Do GRE scores help predict getting a physics Ph.D.? A comment on a paper by Miller et al.

• https://advances.sciencemag.org/content/6/23/eaax3787

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.

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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