I am fitting Bayesian models (using R and rstanarm). Beyond estimating the effect of each predictor (and extracting pointwise indices such as median, MAD and 90% CI), I am also interested in having a general index of effect existence (telling if the effect is "different" (in the common sense) from 0). Two ways I can imagine of doing this are:
- Extracting the probability that the effect is in one particular direction (i.e., the area under the density curve of one "side" (from 0) of the posterior distribution (e.g., the probability that an effect is positive vs. the probabiltiy that the effect is null or opposite)).
- Performing a Bayesian t.test of the posterior distribution against mu=0 and computing the Bayes factor, the odds that the effect distribution is different from 0. Unfortunately, due to the large size of the posterior distribution (for example 4000 draws), the Bayes factor is almost always infinite, even if the distribution heavily overlaps 0 and the opposite side.
What could I do?