Do GRE scores help predict getting a physics Ph.D.? A comment on a paper by Miller et al.
A critique of Miller2019typical.
A problem with a Collider variable.
In causal inference studies stratifying on a “collider”, a downstream variable affected both by the suspected cause and by unmeasured other causes adds a systematic error called collider stratification selection bias to the causal estimand. For example, inadvertent collider conditioning produces a pradoxical effect that maternal smoking appears to protect low-birth weight newborns from mortality, because within the low birth weight stratum, smoking is negatively correlated with even more ominous predictors.
Students with low GREs and GPAs who nonetheless are accepted into high-rank schools are likely to have especially good prior research experience, letters of recommendation, etc., creating a negative correlation within each stratum between those stratum-correlated out-of-model predictors and the predictors used in the model. A similar effect occurs in a different context: although performances on long jumps and 110-m races are likely to be positively correlated in the general population, in the stratum of Olympic decathletes, they have a strongly negative correlation.
See Pearl2018book, Greenland2003quantifying, Hernán2004structural, VanderWeele2014resolutions, Park2011multivariate for more information