In my field, it is common to report odds ratios as estimates from logistic regression results. Now I have fitted a logistic regression model (model with bernoulli family and binary outcome) in brms, and get following “estimates” from
estimate = 1.84
95% CI = 0.43 - 3.55
These are on the log-odds scale, and the results indicate that the 95% CI is completely positive (“significant”, in frequentist / NHST terms).
If I want to transform the data into the odds ratio scale, and I exponentiate the values from the posterior distribution and then calculate a summary statistics like mean / median for the “point estimate”, the results look like this:
Odda Ratio: 5.98
95% CI = 0.72 - 25.56
i.e., the 95% intervals are partly “negative”, or in freq. terminology: non significant. I know this is due to the fact that I don’t have a single value, but a distribution of values, and the mean of an exponentiated distribution is not the same as the exponentiated mean of a distribution. But, how to deal with this issue?
Paul suggested transforming first, and then summarizing:
which leads to the problems I have here. So my question is, if you want to report “Odds Ratios” from Bayesian logistic regression, what approach would you suggest? I think that readers who are less familiar with Bayesian methods are confused by the fact that the results are both “significant” and “not significant” at the same time…