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.
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.