31.000 And Wright got hit with some scathing criticism. 71 00:03:31.000 --> 00:03:36.000 We'll discuss just one brief response that Wright gave. 72 00:03:36.000 --> 00:03:37.007 So Wright himself said 73 00:03:37.007 --> 00:03:41.004 that he never made the preposterous claim 74 00:03:41.004 --> 00:03:43.005 that the theory of path coefficients 75 00:03:43.005 --> 00:03:45.002 provides a general formula 76 00:03:45.002 --> 00:03:49.003 for the deduction of causal relations. 77 00:03:49.003 --> 00:03:51.004 The key point is this, 78 00:03:51.004 --> 00:03:55.005 Wright is providing the causal explanation 79 00:03:55.005 --> 00:03:57.002 in the form of the diagram. 80 00:03:57.002 --> 00:04:01.008 He's providing that, he's not discovering it from the data. 81 00:04:01.008 --> 00:04:05.000 So he was trying to use the diagram and the data together 82 00:04:05.000 --> 00:04:10.007 to weigh the plausibility of his theory. 83 00:04:10.007 --> 00:04:14.007 Now we'll get deeper into this with some examples, 84 00:04:14.007 --> 00:04:18.008 but first we want to take a chance to review some terms 85 00:04:18.008 --> 00:04:22.002 and to get more familiar with path diagrams.