Number of observations needed per model term in Bayesian regression?

PhilipMillroth

Hi,

I am trying to determine whether my dataset is appropriate to do regressions on. However, typically the guidelines on the observations needed vary (for a review see e.g., Austin & Steyerberg, 2015). I can't seem to find any references on this topic in regards to the Bayesian regression implemented in JASP: does it depend on the prior distributions used or the sampling method?

I will fit models at the individual level. I have 81 data points with 4 variables. Depending on how I cross these variables I could end up with as many as 15 model terms, but right now I am looking at using 6 model terms.

Thanks for the help,

/Philip

EJ

Hi Philip,

Theoretically, it does not matter what your sample size is. With low samples sizes, the posterior distributions will not be very different from the prior distributions, because not much has been learned. Of course there may be specific practical problems (crashes due to the algorithms choking) but theoretically there is no issue.

Cheers,
E.J.

PhilipMillroth

Thanks EJ. Do you have any suitable reference that I could use in my manuscript in order to counter a (at the moment hypothesized) frequentist-reviewier that will likely argue that my parameter estimates are not reliable because of the sample size/number of variables ratio, and thus any estimation of evidence is biased.

EJ

Well the reliability of the estimates is indicated directly by the width of the posterior distribution. Your frequentist reviewer would have to explain why the evidence for this specific data set is less reliable than is indicated by your analysis. Basically, the Bayesian outcome is a direct measure of your uncertainty. I am not sure what reference to recommend -- it would have to be something basic. This is purely a frequentist problem, in my opinion.