Yup, you’re right. That’s the right way to handle it, and it yields time as the common cause of temperature and strain, as we’d expect.
Now that I’m knee-deep in it, I do think this crazy concept of separating sets of values of variables from the mappings between the sets has something to it. It isn’t necessary for the example in the main post, but I think the example I gave with mice in one of the other comments still applies. The mapping between points is legitimately a variable unto itself, so it seems like it should be possible to handle it like other variables. It might even be useful to do so, since the mapping is nonparametric.
Anyway, thanks for giving a proper analysis of the problem.
I’m not sure what you see in it. For the mouse thing, it seems to suggest that the correlation between the variables causes the identity of mouse, which is, like the time thing, exactly the wrong way round. You say it “isn’t necessary for the example in the main post” but it’s more than unnecessary—it gives an answer that’s completely backwards.
Yup, you’re right. That’s the right way to handle it, and it yields time as the common cause of temperature and strain, as we’d expect.
Now that I’m knee-deep in it, I do think this crazy concept of separating sets of values of variables from the mappings between the sets has something to it. It isn’t necessary for the example in the main post, but I think the example I gave with mice in one of the other comments still applies. The mapping between points is legitimately a variable unto itself, so it seems like it should be possible to handle it like other variables. It might even be useful to do so, since the mapping is nonparametric.
Anyway, thanks for giving a proper analysis of the problem.
I’m not sure what you see in it. For the mouse thing, it seems to suggest that the correlation between the variables causes the identity of mouse, which is, like the time thing, exactly the wrong way round. You say it “isn’t necessary for the example in the main post” but it’s more than unnecessary—it gives an answer that’s completely backwards.
That’s exactly why it’s interesting.