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In Bayesian statistics, logistic regression can be facilitated by priors, a link function, and a likelihood choice of either the Bernoulli or Binomial distributions.

My question is whether this design choice affects assumptions of independence per observation.

Consider runners running a race, and we are interested in the completion rate (full course within X minutes.) Each runner in observed data will have run the race at least once. However, some runners have run it dozens of times whereas others have run it a handful of times.

Given this context, I have two assumptions.

  1. The Bernoulli likelihood would assume that each run of the race, regardless of runner, was an independent trial. (eg a single data generating process generating iid samples.)
  2. The binomial likelihood would assume independence of runners. (Y iid data generating processes, each conditioned on runner y.)

Are my assumptions here valid?

jbuddy_13
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    no, the binomial likelihood is the result of assuming the underlying Bernoullis are independent. In other words, they are identical assumptions. – John Madden Aug 27 '22 at 19:45
  • So, if I did want to keep as assumption that each runner was independent, but still estimate the overall parameters, this sounds appropriate for a partial pooling model right? Each runner's completion rate will have some pull on the global rate. – jbuddy_13 Aug 27 '22 at 20:31
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    sounds good buddy – John Madden Aug 27 '22 at 22:20
  • See https://stats.stackexchange.com/questions/144121/logistic-regression-bernoulli-vs-binomial-response-variables – kjetil b halvorsen Sep 26 '22 at 23:20

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