They do not appear in the real data, you have one g stronger than all others. This g has as much explanatory power as noise. Frobenius–Perron guarantees it woul

They do not appear in the real data, you have one g stronger than all others. This g has as much explanatory power as noise. Frobenius–Perron guarantees it would always appear whether there is one strong underlying influence on the data or hundreds unrelated ones. Factor analysis used to establish g doesn't and can't have the power to tell. There are numerous and intense attempts to paper over this mathematical fact by circumstantial evidence, I'm not up to date with all the contortions. I don't think they can make linear algebra a causal theory: when you want to replace your data with linear combination of factors there will happen to be a strongest factor. To somewhat answer the direct question: how to check factors. There is Confirmatory Factor Analysis that checks how factors decay. You take out factors you see as accounting for most of the variance in the data and check if indeed not much partial correlation is left. This has most power to negate an influence but next to none or very little power to confirm it not being spurious. These wikipedia pages don't look any good, but I don't want to evaluate that right now or chase better material https://en.wikipedia.org/wiki/Confirmatory_factor_analysis https://en.wikipedia.org/wiki/Confirmatory_factor_analysis https://en.wikipedia.org/wiki/Partial_correlation https://en.wikipedia.org/wiki/Partial_correlation