Note that my suggestion (“…try a model where there are 2 (or 3 or whatever) latent schizophrenia subtypes. So then your modeling task is to jointly (1) assign each schizophrenic patient to one of the 2 (or 3 or whatever) latent subtypes, and (2) make a simple linear SNP predictor for each subtype…”)
…is a special case of @TsviBT’s suggestion (“what about small but not tiny circuits?”).
Namely, my suggestion is the case of the following “small but not tiny circuit”: X OR Y […maybe OR Z etc.].
This OR circuit is nice in that it’s a step towards better approximation almost no matter what the true underlying structure is. For example, if there’s a U-shaped quadratic dependency, the OR can capture whether you’re on the descending vs ascending side of the U. Or if there’s a sum of two lognormals, one is often much bigger than the other, and the OR can capture which one it is. Or whatever.
Thinking about it more, I guess the word “disjoint” in “disjoint root causes” in my comment is not quite right for schizophrenia and most other cases. For what little it’s worth, here’s the picture that was in my head in regards to schizophrenia:
The details don’t matter too much but see 1,2. The blue blob is a schizophrenia diagnosis. The purple arrows represent some genetic variant that makes cortical pyramidal neurons generally less active. For someone predisposed to schizophrenia mainly due to “unusually trigger-happy 5PT cortical neurons”, that genetic variant would be protective against schizophrenia. For someone predisposed to schizophrenia mainly due to “deficient cortex-to-cortex communication”, the same genetic variant would be a risk factor.
The X OR Y model would work pretty well for this—it would basically pull apart the people towards the top from the people towards the right. But I shouldn’t have said “disjoint root causes” because someone can be in the top-right corner with both contributory factors at once.
(I’m very very far from a schizophrenia expert and haven’t thought this through too much. Maybe think of it as a slightly imaginary illustrative example instead of a confident claim about how schizophrenia definitely works.)
Note that my suggestion (“…try a model where there are 2 (or 3 or whatever) latent schizophrenia subtypes. So then your modeling task is to jointly (1) assign each schizophrenic patient to one of the 2 (or 3 or whatever) latent subtypes, and (2) make a simple linear SNP predictor for each subtype…”)
…is a special case of @TsviBT’s suggestion (“what about small but not tiny circuits?”).
Namely, my suggestion is the case of the following “small but not tiny circuit”: X OR Y […maybe OR Z etc.].
This OR circuit is nice in that it’s a step towards better approximation almost no matter what the true underlying structure is. For example, if there’s a U-shaped quadratic dependency, the OR can capture whether you’re on the descending vs ascending side of the U. Or if there’s a sum of two lognormals, one is often much bigger than the other, and the OR can capture which one it is. Or whatever.
Thinking about it more, I guess the word “disjoint” in “disjoint root causes” in my comment is not quite right for schizophrenia and most other cases. For what little it’s worth, here’s the picture that was in my head in regards to schizophrenia:
The details don’t matter too much but see 1,2. The blue blob is a schizophrenia diagnosis. The purple arrows represent some genetic variant that makes cortical pyramidal neurons generally less active. For someone predisposed to schizophrenia mainly due to “unusually trigger-happy 5PT cortical neurons”, that genetic variant would be protective against schizophrenia. For someone predisposed to schizophrenia mainly due to “deficient cortex-to-cortex communication”, the same genetic variant would be a risk factor.
The X OR Y model would work pretty well for this—it would basically pull apart the people towards the top from the people towards the right. But I shouldn’t have said “disjoint root causes” because someone can be in the top-right corner with both contributory factors at once.
(I’m very very far from a schizophrenia expert and haven’t thought this through too much. Maybe think of it as a slightly imaginary illustrative example instead of a confident claim about how schizophrenia definitely works.)