Collider bias: food and location among surviving restaurants

Question

A food critic notices that among restaurants that have stayed in business for years, food quality and location quality are negatively correlated: the best food is often in inconvenient spots, and the prime locations often serve mediocre food. When restaurants first open, the two are unrelated. He concludes that great chefs deliberately avoid good locations.

Explain why survival induces this negative correlation, and why his conclusion does not follow.

Accepted Answer

This is collider bias, here in its survivorship form. Staying in business is a common effect of food quality and location quality, and conditioning on survival manufactures a trade-off between them. The mechanism. A restaurant survives if it is good enough on at least one axis: excellent food can sustain an out-of-the-way spot, and a prime location can sustain unremarkable food. A restaurant that is weak on both closes and drops out of the sample. So among survivors, weak food must be paired with a great location (or it would have closed) and a weak location must be paired with great food. Th…

Collider bias: food and location among surviving restaurants

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