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I have empirical data from 20 subjects (8 summary datapoints for each subject). I'm trying to calculate the BICs for three potential models of my data.

For each subject, I can calculate the likelihood of the 8 datapoints given each model. I can then obtain a BIC for each model and each participant.

How would I calculate a BIC for the full dataset?

Calculating a BIC for the full dataset of 20 subjects would require that I calculate the likelihood of the 20*8 datapoints, which leaves me with a very low likelihood and very high BIC.

But doing statistics on the individual BICs doesn't sound like a reasonable option either.

I know it's a basic question, but I haven't found a clear way to solve it.

elisa
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    It is unclear what do you mean... BIC is something that you calculate per model. *not* per subject. It is used to compare models. Why do you want to calculate it per subject? How do you want to use it afterwards? – Tim Jul 01 '16 at 12:39
  • @Tim Exactly. I want to calculate it per model. I want to use it afterwards to find the best model. But how do I calculate it per model, if I have per-subject predictions? – elisa Jul 01 '16 at 13:03
  • You calculate [likelihood](http://stats.stackexchange.com/questions/112451/maximum-likelihood-estimation-mle-in-layman-terms) of a model, it has no connection whatsoever to predictions that you make using the model. So I'm afraid that it's still unclear what do you mean... – Tim Jul 01 '16 at 13:11
  • I calculate the likelihood of my model given my (per-subject) data. So I need the predictions that each model makes, for each subject – elisa Jul 01 '16 at 13:13

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