I have a questioned regarding the interpretation of credible intervals retrieved from, e.g., a brms model.
From this article (link below), I understand that significance is defined as both upper- and lower-95%-credible intervals etiher above or below zero - as the parameter value zero, is defined as no effect. (Understanding and interpreting confidence and credible intervals around effect estimates - PubMed)
However, when the credible intervals of a variable are then said to be significant, what are they then significant compared to?
Let me give an example:
Given a model with e.g. three variables, each of either two or three levels:
Time ~ Shoes + Experience + Age
where time is the time (in minutes) it takes participants to run a certain track, “Shoes” is a categorical factor of three levels indicating the brand of shoes participants are wearing (Nike, Adidas, or Puma), “Experience” is a categorical factor of three levels (Beginner, intermediate, pro), and Age is a categorical factor of two levels (Young or old).
The coefficient table with credible intervals is extracted, where the intercept contains the alpha-numerically lowest values of each variable. :
Intercept -3.13 -1.51
Nike -1.20 -1.00
Puma -1.32 4.55
Intermediate -1.44 -1.24
Pro -3.22 -2.24
Young -1.39 2.67
Thus, the intercept, “Nike”, “intermediate” and “Pro” all have significant, negative effects on the time, indicating that they significantly reduce the time it takes participants to run the track. BUT compared to what?
I hope my question makes sense, otherwise I’ll gladly try and elaborate, and I hope you guys can help me understand how Bayesian credible intervals should be interpreted.
Any literature on the topic would also be very much appreciated!