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.

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    $\begingroup$ 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? $\endgroup$ – Tim Jul 1 '16 at 12:39
  • $\begingroup$ @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? $\endgroup$ – elisa Jul 1 '16 at 13:03
  • $\begingroup$ You calculate likelihood 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... $\endgroup$ – Tim Jul 1 '16 at 13:11
  • $\begingroup$ I calculate the likelihood of my model given my (per-subject) data. So I need the predictions that each model makes, for each subject $\endgroup$ – elisa Jul 1 '16 at 13:13

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