This makes me think of causal networks ala Judea Pearl. The goal is to come up with a causal model (via lifting out general factors) such that the children are conditionally independent given the parent, or at least approximately independent- where most of the correlation comes from the general factor.
Example: In the diagram you made “Seeking education” and “Getting a job” are correlated (both happen when you intend to specialize), but conditional on “Intent to specialize” they’re independent or even anticorrelated if you wouldn’t do both at once.
It’s common to estimate general factors by taking a bunch of correlated variables and assuming they become independent conditional on the general factor, but in reality there are often multiple broad-ranging factors in an area, so in practice the resulting estimates would be some linear combination of all of those general factors.
I think this sort of combo tends to work well for many purposes as it efficiently captures a lot of uncertainty, but sometimes it can “go wrong”, e.g. when one intends to compare the factor across different contexts whose overall levels are produced by radically different combinations of those general factors, or when there are nonlinearities. I’ve been thinking I should write a new framing practicum, about “Mixings”, to better capture this.
This makes me think of causal networks ala Judea Pearl. The goal is to come up with a causal model (via lifting out general factors) such that the children are conditionally independent given the parent, or at least approximately independent- where most of the correlation comes from the general factor.
Example: In the diagram you made “Seeking education” and “Getting a job” are correlated (both happen when you intend to specialize), but conditional on “Intent to specialize” they’re independent or even anticorrelated if you wouldn’t do both at once.
Yep.
It’s common to estimate general factors by taking a bunch of correlated variables and assuming they become independent conditional on the general factor, but in reality there are often multiple broad-ranging factors in an area, so in practice the resulting estimates would be some linear combination of all of those general factors.
I think this sort of combo tends to work well for many purposes as it efficiently captures a lot of uncertainty, but sometimes it can “go wrong”, e.g. when one intends to compare the factor across different contexts whose overall levels are produced by radically different combinations of those general factors, or when there are nonlinearities. I’ve been thinking I should write a new framing practicum, about “Mixings”, to better capture this.