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RM-ANOVA with informed priors

Dear All,

I was wondering what options there may be to create priors in an RM-ANOVA, which have been informed from existing data. I had collected data in an initial experiment, but then replicated the study on a much larger scale. I am hoping to use the data from the first study to informed the priors to be be used in the analyse in the follow-up study.

Kind regards,

Michael

Comments

  • EJEJ Posts: 444

    Hi Michael,

    This is tricky. One thing you could do is compute the BF for the initial sample, and then for the complete sample; dividing them out yields the BF for the replication sample after updating the priors with the initial sample. This only works when the data are exchangeable, so when it is a close replication. For details see https://psyarxiv.com/u8m2s/

    Cheers,
    E.J.

    Thanked by 1Michael
  • MichaelMichael Posts: 4

    Dear E.J.,

    Many thanks for your reply - I will read the paper with great interest.
    Just to clarify, are the updated priors in an ANOVA taken as the posterior odds (p(m|data)) from the initial analysis?

    Kind regards,

    Michael

  • EJEJ Posts: 444

    Hi Michael,
    The updated priors are on the model parameters. But this happens implicitly, that is, the BF you obtain is the same one that you could also have obtained in case you had been able to properly update the prior distributions on the model parameters. :-)
    E.J.

    Thanked by 1Michael
  • MichaelMichael Posts: 4

    Okay, this makes sense! Perfect :-)
    Thanks again E.J.!

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